The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions
Julien Aubert$^{1
Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual time scale range where Earth's core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth's core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth's core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfv�n torsional waves, and non-axisymmetric, quasi-geostrophic Alfv�n and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal time scales, thereby providing a constraint on the extent of the $f^{-4$ range observed in the geomagnetic frequency power spectrum. As the model approaches Earth's core conditions, this spectral broadening arises because \rev{the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also extract an increasing amount of energy from the underlying convection as their key time scale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion time scale to the Alfv�n time scale, highlighting the dominance of Alfv�n waves in the signal and the stabilising control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth's core conditions supports the detectability of Alfv�n waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.
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\begin{frontmatter}
\title{The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions}
\author{Julien Aubert$^{1}$ and Nicolas Gillet$^{2}$}
\address{$^{1}$ Universit� de Paris, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France.\\
$^{2}$ CNRS, ISTerre, University of Grenoble Alpes, Grenoble, France}

\begin{abstract}
Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual time scale range where Earth's core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and  jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth's core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth's core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfv�n torsional waves, and non-axisymmetric, quasi-geostrophic Alfv�n and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal time scales, thereby providing a constraint on the extent of the $f^{-4}$ range observed in the geomagnetic frequency power spectrum. As the model approaches Earth's core conditions, this spectral broadening arises because \rev{the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also} extract an increasing amount of energy from the underlying convection as their key time scale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion time scale to the Alfv�n time scale, highlighting the dominance of Alfv�n waves in the signal and the stabilising control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth's core conditions supports the detectability of Alfv�n waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.
\end{abstract}

\begin{keyword}
Dynamo: theories and simulations; satellite magnetics; Rapid time variations.
\end{keyword}

\end{frontmatter}

\section{\label{intro}Introduction}
The geomagnetic signal emanating from Earth's convecting fluid outer core contains energy over a wide range of time scales, from the longest paleomagnetic features on hundreds of million years down to the shortest variations observed over years and less at observatories and in satellite surveys. Throughout this range, time series of the palaeomagnetic dipole \citep{Constable2005,Panovska2013} as well as series of the field components at ground observatories \citep{DeSantis2003,Lesur2018} support the existence of several power-law ranges in the geomagnetic frequency power spectrum. At centennial periods and longer, synthetic time series produced by numerical simulations of the geodynamo have been used to relate the properties of this spectrum to key features of Earth's core geodynamics and magnetohydrodynamics \citep{Olson2012} and to calibrate stochastic evolution models describing these processes \citep{Buffett2015,Meduri2016}. At shorter time scales, within the range of geomagnetic secular variation that spans periods from centuries down to years, it has however been challenging to follow the same kind of approach because of the traditional limitations of geodynamo simulations. 

The situation has improved recently with a new generation of models \citep[see a recent review in][]{Wicht2019} working in a regime closer to the physical conditions of the core. A key physical time scale in the secular variation range is the core overturn time $\tau_{U}=D/U\approx 130 \ut{years}$, estimated using the core thickness $D=2260\ut{km}$ and a characteristic core surface fluid velocity $U=17 \ut{km/yr}$. Comparison with numerical simulations \citep{Bouligand2016,Aubert2018} has revealed that this time scale relates to a corner frequency in the geomagnetic field power spectrum, and marks the start of a high-frequency range with a spectrum following the power law $P\sim f^{-4}$ (with $f$ the frequency) similar to that inferred from observatory time series \citep{DeSantis2003}. This range may extend up to frequencies of about $1\ut{yr^{-1}}$ \citep{Lesur2018}, though the separation of the internally generated geomagnetic field from external sources is already difficult at this point. At such high frequencies, fast hydromagnetic waves are expected to be present in the geomagnetic signal. Recent advances in geomagnetic field modelling have for instance enabled the retrieval of torsional Alfv�n waves in the core \citep{Gillet2010,Gillet2015}, at a fundamental period close to 6 years. Other types of Alfv�n waves also appear to play a key role in the description of geomagnetic jerks \citep{Aubert2019}. The main goal of this study is to explore the role of these waves in structuring the geomagnetic power spectrum at high frequencies. More generally, we wish to understand the interplay between fast hydromagnetic waves and the slower convection of Earth's core. This is also essential for linking the rapid geomagnetic signals now routinely observed with satellites to the physical properties of Earth's core, and for the prospect of developing better geomagnetic predictions at horizons of human interest.

This problem may be viewed from a different angle by associating the time scales relevant to the geomagnetic variations to a hierarchy of force balances in the core. It has long remained difficult to grasp the place taken by the Lorentz force in this hierarchy, because of the non-linear nature of this force and the self-sustained character of the magnetic field. The situation has however been largely clarified recently, following theoretical advances \citep{Davidson2013,Calkins2015,Aurnou2017,Calkins2018} and advancing numerical explorations of the geodynamo simulation parameter space \citep{Aubert2017,Schaeffer2017,Aubert2019b,Schwaiger2019,Schwaiger2021}. Throughout this parameter space indeed, the rapid planetary rotation implies that at the system scale, the leading-order equilibrium in amplitude occurs between the Coriolis and pressure forces. In most models, this quasi-geostrophic (QG) equilibrium is perturbed at the next order with a triple MAC balance between the buoyancy, Lorentz and residual ageostrophic component of the Coriolis force. In conditions approaching those of Earth's core, the MAC balance is exactly satisfied at a rather large scale $d_{\perp} \sim D/10$, where magnetic energy is fed into the system from the buoyancy force \citep{Aubert2019b}. Writing the QG-MAC balance yields two other independent estimates of the core overturn time $\tau_{U}$ \citep[e.g.][]{Davidson2013}
\begin{equation}
\tau_{U} = \dfrac{D}{U} \approx \dfrac{\rho \Omega d_{\perp}}{g_{o} C} \approx  \dfrac{\rho \mu \Omega d_{\perp}^{2}}{B^2}.\label{MACts}
\end{equation}
Using typical values for the rotation rate $\Omega=7.29~\te{-5}\ut{s^{-1}}$, density $\rho=11000\ut{kg/m^3}$, magnetic permeability $\mu=4\pi\te{-7}\ut{H/m}$, core surface gravity $g_{o}=10\ut{m/s^2}$, convective density anomaly $C=\te{-5}\ut{kg/m^3}$ \citep[e.g.][]{Jones2015,Aubert2020} and magnetic field strength $B=4\ut{mT}$ \citep{Gillet2010}, both estimates lead to $\tau_{U}=\mathcal{O}(\te{2})\ut{yr}$, consistent with the first direct estimate mentioned above. Through the QG-MAC balance, the core overturn time scale is therefore that of the slow convective evolution of the velocity field, adjusting in an inertia-less manner to the creation and advection of density anomaly and magnetic field structures. A range of length scales and amplitudes is obviously expected for these structures, such that a broader range of convective time scales is expected around $\tau_{U}$, which appears open-ended on the long side but bound to decadal periods on the short side \citep{Aubert2018}. 

While recent advanced dynamo models largely preserve the dynamics described by earlier models on time scales of centuries and longer \citep{Aubert2017,Aubert2018}, their strength and purpose is to render the interannual and decadal range of time scales much shorter than $\tau_{U}$, where the dynamics can become inertial again and take the form of rapid responses to transient disruptions in the QG-MAC balance. At conditions approaching those of Earth's core, inertia indeed comes several orders of magnitude below the MAC forces \citep{Aubert2019b}, such that the flows and magnetic signals associated with these disruptions are expected to remain small respectively to the convective flow and main magnetic field. This should naturally lead to quasi-linear perturbations in the governing equations and, in the presence of restoring forces, wave propagation. \rev{The rapid, inertia-bearing (I) waves that have been theoretically investigated \citep[e.g.][]{Finlay2008houches} also mainly involve the magnetic (M) and Coriolis (C) forces (with buoyancy sustaining rapid waves only in contexts of stable stratification). At the axisymmetric level, the Coriolis force identically vanishes on axial cylindrical surfaces, leading to purely MI torsional waves that represent} a purely geostrophic case of Alfv�n waves. These have been identified in Earth's core by \cite{Gillet2010,Gillet2015} and have become increasingly clear in numerical simulations as the model parameters have become more realistic \citep{Wicht2010,Teed2014,Schaeffer2017,Aubert2018}. The relevant time scale for torsional waves is the Alfv�n time
\begin{equation}
\tau_{A}=\dfrac{D\sqrt{\rho\mu}}{B},
\end{equation}
which, using the estimates quoted above, indeed satisfies $\tau_{A}\approx 2\ut{yr}\ll\tau_{U}$ in Earth's core. \rev{At the non-axisymmetric level, the Coriolis force in principle takes over the inertial force \citep{Lehnert1954,Hide1966,Finlay2010,Labbe2015}, leading to slow MC modes that do not contribute to rapid dynamics. In interesting recent developments, it has however been shown that the influence of the Coriolis force can be mitigated in a variety of ways, leading to fast, quasi-geostrophic (axially columnar), non-axisymmetric dynamics. Starting their survey from low-frequency MC modes, \cite{Gerick2020} have identified modes approaching the Alfv�n frequency $1/\tau_{A}$ from below as their radial complexity is increased. Their kinetic to magnetic energy ratio also increases, meaning that the influence of inertia is gradually restored. In advanced numerical dynamo simulations that may be seen as an extreme case of spatial complexity, \cite{Aubert2018} have highlighted a spatial segregation of the force balance. In regions where the magnetic field is relatively homogeneous, localised and nearly MI Alfv�n wave dynamics is observed with frequencies also closely approaching the Alfv�n frequency from below. The MC part of the balance remains confined close to regions of strong magnetic field heterogeneity. Despite the constraints set by the Coriolis force, MI Alfv�n waves therefore appear to be possible at any spatial scale, but detecting these} in the geomagnetic signal is a challenge as \rev{they evolve close to, or at kinetic to magnetic energy equipartition.} Their magnetic signature is therefore nominally small respectively to the main magnetic field produced by convection, the energy of which exceeds the total kinetic energy in Earth's core by a factor $A^{-2}=(\tau_{U}/\tau_{A})^{2} \approx 5000$. In this respect, wave focusing below the core-mantle boundary has recently been proposed as a way to overcome this challenge and also to explain the signature of recent geomagnetic jerks \citep{Aubert2019}. 

\rev{At frequencies in excess of the Alfv�n frequency and up to twice the rotation rate $\Omega$ (on the order of an Earth day), CI inertial waves populate}  a discrete and dense frequency spectrum \citep{Rieutord1997}. The issue of detectability may be seen as even worse here \rev{as the kinetic to magnetic energy ratio of inertial waves further increases with increasing frequency \citep{Gerick2020}, such that they weakly interact with the magnetic field.} There remains however the possibility of slow, quasi-geostrophic 'Rossby' modes \citep{Zhang2001,Busse2005,Canet2014} with a pulsation $\omega\ll \Omega$ approaching the Alfv�n frequency from above as the spatial complexity is increased, which enter the realm of interannual geomagnetic signals and also \rev{carry higher amounts of magnetic energy}. The second goal of this study is to use our models to better quantify the detectability of Alfv�n and slow Rossby waves in Earth's core.

We report here on a new numerical geodynamo model that enables a joint exploration of all these waves and convective features at an unprecedentedly realistic level of separation between the key time scales $\tau_{U}$, $\tau_{A}$ and $\tau_\Omega$. Being to date the closest to Earth's core conditions, this model also considerably enlarges the parameter range over which an asymptotic scaling analysis relevant to Earth's core can be performed, which forms the third goal of this study. The manuscript is organised as follows: section \ref{model} presents the existing path theory and the new numerical model. Results are presented in section \ref{results} and discussed in section \ref{discu}. 

\section{\label{model}Model and Methods}
\subsection{Model set-up and numerical method}
We use a standard numerical model for Boussinesq convection, thermochemical density anomaly transport, and magnetic induction in the magnetohydrodynamic approximation. Full details on the equation set, boundary conditions and numerical method can be found in \cite{Aubert2013b,Aubert2017} and \cite{Aubert2018}, where the specific configuration is denoted as 'CE' (Coupled Earth). The unknown fields are the velocity field $\vecu$, magnetic field $\vecB$ and density anomaly field $C$. The fluid domain is an electrically conducting and rotating spherical shell of thickness $D=r_{o}-r_{i}$ and aspect ratio $r_{i}/r_{o}=0.35$ representing the Earth's outer core. The shell takes place between an inner core of radius $r_{i}$, and a solid mantle between radii $r_{o}$ and $r_\mathrm{E}=1.83 r_{o}$ (the surface of the Earth), both of which are conducting and electromagnetically coupled to the fluid shell. The electrical conductivity of the inner core is set to the same value $\sigma$ as that of the outer core, while the mantle features a thin conducting layer at its base of thickness $\Delta$ and conductivity $\sigma_{m}$ such that the ratio of conductances is $\Delta\sigma_{m}/D\sigma=\te{-4}$. The inner core is furthermore  gravitationally coupled to the mantle, and the three layers can present axial differential rotations with respect to each other, with the constant axial rotation of the ensemble defining the planetary rotation vector $\vc{\Omega}=\Omega\vc{e}_{z}$. Moments of inertia for these three layers respect their Earth-like proportions. A homogeneous mass anomaly flux $F$ imposed at radius $r=r_{i}$ drives convection from below, and the mass anomaly flux vanishes at $r=r_{o}$ (neutral buoyancy beneath the outer surface). A volumetric buoyancy sink is present in the volume to ensure mass conservation. On top of this homogeneous buoyancy distribution, lateral heterogeneities in the mass anomaly flux are superimposed at $r=r_{i}$ and $r=r_{o}$, respecting the 'CE' setup. Stress-free mechanical boundary conditions are also imposed on the fluid shell. This removes the need to resolve extremely thin viscous boundary layer that have a negligible influence on the solution \citep{Aubert2017}. As in our previous work, all models presented here produced a self-sustained, dipole dominated magnetic field of Earth-like geometry \citep{Christensen2010} that did not reverse polarity during the integration time. 

We consider a spherical coordinate system $(r,\theta,\varphi)$ with unit vectors $\vc{e}_{r},\vc{e}_{\theta},\vc{e}_{\varphi}$ associated to the cylindrical system $(s,z,\varphi)$ of unit vectors $\vc{e}_{s},\vc{e}_{z},\vc{e}_{\varphi}$. The numerical implementation involves a decomposition of $\vecu$, $\vecB$ and $C$ in spherical harmonics up to degree and order $\ell_{\mathrm{max}}$ and a discretisation in the radial direction on a second-order finite-differencing scheme with $NR$ grid points. We use the spherical harmonics transform library  SHTns \citep{Schaeffer2013} freely available at {\tt https://bitbucket.org} {\tt/nschaeff}{\tt/shtns}. We use a second-order, semi-implicit time stepping scheme. The solution is approximated using smoothly ramping hyperdiffusivity applied on the velocity and density anomaly fields, but not on the magnetic field that remains fully resolved. The functional form of hyperdiffusivity involves a cut-off $\ell_{h}=30$ below which hyperdiffusivity is not applied, and an exponential ramping parameter $q_{h}$ such that $(\nu_\text{eff},\kappa_\text{eff})=(\nu,\kappa)\, q_{h}^{\ell-\ell_{h}}$, describing the increase of hyperdiffusivity with spherical harmonic degree $\ell$ for $\ell\ge\ell_{h}$. When compared against fully resolved references \citep{Aubert2019b}, the approximated solutions adequately preserve the QG-MAC balance and the large-scale morphology of the solution. They enable the computation of long temporal sequences that would otherwise not be feasible and are therefore tailored towards the present analysis of dynamics in the time domain. Values of $NR$, $\ell_\mathrm{max}$ and $q_{h}$ used in our models are reported in Table \ref{inputs}.

\subsection{Path theory, dimensionless inputs and outputs}
We recall here the four main parameters of the model, the flux-based Rayleigh, Ekman, Prandtl and magnetic Prandtl numbers:
\begin{equation}
Ra_{F}=\dfrac{g_{o}F}{4\pi\rho\Omega^{3}D^{4}},~ E=\dfrac{\nu}{\Omega D^{2}},~ Pr=\dfrac{\nu}{\kappa},~ Pm=\dfrac{\nu}{\eta}.
\end{equation}
Aside of the already introduced planetary rotation rate $\Omega$, core thickness $D$, core surface gravity field $g_{o}$, core density $\rho$, bottom-driven mass anomaly flux $F$, these expressions involve the viscous, thermo-chemical and magnetic diffusivities $\nu$, $\kappa$ and $\eta$ (with $\eta=1/\mu\sigma$). \rev{Details on the correspondance between flux-based and canonical Rayleigh numbers may be found in \cite{ChristensenAubert2006}}. Our main model case in this study uses the path theory \citep{Aubert2017} that bridges the parameter space gap between our previous coupled Earth model \citep{Aubert2013b} and Earth's core conditions by relating these four parameters to a single variable $\epsilon$:
\begin{eqnarray}
Ra_{F}(\epsilon)=\epsilon Ra_{F} (1),~ E(\epsilon)=\epsilon E (1),~ Pr(\epsilon)=1,~ Pm(\epsilon)=\sqrt{\epsilon} Pm (1).
\end{eqnarray}
Here $Ra_{F}(\mathrm{1})=2.7~\te{-5}$, $E(\mathrm{1})=3~\te{-5}$ and $Pm(\mathrm{1})=2.5$ are the control parameters of the coupled Earth dynamo model. \rev{The choice of a constant $Pr=1$ along the path stems from the thermal and chemical density anomalies being blended together in a co-density approach, and is also relevant given that hyperdiffusivity of equal strength is applied to the velocity and density anomaly fields.} Previously \citep{Aubert2017,Aubert2018}, we have explored this path down to $\epsilon=3.33~\te{-4}$, halfway in a logarithmic progression scale between the start ($\epsilon=1$) and the Earth's core conditions located at $\epsilon=\te{-7}$. Here we mainly report on a model at $\epsilon=\te{-5}$, at 71 percent of this path on the same logarithmic scale (from hereafter the 71p model). Table \ref{inputs} reports on the input parameters of this main model case, and of the other cases used in this study. To date, the 71p model is the closest to Earth's core conditions that has been reached in a numerical geodynamo simulation, in particular regarding the nearly inviscid behaviour achieved at large scales, as witnessed by the Ekman number $E=3~\te{-10}$. \rev{This is of course made possible by the hyperdiffusive approximation and the use of stress-free boundaries. For comparison, the fully resolved numerical simulation currently closest to core conditions is that of \cite{Schaeffer2017}, operating at $E=3~\te{-7}$.}
 
\begin{table}
\caption{\label{inputs} Input parameters of numerical models (see text for definitions). All models have $Pr=1$. Model cases with a star have been previously published in \cite{Aubert2017,Aubert2018,Aubert2019}}
\vspace*{\baselineskip}

\begin{center}
\setstretch{0.8}\small
\hspace*{-1cm}\begin{tabular}{lrm{1.5cm}m{1.2cm}rrrrm{0.5cm}m{0.5cm}}
\hline\\[-0.5cm]
Case & $\epsilon$ & Path position (percent) & run length ($\tau_{U}$ units) & $E$ & $Ra_{F}$ & $Pm$ & $NR$ & $\ell_\mathrm{max}$ & $q_{h}$\\
\hline
29p* & $\te{-2}$ & 29 & 332 & $3~\te{-7}$ & $2.7 ~\te{-7}$ & 0.25 & 320 & 133 & 1.07\\
Midpath* & $3.33~\te{-4}$ & 50 & 196 & $\te{-8}$ & $9 ~\te{-9}$ & 0.045 & 624 & 133 & 1.10\\
71p & $\te{-5}$ & 71  & 117 & $3~\te{-10}$ & $2.7~\te{-10}$ & $7.9~\te{-3}$ & 1248 & 133 170 & 1.14 1.09 \\
50pRa+ & & off-path & 109 & $\te{-8}$ & $3.6~\te{-8}$ & 0.045 & 624 & 133  & 1.13 \\
50pRa+Pm- & & off-path & 68 & $\te{-8}$ & $3.6~\te{-8}$ & 0.023 & 624 & 133  & 1.13 \\
50pPm+ & & off-path & 37 & $\te{-8}$ & $9~\te{-9}$ & 0.1125 & 624 & 133  & 1.10\\
\hline
\end{tabular}
\end{center}
\end{table}

In our previous analyses that stopped at 50 percent of the path \citep[the so-called Midpath model,][]{Aubert2017,Aubert2018,Aubert2019}, it was found that many of the important diagnostics related to waves evolve rather subtly, and scale with weak powers of $\epsilon$. To reach our main goals, it is therefore necessary to cover a wide range of this parameter. This is the main reason that motivated a direct leap from 50 to 71 percent of the path here, rather than the progression in half-decades of $\epsilon$ that we favoured previously. The 71p model has been initialised by taking a state from the Midpath model. Initial transients could almost be eliminated by applying a new approach. First we applied the path scaling laws \citep{Aubert2017} to cast the amplitudes of $\vecu,\vecB,$ and $C$ towards predictions close to their actual values at 71 percent of the path. The numerical mesh was then refined to achieve $NR=1248$ and $\ell_{max}=133$. Finally the computation was restarted with the physical parameters relevant to 71 percent of the path and hyperdiffusivity parameters $\ell_{h}=30$ and $q_{h}=1.14$. After 9.5 overturn times $\tau_{U}$, the lateral resolution has been increased to $\ell_{max}=170$, enabling a partial relaxation of the hyperdiffusivity strength down to $q_{h}=1.09$ for the rest of the computation (about 107.5 overturns). Three secondary models have also been derived from the Midpath model by changing its Rayleigh number (label Ra+) or its magnetic Prandtl number (labels Pm+/-). These models complement the series computed along the path with a limited exploration across the path around the Midpath position. 

\begin{table}
\caption{\label{outputs1} Output parameters, presented in a. as dimensionless ratios of time scales, and in b. as dimensional time scales obtained by setting a dimensional value to the magnetic diffusion time $\tau_{\eta}$ (see text). Estimates for Earth's core are also reported in panel b \citep[taken from][]{Gillet2010,Lhuillier2011b,Christensen2012,Aubert2017,Aubert2018,Aubert2019}.}
\begin{center}
a.\vspace*{\baselineskip}

\hspace*{-1cm}\begin{tabular}{lrrrrrrrrrr}
\hline\\[-0.5cm]
Case & $Ro=\dfrac{\tau_{\Omega}}{\tau_{U}}$ & $\lambda=\dfrac{\tau_{\Omega}}{\tau_{A}}$ & $Rm=\dfrac{\tau_\eta}{\tau_{U}}$ & $A=\dfrac{\tau_{A}}{\tau_{U}}$ & $S=\dfrac{\tau_{\eta}}{\tau_{A}}$ & $\dfrac{\tau_{\mathrm{SV}}^{1}}{\tau_{\eta}}$ & $\dfrac{\tau_{\mathrm{SA}}^{0}}{\tau_{\eta}}$\\[0.3cm]
\hline
29p* & $1.26~\te{-3}$ & $5.15~\te{-3}$ & 1046 & 0.244 & 4286 & $3.12~\te{-3}$ & $1.11~\te{-4}$ \\
Midpath* & $2.40~\te{-4}$ & $2.10~\te{-3}$ & 1082 & 0.114 & 9491 & $3.06~\te{-3}$ & $8.72~\te{-5}$\\
71p   & $4.31~\te{-5}$ & $8.82~\te{-4}$ & 1136 & 0.049 & 23234 & $2.89~\te{-3}$ & $7.88~\te{-5}$ \\
50pRa+  & $4.45~\te{-4}$ & $3.16~\te{-3}$ & 2003 & 0.141 & 14235 & $1.65~\te{-3}$ & $3.78~\te{-5}$ \\
50pRa+Pm- & $4.78~\te{-4}$ & $3.10~\te{-3}$ & 1101 & 0.155 & 7100 & $3.1~\te{-3}$ & $9.09~\te{-5}$ \\
50pPm+ & $2.22~\te{-4}$ & $2.37~\te{-3}$ & 2495 & 0.094 & 26671 & $1.32~\te{-3}$ & $2.62~\te{-5}$ \\
\hline
\end{tabular}
\vspace*{\baselineskip}

b.\vspace*{\baselineskip}

\hspace*{-1cm}\begin{tabular}{lrrrrrrrrrr}
\hline\\[-0.5cm]
Case & $\tau_{\eta}$ (yr) & $\tau_{U}$ (yr) & $\tau_{A}$ (yr) & $2\pi\tau_{\Omega}$ (days) & $\tau_{\mathrm{SV}}^{1}$ & $\tau_{\mathrm{SA}}^{0}$  \\[0.2cm]
\hline
29p* & 135000 & 129 & 31.5 & 373 & 421 & 15.0\\
Midpath* & 135000 & 125 & 14.3 & 69  & 413 & 11.8 \\
71p  & 135000 & 119 & 5.8 & 11.8 & 390 & 10.6\\
50pRa+  & 245600 & 123 & 17.3 & 125 & 405 & 9.3\\
50pRa+Pm- & 135000 & 123 & 19 & 134 & 419 & 12.3\\
50pPm+ & 305900 & 123 & 11.5 & 62 & 404 & 8.0\\
Earth & $6~\te{4}-3~\te{5}$ & $\approx 130$ & $\approx 2$ & 1 &  $\approx 415$ & $\approx 10$ \\
\hline
\end{tabular}
\end{center}
\end{table}

The root-mean-squared velocity and magnetic field amplitudes $U$ and $B$ measured in the shell over the course of the simulation give access to the overturn and Alfv�n time scales $\tau_{U}=D/U$ and $\tau_{A}=D\sqrt{\rho\mu}/B$. These are presented in Table \ref{outputs1}a as dimensionless ratios taken respectively to the two other important time scales in the system, the rotational time scale $\tau_{\Omega}=1/\Omega$ and the magnetic diffusion time $\tau_{\eta}=D^{2}/\eta$. As we advance along the path towards Earth's core conditions (or decrease $\epsilon$), the numerical models preserve an approximately constant value of the magnetic Reynolds number $Rm=\tau_{\eta}/\tau_{U}\approx 1000$, while they enlarge the time scale separation between $\tau_{\eta},\tau_{U}$ with the Alfv�n and rotational time scales. Time scale separation can be measured using the Alfv�n number $A=\tau_{A}/\tau_{U}$, Lundquist number $S=\tau_{\eta}/\tau_{A}$, Rossby number $Ro=\tau_{\Omega}/\tau_{U}$ and Lehnert number $\lambda=\tau_{\Omega}/\tau_{A}$. Along the lines introduced by \cite{Jault2008}, \cite{Gillet2011} and \cite{Aubert2017}, the asymptotic regime relevant to the geodynamo may be formalised through the two conditions $\lambda \ll 1$ and $A \ll 1$, which in turn imply $Ro \ll 1$ and (if $Rm \gg 1$) $S�\gg 1$. In \cite{Aubert2018} the entry into this regime has been located at 29 percent of the path, from the consideration of flow and magnetic acceleration signatures. The 71p model provides the largest and most realistic separation between the four important time scales $\tau_{\eta},\tau_{U},\tau_{A},\tau_{\Omega}$ that has been obtained to date in a geodynamo simulation. The unidimensional nature of the path however implies that all time scales are covarying, which may lead to difficulties in disentangling the exact effect of each of these scales. For this reason, the three other secondary models taken across the path close to Midpath conditions will be useful in the analysis presented in section \ref{results}. 

\subsection{\label{pathcomp}Additional dimensionless outputs for scaling along the path}
\begin{table}
\caption{\label{outputs2} Additional dimensionless outputs of the 71p model.}
\vspace*{\baselineskip}

\begin{center}
\begin{tabular}{rl}
\hline
Ohmic fraction $f_\mathrm{ohm}$ & 0.89 \\
magnetic diffusion length scale $d_\mathrm{min}/D$ & $1.82~\te{-2}$\\
Taylorisation level on axial cylinders $\mathcal{T}$ & $6.5~\te{-3}$\\
\hline
\end{tabular}
\end{center}
\end{table}

The computation of the 71p model also provides an opportunity to update the scaling analysis initially presented in \cite{Aubert2017}, which stopped at 50 percent of the path. For this purpose, here we list and report on the few additional time-averaged dimensionless outputs that are needed \citep[see][for full definitions and Table \ref{outputs2} for values]{Aubert2017}: the fraction $f_\mathrm{ohm}$ of convective power that is dissipated in Ohmic losses, the magnetic diffusion length scale $d_\mathrm{min}/D$, or square root of the ratio between time-averaged magnetic energy and Ohmic losses, and the time-averaged level of enforcement $\mathcal{T}$ of the Taylor constraint on axial cylindrical surfaces in the shell. As done at previous positions along the path \citep{Aubert2017,Aubert2019}, we also determine a scale-dependent representation of the force balance in the 71p model, where the root-mean-squared amplitude of each force is represented as a function of the spherical harmonic degree $\ell$. This scale-dependent force balance tool has previously revealed its strength in deciphering the complex hierarchy of forces present in the system, including the non-trivial roles of hydrodynamic and magnetic pressure, and in associating the successive balances coming along this hierarchy to physically grounded length scales \citep{Aubert2017,Aubert2019b,Schwaiger2019,Schwaiger2021}.

\subsection{\label{doutputs}Integral dimensional outputs}
For the purpose of geophysical applications, it has become common practice to cast the dimensionless outputs of the numerical model back into the dimensional world, in a way that is rationalised by the physical equilibria preserved along the path to Earth's core \citep[see e.g.][for a detailed discussion]{Aubert2020}. Length scales are dimensioned by setting $D=2260\ut{km}$ as Earth's outer core thickness. Along the path, an in agreement with our previously used conventions \citep{Aubert2019}, the time basis is provided by setting the magnetic diffusion time to $\tau_{\eta}=135000\ut{yr}$, corresponding to a magnetic diffusivity $\eta=1.2~\ut{m^2/s}$ at the mid-point of current estimates \citep{Aubert2017}. The resulting dimensional time scales values are summarised in Table \ref{outputs1}b. Together with the constant value $Rm\approx1000$ obtained along the path, this choice for $\tau_{\eta}$ ensures a geophysically realistic value $\tau_{U}\approx 130\ut{yr}$ for the convective overturn time. \rev{This also leads to} geophysically realistic values for two other important time scales pertaining to convectively driven geomagnetic signals, the secular variation and acceleration time scales $\tau_{\mathrm{SV}}^{1}\approx 400\ut{yr}$ and $\tau_{\mathrm{SA}}^{0}\approx 10\ut{yr}$ \citep[see][for definitions and discussion]{Lhuillier2011b, Christensen2012,Aubert2018}. This implies that all models taken along the path are adjusted for an adequate simulation of slow inertialess convection and convection-driven geomagnetic variations in the decadal to secular range. Turning now to the time scales pertaining to fast hydromagnetic waves, the progress made by the 71p model over previous efforts becomes tangible when we consider the dimensional value of the Alfv�n time scale $\tau_{A}=5.8\ut{yr}$, now only a factor 3 away from the Earth value. Likewise, the duration of a physical day is $2\pi\tau_{\Omega}=11.8\ut{days}$ is now only an order of magnitude away from an Earth day. 

For the series of 50p models taken across the path, we also aim at preserving the realism of convection-driven geomagnetic signals i.e. also achieving realistic values for $\tau_{U}, \tau_{\mathrm{SV}}^{1}$ and $\tau_{\mathrm{SA}}^{0}$. This is straightforwardly achieved by adjusting $\tau_{\eta}$ in proportion of the magnetic Reynolds numbers achieved by these models. Model 50pRa+Pm- uses a combination of Rayleigh and magnetic Prandtl number such that $Rm$ keeps a value close to that of models along the path, so the same time basis $\tau_{\eta}=135000\ut{yr}$ is used. The time basis of models 50pRa+ and 50pPm+ is adjusted accordingly to the ratio between their magnetic Reynolds number and that of model 50pRa+Pm-, leading to the respective time bases $\tau_{\eta}=245600\ut{yr}$ and $\tau_{\eta}=305900\ut{yr}$. Interestingly, these two models also sample a geophysically relevant range for possible values of $\tau_{\eta}$ and $Rm$, particularly concerning the possibility of high thermal and electrical conductivity in the core \citep[e.g.][]{Pozzo2012}. 

As in our previous studies \citep{Aubert2018,Aubert2019,Aubert2020}, other outputs of the model are dimensioned by using the invariants of the parameter space path, particularly the stability of the magnetic Reynolds number and the QG-MAC force balance. The velocity field $\vecu$ and Alfv�n velocity $\vecB/\sqrt{\rho\mu}$ are first expressed in a dimensionless manner in units of $\eta/D$, to respectively give local values of the magnetic Reynolds number $Rm$ and Lundquist number $S$. The results are then multiplied by the dimensional value of $\eta/D$ obtained from the choices made above. As we noted previously \citep{Aubert2018}, from $\vecB/\sqrt{\rho\mu}$ a dimensional value of $\vecB$ can be obtained, but this value is not realistic unless we are at the end of the path. At 71 percent of the path, this procedure yields $B=1.4\ut{mT}$ and the mismatch with the Earth estimate $B=4\ut{mT}$ \citep{Gillet2010} is no longer large, because the Alfv�n time scale is now close to the Earth value (Table \ref{outputs1}b). For the purpose of comparing the output of our path models to the geomagnetic field, and following our conventions taken for other path positions \citep{Aubert2018,Aubert2019}, we simply adopt $B=4\ut{mT}$ for dimensioning the magnetic field amplitude in all models. Finally, to dimension the density anomaly field $C$ we take advantage of the preservation of the balance between buoyancy and Coriolis force along the path \citep{Aubert2020}. The dimensionless density anomaly field is therefore expressed in units of $\rho\Omega\eta/g_{o}D$ and the result is then multiplied with Earth's core dimensional estimate for $\rho\Omega\eta/g_{o}D$ obtained with our choices for $\eta$ and the other values provided in section \ref{intro}. 

\subsection{\label{methodseries}Time series extracted from the simulation}
The physical time span integrated for the 71p model is 117 core overturns $\tau_{U}$ (Table \ref{outputs1}a), which corresponds to 14000 years of physical time, using the rescaling procedures introduced in section \ref{doutputs}. It should be emphasized that achieving this run length while simulating strongly scale-separated dynamical features comes at a sizeable numerical cost. The numerical time step of the computation has indeed been capped to about a hundredth of the rotational time $\tau_{\Omega}$. This is needed because of the explicit treatment of the Coriolis force in the time stepping scheme. In the later part of the computation, the time step for instance corresponds to 0.3 hours of physical time. The 71p run required about 246 million numerical time steps and 15 million single-core CPU hours spent over the course of 2 years. These figures highlight that the 71p model is an extreme computational endeavour, despite the use of approximations to reduce its spatial complexity. To tackle this challenge, significant code optimisations have been performed during the computation, to reach a wall time per iteration of 0.06 seconds on 2560 cores of the AMD-Rome partition of GENCI-TGCC in France. 

A number of output time series are extracted from the model in addition to the time-averaged diagnostics introduced above. As time scales shorter than the numerical day $2\pi\tau_{\Omega}$ (11.8 days in the 71p model) contain a negligible amount of energy \citep{Aubert2018}, the temporal spacing between samples has been set to this value. Time series of the core surface magnetic field $\vecB(r_{o},\theta,\varphi,t)$ and velocity field $\vecu(r_{o},\theta,\varphi,t)$ have been systematically recorded up to spherical harmonic degree 30. \rev{As magnetic time series in our earlier models \citep{Aubert2018,Aubert2019} were only recorded up to degree 13, here we further truncate $\vecB(r_{o},\theta,\varphi,t)$ after degree 13 for consistency.} Time derivatives $\dot{\vecu}=\partial \vecu/\partial t$ (the flow acceleration), \rev{$\dot{\vecB}$ (the magnetic variation) and $\ddot{\vecB}$ (the magnetic acceleration)} are computed by finite-differencing. We define time series for the energies $E_\mathrm{SV}, E_\mathrm{SA}$ of the magnetic variation and acceleration as
\begin{eqnarray}
E_{\mathrm{SV}}(t)= \dfrac{1}{S} \int_{S} \dot{\vecB}^{2}(r_{o},\theta,\varphi,t)~\mathrm{d}S,\\
E_{\mathrm{SA}}(t)= \dfrac{1}{S} \int_{S} \ddot{\vecB}^{2}(r_{o},\theta,\varphi,t)~\mathrm{d}S.
\end{eqnarray}
Here $S$ is the spherical surface at $r=r_{o}$. These quantities can also be evaluated at Earth's surface $S_\mathrm{E}$ located at $r_\mathrm{E}=1.83r_{o}$, where $\vecB$ can be upward-continued by assuming an insulating mantle. As in our previous study \citep{Aubert2019}, an Earth surface jerk energy time series is defined in a way that factors in the limited resolution of geomagnetic observations, as a sliding energy difference of magnetic acceleration averaged over consecutive 3-years windows:
\begin{equation}
E_\mathrm{J} (t) = \dfrac{1}{S_\mathrm{E}} \int_{S_{\mathrm{E}}} \left(\left[\ddot{\vecB}\right]_{t}^{t+3 \ut{yr}}-\left[\ddot{\vecB}\right]_{t-3 \ut{yr}}^{t}\right)^{2}(r_{E},\theta,\varphi,t)~\mathrm{d}S,\label{EJdef}
\end{equation}
where the square brackets stand for time averaging. We define the energy associated to the core surface flow acceleration $\dot{\vecu}(\vc{r_{o}},t)$ up to spherical harmonic degree 30 as
\begin{equation}
K(t)=\dfrac{1}{S} \int_{S} \dot{\vecu}^{2}(r_{o},\theta,\varphi,t)~\mathrm{d}S.
\end{equation}
We label as $\dot{\vecu}^\mathrm{S}(r_{o},\theta,\varphi,t)$ the equator-symmetric component of $\dot{\vecu}$, with the associated energy $K^\mathrm{S}$. In the asymptotic regime reached beyond 29 percent of the path, the large-scale flow acceleration is dominantly equator-symmetric \citep{Aubert2018}, as confirmed here by ratios $K^\mathrm{S}/K$ increasing from 0.7 to 0.84 between 29 and 71 percent of the path. We further denote as $\dot{u}_{\varphi}^\mathrm{ZS}(r_{o},\theta,\varphi,t)$ the axisymmetric (zonal) average of $\dot{\vecu}^\mathrm{S}\cdot\vc{e}_{\varphi}$, and the corresponding energy as $K^\mathrm{ZS}$. By using a standard Thomson multitaper method with concentration half-bandwidth $W=4/\Delta t$ (where $\Delta t$ is the run length), we also decompose the Earth-surface magnetic accceleration $\ddot{\vecB}(r_{E},\theta,\varphi)$, the core surface flow accelerations $\dot{\vecu}(r_{o},\theta,\varphi)$ and $\dot{u}_{\varphi}^\mathrm{ZS}(r_{o},\theta,\varphi)$ in the frequency domain to calculate the respective energy density spectra $\hat{E}_\mathrm{SA}(f)$, $\hat{K}(f)$ and $\hat{K}^{\mathrm{ZS}}(f)$. Given the duration of our runs (see Table \ref{inputs}) this ensures that the overturn frequency $1/\tau_{U}$ is well resolved in all model cases. 

For reasons of storage space, full three-dimensional outputs of the simulation state at native resolution are available only in selected portions of the numerical computation. In these portions and as in \cite{Aubert2018}, we introduce the \rev{azimuthal} acceleration on geostrophic cylinders (whose axis is aligned with the rotation axis $\vc{e}_{z}$):
\begin{equation}
\dot{u}_{g}(s,t)= \dfrac{1}{2\pi(z_{+}-z_{-})}\int_{0}^{2\pi}\int_{z_{-}}^{z_{+}} \dot{\vecu}(s,\varphi,z,t)\cdot\vc{e}_{\varphi}\, \mathrm{d} z \mathrm{d}\varphi,\label{ug}
\end{equation}
\rev{as well as the Alfv�n speed given by the part of poloidal magnetic field permeating these cylinders:}
\begin{equation}
c_{A}^{2}(s,t) = \dfrac{1}{2\pi(z_{+}-z_{-})\rho\mu}\int_{0}^{2\pi}\int_{z_{-}}^{z_{+}} (\vecB(s,\varphi,z,t)\cdot\vc{e}_s)^2\, \mathrm{d} z \mathrm{d}\varphi.\label{ca}
\end{equation}
Here $z_{-}$ \rev{and} $z_{+}$ are the ordinates along $\vc{e}_{z}$ of the intersections between geostrophic cylinders of radius $s$ and the spherical boundaries of the shell. 

\section{\label{results}Results}
\subsection{\label{pathupdate}The 71p model versus earlier solutions along the parameter space path}
\begin{figure}
\centerline{\includegraphics[width=9cm]{forcebal_3e10.pdf}}
\caption{\label{forcebal} Root-mean-squared amplitude of the forces in a snapshot of the 71p model, presented as functions of the spherical harmonic degree $\ell$ (see section \ref{pathcomp}). All forces are normalised respectively to the maximum reached by the pressure gradient. The snapshot was taken from the later part of the run where $\ell_\mathrm{max}=170$ and $q_{h}=1.09$ (see Fig. \ref{SVSAmorph}).}
\end{figure}

Our first task is to update our previous analysis of the path in parameter space \citep{Aubert2017,Aubert2018,Aubert2019} in the light of the new data point acquired at 71 percent of this path. Figure \ref{forcebal} presents a scale-dependent force balance diagram obtained with a snapshot of the 71p model. Similarly to our previous results at earlier positions along the path \citep{Aubert2017,Aubert2018,Aubert2019}, a leading-order QG balance is still observed between the pressure and Coriolis forces. At the next order follows a MAC balance between the buoyancy, Lorentz and ageostrophic Coriolis forces. The cross-over between the Lorentz and buoyancy forces defines the harmonic degree $\ell_{\perp}=\pi D/d_{\perp}$ where the triple balance is exactly respected, with a value $\ell_{\perp}=13$ that has only slightly evolved since Midpath conditions where $\ell_{\perp}=12$ \citep{Aubert2019b}. This scale, at which convective energy is injected into the magnetic field, is therefore confirmed to remain stable along the path. At the second order in amplitude, inertial forces are now located two orders of magnitude below the MAC forces. As previously shown in \cite{Schwaiger2019}, the widening of the gap between MAC and inertial forces along the path scales with the inverse squared Alfv�n number $A^{-2}$, in line with the evolution observed between Midpath \citep[see Fig. 1 in][]{Aubert2018} and 71 percent of path conditions. In the 71p model, viscosity comes five order of magnitude below the Coriolis force at large scales. Our choice for spatial resolution and strength of hyperdiffusivity in the later part of the run (from where the snapshot was taken) result in a negligible influence of viscosity up to spherical harmonic $\ell\approx 80$, after which its strength ramps up and exceeds that of inertia, as was previously the case in the Midpath model.

\begin{figure}
\centerline{\includegraphics[width=14cm]{71scalings.pdf}}
\caption{\label{scalings} Evolution of the Rossby number $Ro$ (a), Lehnert number $\lambda$ (b), Alfv�n number $A$ (c), Ohmic fraction $f_\mathrm{ohm}$ (d), magnetic dissipation length scale $d_\mathrm{min}$ (e) and Taylor constraint enforcement level $\mathcal{T}$ (f) along the parameter space path, as functions of the path parameter $\epsilon$ (Earth's core conditions are towards the left of the graphs). Shown are results from hyperdiffusive solutions along the path (LES or large-eddy-simulations) up to 71 percent of the path ($\epsilon=\te{-5}$), and the direct numerical simulations (DNS) up to 21 percent of the path ($\epsilon=3.33~\te{-2}$). See Tables \ref{outputs1}a and \ref{outputs2} for data between 29 and 71 percent of the path, and \cite{Aubert2017,Aubert2019b} for other numerical values. Green and orange lines respectively show the results of least-squares power-law fits to the LES and DNS data, which closely adhere to the theories of \cite{Aubert2017,Davidson2013}, respectively. Shaded grey areas represent the $\pm 1$ standard deviation, where applicable.}
\end{figure}

The stability of the force balance implies that previously determined scaling laws for the main model outputs are essentially unchanged when adding the 71p model data. We have previously shown \citep{Aubert2017} that along the path \rev{and for the hyperdiffusive, large-eddy (LES) simulations}, the QG-MAC balance, together with the constancy of the magnetic Reynolds number $Rm$ imply the following scaling laws for the Rossby number and ohmic fraction-corrected Lehnert number:
\begin{eqnarray}
Ro \sim \epsilon^{1/2},\\
\lambda/f_\mathrm{ohm}^{1/2} \sim \epsilon^{1/4}.
\end{eqnarray}
The way the path models adhere to these scalings is essentially unchanged when adding the 71p model data points (Fig. \ref{scalings}a,b). From this, the scaling $A=Ro/\lambda \sim \epsilon^{1/4}$ is also respected (Fig. \ref{scalings}c). Relative to the Midpath model ($\epsilon=3.33~\te{-4}$), the Ohmic fraction has increased at 71 percent of the path to reach $f_\mathrm{ohm}=0.89$ (Fig. \ref{scalings}d), meaning that despite the use of hyperdiffusivity, dissipation is essentially of Ohmic nature in this model. The magnetic dissipation length scale $d_\mathrm{min}$ remains essentially invariant along the path  (Fig. \ref{scalings}e, note the linear ordinate axis), a consequence of the constant magnetic Reynolds number and constrained spatial structure of the solution. Finally, the level to which the solution approaches a Taylor state \citep{Taylor1963} can be measured by the Taylorisation level $\mathcal{T}$ (Fig. \ref{scalings}f), with the 71p model exhibiting the highest levels of taylorisation observed to date along the path (lowest value of $\mathcal{T}$). Somewhat surprisingly, this model appears to respect the Taylor constraint even more strongly than the expectation that could be drawn from the previous models. For reference, the scaling results from fully resolved direct numerical simulations (DNS) are also reported on Fig. \ref{scalings}. These simulations have so far been computed only down to 21 percent of the path \citep[$\epsilon=3.33~\te{-2}$,][]{Aubert2019b}. In this previous study, we have shown that these adhere to the power laws predicted by the QG-MAC theory \citep{Davidson2013,Aubert2017} i.e. $Ro \sim \epsilon^{4/9}$, $\lambda/f_\mathrm{ohm}^{1/2} \sim \epsilon^{1/3}$, $d_\mathrm{min}\sim\epsilon^{1/12}$. The difference between path and DNS theories scalings essentially stems from the fact that the length scales are constrained by hyperdiffusivity in the former situation, while they are weakly evolving in the latter case. 

\begin{figure}
\centerline{\includegraphics[width=14cm]{SVSAmorph-c.jpg}}
\caption{\label{SVSAmorph} Magnetic variation and acceleration properties of the 71p model. a,c: Hammer projections of the \rev{time-averaged}, root-mean squared radial magnetic variation $\dot{\vecB}\cdot\vc{e}_{r}$ (a) and acceleration $\ddot{\vecB}\cdot\vc{e}_{r}$ (c) at the core surface, from magnetic field output up to spherical harmonic degree 13. b,d: Time series of the magnetic variation and acceleration energies $E_\mathrm{SV}$ (b) and $E_\mathrm{SA}$ (d) at the core surface. Red lines in (b,d) mark the time-averaged values $[E_\mathrm{SV}]$ and $[E_\mathrm{SA}]$. The blue and green bands between (b) and (d) locate the notable events related to spatial and temporal resolution changes in the model computation.}
\end{figure}

In Fig. \ref{SVSAmorph} we next turn to key aspects of magnetic variation and acceleration in the 71p model, which we analyse in a manner similar to Fig. 3 of \cite{Aubert2018}. Consistently with the defining principles of the path, and with the approximately constant values of $\tau_{U},\tau_\mathrm{SV}^{1}$ observed along this path (Table \ref{outputs1}), the properties of magnetic variation at 71 percent of the path (Fig. \ref{SVSAmorph}a,b) remain essentially similar to those observed since the start of the path, with an Earth-like geographic localisation that is essentially dictated by the \rev{heterogeneous mass anomaly flux imposed at the inner boundary} \citep{Aubert2013b}. The pattern of magnetic acceleration is also similar to that previously obtained from 29 percent of the path onwards, with this acceleration being mainly observed within an equatorial band in the Eastern hemisphere ($0^\mathrm{o}\mathrm{E}-180^\mathrm{o}\mathrm{E}$). The 71p model confirms that the relative dominance of equatorial over polar magnetic acceleration continues to increase as we advance along the path. As was the case in previous models, the 71p model features intermittent pulses in the magnetic acceleration energy, with a clear increase in strength and frequency relative to the Midpath conditions. Relatively to the midpath Model, the time-averaged acceleration energy $[E_\mathrm{SA}]$ of the 71p model (red line in Fig. \ref{SVSAmorph}d) consequently increases by about 25 percent, while $[E_\mathrm{SV}]$ is almost unchanged (Fig. \ref{SVSAmorph}b), leading to a time scale $\tau_\mathrm{SA}^{0}\approx \sqrt{[E_\mathrm{SV}]/[E_\mathrm{SA}]}=10.6\ut{yr}$ slightly shorter that its Midpath value $11.8\ut{yr}$ (Table \ref{outputs1}b). The general picture provided by the magnetic variation and acceleration in the 71p model is therefore consistent with the previously described evolution along the path. The kinematics and convectively-driven part of the dynamics remain invariant, and the dynamics is also gradually enriched in short-term, intermittent acceleration pulses.

\begin{figure}
\centerline{\includegraphics[width=14cm]{jerkpdf-c.jpg}}
\caption{\label{EJ} a: Time series of the Earth surface jerk energy $E_\mathrm{J}$ (see section \ref{methodseries}). b: Distribution of jerk energy as a function of the jerk recurrence time, for models previously computed in the range 29 percent to 50 percent of the parameter space path \citep{Aubert2019} and the 71p model. Shown in dashed line is the expected distribution at 71 percent of the path from an extrapolation $E_\mathrm{J}\sim \epsilon^{-0.19}$ previously obtained from the behaviours between 29 and 50 percent of the path \citep{Aubert2019}. c: Distribution of jerk energy in the 71p model (sampled each year) as a function of the latitude of the amplitude maxima observed in the radial magnetic acceleration at the core surface. Jerk statistics in b,c are computed in the time window  $[4200\ut{yr},14200\ut{yr}]$ where the spatio-temporal resolution of the computation is optimal (see coloured bands under Fig. \ref{SVSAmorph}b). This interval also avoids two spurious acceleration pulses near times 1130 and 4180 years, corresponding to resolution changes.}
\end{figure}

The magnetic acceleration pulses have been previously related to the dynamics and emergence of non-axisymmetric Alfv�n waves at the core surface, on a rapid time scale commensurate with $\tau_{A}$. This leads to geomagnetic signatures that reproduce the characteristics of recent geomagnetic jerks \citep{Aubert2019}. To characterise the evolving properties of magnetic acceleration pulses and jerks along the parameter space path, we previously found useful to analyse time series of the jerk energy $E_\mathrm{J}$ (Fig. \ref{EJ}a and equation  \ref{EJdef}). This quantity mirrors the occurence of acceleration pulses in a way that is more straightforwardly comparable to satellite-based determinations of the geomagnetic acceleration. New to the 71p model is the occurrence of extremely fast magnetic acceleration pulses (for instance at times 11070 and 11740 in Fig. \ref{SVSAmorph}d) that are smoothed by the 3-year averaging process involved in the definition of $E_\mathrm{J}$ (see corresponding times in Fig. \ref{EJ}a). Indeed, while this observation-based averaging window was clearly shorter than the typical Alfv�n time over which the jerks develop in the models at 29 to 50 percent of the path, in the 71p model it is now only slightly shorter than $\tau_{A}=5.8\ut{yr}$. Jerk recurrence statistics are computed in Fig. \ref{EJ}b as in \cite{Aubert2019}, by dividing the duration of the 71p model run with the number of samples reaching or exceeding a given value of $E_\mathrm{J}$ and representing the resulting estimates for jerk recurrence time as a function of $E_\mathrm{J}$. This representation confirms that the 71p model produces significantly more energetic jerks than the Midpath model at any recurrence time. However, the energy levels that are obtained are slightly recessed relative to the extrapolation that could be made in \cite{Aubert2019} from models spanning 29 to 50 percent of the path. This obviously relates to the smoothing effect described above. It is finally useful to analyse the distribution of $E_\mathrm{J}$ with the latitude of maxima in the associated magnetic acceleration pulses at the core surface (Fig. \ref{EJ}c). Consistently with the root-mean-squared pattern seen in Fig. \ref{SVSAmorph}c, magnetic acceleration pulses occur preferably at high latitudes (near the projection on the core-mantle boundary of the geostrophic cylinder tangent to the inner core, hereafter called the tangent cylinder) and the equator, with equatorial dominance for the strongest events. \rev{The residual equatorial asymmetry observed in Fig. \ref{EJ}c for strong events links with the rarity of such events and the limited duration of the sequence.} In the 71p model, about 80 percent of the events of magnitude $E_\mathrm{J}\ge 100 \ut{nT^{2}/yr^{4}}$ have core surface foci at latitudes less than 20 degrees away from the equator. The 71p model therefore pursues the trend previously reported in \cite{Aubert2018} towards equatorial localisation of pulses and jerks as we advance along the path. 
 
\subsection{\label{interplay}Frequency ranges for waves and convection}

\begin{figure}
\centerline{\includegraphics[width=14cm]{psd_surface_Bintnorm-c.jpg}}
\caption{\label{psd} Frequency domain spectral density $\hat{E}_\mathrm{SA}(f)$ of the magnetic acceleration energy  at Earth's surface (a,c,e), and $\hat{K}(f)$ of the flow acceleration energy  at the core surface (b,d,f), for models taken along (a,b) and across (c,d)  the parameter space path. a,b: spectra of the 29 percent, 50 percent and 71 percent of path models, plotted together in a. with the additional contribution of core surface magnetic diffusion in the 71p model. b,d: spectra of the 50 percent of path, 50pRa+Pm-, 50pRa+ and 50pPm+ models. In a-d the dashed vertical line marks the overturn frequency $f_{U}=1/\tau_{U}$. Flat and slanted grey lines respectively mark the power-laws $f^{0}$ and $f^{-2}$\rev{, the crossing of which defines the cut-off frequency $f_{c}$}. The relative positions and numerical values of the time scales $\tau_{\eta}$, $\tau_{U}$ and $\tau_{A}$ are also recalled. e,f: respective compounds of a,c and b,d, with frequency axis rescaled for each model by $(S/S_{50\%})^{-1/2}$, where $S=\tau_{\eta}/\tau_{A}$ and $S_{50\%}$ is the Lundquist number of the Midpath model.}
\end{figure}

In Fig. \ref{psd} we present the energy density spectra $\hat{E}_\mathrm{SA}(f)$ and $\hat{K}(f)$ of the Earth surface magnetic acceleration energy and core surface flow acceleration energy for models located between 29 and 71 percent of the path as well as across the path at 50 percent. At frequencies up to that of the overturn, $f_{U}=1/\tau_{U}=U/D$, Fig. \ref{psd}a-d confirms that all models feature similar spectral energy densities, an indication of the invariant dynamics caused by slow secular convection. At frequencies beyond $f_{U}$, all models also feature a range where the energy density profile is flattened. Considering that each successive time derivative multiplies the energy density by $f^{2}$, this flat range corresponds to a $f^{-2}$ range in the energy spectral density of the observed geomagnetic variation, and to a $f^{-4}$ range in that of the magnetic energy, both of which have received reasonable observational support \citep{DeSantis2003,Lesur2018}. The flat range for flow acceleration corresponds to a $f^{-2}$ range for flow velocity, which has previously been assumed as part of stochastic core flow modelling strategies \citep{Gillet2015,Gillet2019}. In the vicinity of the overturn frequency $f_{U}$, it is logical to associate this range of approximately flat spectra energy density to the signature of convective motions. At higher frequencies towards the decadal range, decay spectral tails following a $f^{-2}$ power law are observed both in flow and magnetic acceleration energies. \rev{A cut-off frequency $f_{c}$ that marks the start of the decay range is defined from the crossing between the flat ($f^{0}$) and slanted ($f^{-2}$) grey lines in Fig. \ref{psd}a-d. The decay spectral tails} can no longer be associated with convection because they are not invariant as we progress along the path (Fig. \ref{psd}a,b), as now better illustrated with the new data brought by the 71p model \rev{and the associated increase of the cut-off frequency $f_{c}$}. The combination of models along (Fig. \ref{psd}a,b) and across the path (Fig. \ref{psd}c,d) enables us to pinpoint the main control on $f_{c}$ as well as on the energy density within the decay range. The influence of the rotational time scale $\tau_{\Omega}$ can be immediately ruled out because the spectra of cross-path models with constant $Ro$ or $\lambda$ (see table \ref{outputs1}a) do not superimpose. The key time scale therefore appears to be the Alfv�n time $\tau_{A}$, but the question remains whether it should be considered in proportion of the overturn time $\tau_{U}$ (i.e by using the Alfv�n number $A$ as a control) or magnetic diffusion time $\tau_{\eta}$ (i.e by using $S$). 

\rev{A least-squares fit performed on the $f_{c}$ values extracted from Figs. \ref{psd}a-d yields $f_{c}\sim S^{0.5\pm 0.05}$, indicating that} all spectra can be collapsed by rescaling the frequency axis in proportion of $S^{-1/2}$, \rev{as further verified in} Fig. \ref{psd}e,f. \rev{The alternative scaling $f_{c}\sim A^{-1/2}$ can be readily discarded as the Alfv�n numbers for the two cases 50pRa+ and 50pPm+ with magnetic Reynolds numbers $Rm=\tau_{\eta}/\tau_{U}\ge 2000$ obviously fail to compensate the shift with the other cases at $Rm\approx 1000$ (see table \ref{outputs1}a).} Given that the overturn frequency $f_{U}$ is constant prior to re-scaling the frequency axis, the scaling for the cut-off frequency hence writes 
\begin{equation}
f_{c} \approx f_{U} (S/S_{0})^{1/2},\label{cutoff}
\end{equation}
with $S_{0}\approx 900$ from our results. The cut-off frequency $f_{c}$ and $f^{-2}$ decay tails are similar for both the flow and magnetic acceleration energy spectra. In the decay range $f\ge f_{c}$, the functional form of these energy densities is therefore
\begin{eqnarray}
\hat{E}_\mathrm{SA}(f) \approx E_\mathrm{SA}^\mathrm{max} \left(\frac{f}{f_{c}}\right)^{-2} \approx \dfrac{E_\mathrm{SA}^\mathrm{max}f_{U}^{2}}{S_{0}} ~ S f^{-2},\label{Mscal}\\
\hat{K}(f) \approx K^\mathrm{max} \left(\frac{f}{f_{c}}\right)^{-2} \approx \dfrac{K^\mathrm{max}f_{U}^{2}}{S_{0}} ~ S f^{-2}\label{Kscal}.
\end{eqnarray}
Here $E_\mathrm{SA}^\mathrm{max}, K^\mathrm{max}$ are the values of the plateaus reached in the flat energy density range. Within the decay tails, the flow and magnetic energy densities therefore linearly increase with the number $S$ of Alfv�n wave periods contained within a magnetic diffusion time. This strongly suggests that these decay tails $f\ge f_{c}$ are dominated by the contribution from Alfv�n waves. The range $f\le f_{U}$ is the convective range, and the interval $[f_{U},f_{c}]$ where energy density presents a plateau is the range of interplay between waves and convection. As the Lundquist number $S$ increases, the plateau broadens because of the elevated contribution from Alfv�n waves at its rightmost edge\rev{, with $S_{0}$ in equation (\ref{cutoff}) representing the minimal Lundquist number needed for this effect to occur, or more generally for waves to be significant in the simulation.} Writing the time-derivative of the magnetic induction equation 
\begin{equation}
\ddot{\vecB}=\nabla\times\left(\dot{\vecu}\times \vecB\right)+\nabla\times\left(\vecu\times \dot{\vecB}\right)+\eta\boldsymbol{\Delta} \dot{\vecB},\label{MISA}
\end{equation}
the similar spectral shapes (\ref{Mscal},\ref{Kscal}) also indicate that in the wave range at $f\ge f_{c}$, the first term in the right-hand-side dominates the production of magnetic acceleration, as previously anticipated for rapid dynamics \citep{Lesur2010b,Christensen2012,Aubert2018}. A direct calculation of the contribution by core surface magnetic diffusion to $\hat{E}_\mathrm{SA}(f)$ (Fig. \ref{psd}a) confirms that the term 
$\eta\boldsymbol{\Delta} \dot{\vecB}$ in (\ref{MISA}) is subdominant. The diffusive effects observed through the control of $S$ on $\hat{E}_\mathrm{SA}(f)$ and $\hat{K}(f)$ therefore originate in the bulk of the core. Incidentally, the functional forms (\ref{Mscal},\ref{Kscal}) may also be rewritten by involving the ratio $[(U/f) / \delta]^{2}$, where $U/f$ is a length scale excited by convection at frequency $f$ and $\delta=\sqrt{\eta \tau_{A}}$ is the bulk magnetic diffusion length scale at the Alfv�n time. 

\subsection{Axisymmetric torsional Alfv�n waves.}
\begin{figure}
\centerline{\includegraphics[width=14cm]{TW71-c.jpg}}
\caption{\label{TW71}Time-cylindrical radius diagrams of the geostrophic flow acceleration $\dot{u}_{g}$ (equation \ref{ug}) sampling the interior of the fluid in the Northern part of the tangent cylinder (a), and the region outside the tangent cylinder (b), at native resolution in the 71p model. c: time-cylindrical radius diagram obtained at the core surface and outside the tangent cylinder by representing the equator-symmetric, axisymmetric azimuthal flow acceleration $\dot{u}_{\varphi}^\mathrm{ZS}$ up to spherical harmonic degree 30. Note the larger extremes of the color map in a. relatively to b,c. Green curves in a.,b. correspond to outwards and inwards ray-tracing theoretical propagation tracks at the column-averaged Alfv�n speed $c_{A}(s,t)$ (equation \ref{ca}).}
\end{figure}

We can pursue our analysis by examining either the flow or magnetic acceleration signal carried by the waves. The former is more convenient, because rapid azimuthal flow acceleration presents a highly columnar (and therefore equator-symmetric) structure at advanced positions along the path. Torsional waves are a straightforward and interesting case study of the Alfv�n waves present in the system, because they can be easily isolated in the axially-columnar, axisymmetric, azimuthal part $\dot{u}_{g}$ of $\dot{\vecu}$ defined by equation (\ref{ug}). Fig. \ref{TW71}a,b shows time-cylindrical radius representation of $\dot{u}_{g}$ during a 100-yr sequence of the 71p model. As in Fig. 10 of \cite{Aubert2018}, the presence and dominance of torsional waves in this signal is attested using the similarity of the patterns with ray-tracing tracks that represent propagation at the theoretical speed $c_A(s,t)$ (equation \ref{ca}) commensurate with the one-dimensional Alfv�n velocity $D/\sqrt{3}\tau_{A}\approx 225 \ut{km/yr}$. Compared to Fig. 10 of \cite{Aubert2018}, the signal outside the tangent cylinder (Fig. \ref{TW71}b) has logically increased in propagation speed (because of the decrease of $\tau_{A}$ from Midpath to 71p conditions), but less trivially also in amplitude. The waves in the northern part of the tangent cylinder (Fig. \ref{TW71}a) are even faster (as they sample a stronger magnetic field), and also more intense. \rev{As the model features a jump in $c_{A}$ of about 15 percent across the tangent cylinder at $s=1220 \ut{km}$, similarly to \cite{Teed2014} we mainly observe wave transmission across this interface, in agreement with classical electromagnetic continuity relationships \citep[e.g.][]{Alfven1963}. Wave excitation and reflection events at the tangent cylinder are less obvious but can also be seen sporadically. In contrast, reflected patterns at the core-mantle boundary are clearer in Fig. \ref{TW71}b, and qualitatively suggest an increase of the reflection coefficient relative to Midpath conditions \citep[Fig. 10 of][]{Aubert2018}, where reflection was elusive. Given that our simulations operate with stress-free boundary conditions, this results appears to be at variance with the plane layer theory laid out in \cite{Schaeffer2012,Schaeffer2016,Gillet2017}, which predicts that the reflection coefficient should not depend on the imput parameters varied along the path (most notably $Pm$), and should even decrease due to the presence of a conducting outer layer and the increasing Lundquist number $S$. We anticipate that the discrepancy ties with the treatment of the singularity present for torsional waves at the equator of the core-mantle boundary, which is probably affected by hyperdiffusivity as the wave pattern shrinks down to small latitudinal length scales. The 71p model is less affected by this problem than the Midpath model as it operates with higher native resolution and reduced hyperdiffusivity (see table \ref{inputs}). With stress-free boundaries and the conducting layer, the plane layer theory predicts a reflection coefficient $R=(1-Q)/(1+Q)$ \citep{Schaeffer2016}, where the quality factor writes $Q= S (\Delta \sigma_{m}/ D \sigma) (B_r (r_{o})/B)$. The conductance ratio is $\Delta \sigma_{m}/ D \sigma=\te{-4}$ for all models along the path, and the ratio $B_r (r_{o})/B\approx 1/8$ of the radial magnetic field at the core surface to internal magnetic field is also approximately constant, as a consequence of static invariance of the solution. For the 71p model this theory therefore predicts $Q=0.3$ and $R=0.5$, qualitatively in line with Fig. \ref{TW71}b.}

\begin{figure}
\centerline{\includegraphics[width=8cm]{ZA30spectra-c.jpg}}
\caption{\label{ZA30} Frequency domain spectral density $\hat{K}^\mathrm{ZS}(f)$ of the core surface azimuthal, equator-symmetric and axisymmetric acceleration energy for models taken (a) along and (b) across the parameter space path. a: spectra of the start, 29 percent, 50 percent and 71 percent of path models. b: spectra of the 50 percent of path, 50pRa+Pm-, 50pRa+ and 50pPm+ models. The numerical values of the time scales $\tau_{U}$ and $\tau_{A}$ are also recalled in a,b. In a., the arrows locate the frequency of the fundamental Alfv�n wave $f=(\sqrt{3}r_{o}\tau_{A})^{-1}$ for models along the path, and the slanted grey line marks the power law $f^{-6}$. c: compound of a.,b., with frequency axis rescaled for each model by $A/A_{50\%}$, where $A=\tau_{A}/\tau_{U}$ and $A_{50\%}$ is the Alfv�n number of the Midpath model.}
\end{figure}

\rev{At the conditions of low inertia and viscosity where our models operate, torsional waves are excited by} perturbations of the Lorentz force averaged over axial cylinders, with these perturbations being linked to the underlying convection \rev{\citep{Teed2014,Teed2019}. This process naturally leads to} excitation of large-scale nature. This explains why almost all of the signal present in $\dot{u}_{g}$ and evaluated from bulk data at native resolution (Fig. \ref{TW71}b) can be retrieved in a time-cylindrical radius diagram of $\dot{u}_{\varphi}^{\mathrm{ZS}}$ (Fig. \ref{TW71}c), the equator-symmetric zonal flow acceleration at the core surface up to spherical harmonic degree 30. In Fig. \ref{ZA30} we further analyse the associated energy density spectra $\hat{K}^\mathrm{ZS}(f)$ in the frequency domain. Beyond 29 percent of the path (Fig. \ref{ZA30}a), most of the signal corresponds to the contribution from torsional waves, with the invariant contribution from axisymmetric thermal winds (estimated by representing the start of path model in Fig. \ref{ZA30}a) being subdominant. In these advanced models, $\hat{K}^\mathrm{ZS}(f)$ features a plateau centered around the fundamental wave frequency $f_{0}=(\sqrt{3}r_{o}\tau_{A})^{-1}$ (the factor $\sqrt{3}$ accounting for the conversion between isotropic and one-dimensional wave velocity), terminated at high frequencies by a $f^{-6}$ decay associated with the limited length scale content of the excitation source, and much steeper than that observed for the full core surface flow in Fig. \ref{psd}b. The evolution of this spectral shape along the path reflects a wave content that remains at large and invariant spatial scales while moving towards higher frequencies as the Alfv�n velocity is increased. Using cross-path models (Fig. \ref{ZA30}b) again together with along-path cases, the cut-off frequency is indeed confirmed to extend linearly with the inverse Alfv�n number $1/A=\tau_{U}/\tau_{A}$ (Fig. \ref{ZA30}c), and a possible scaling with $S$ can be discarded. The influence of magnetic diffusion is marginal here, because of the large length scales at which the waves are excited, and because radial core surface diffusion is subdominant (recall Fig. \ref{psd}a). Effects of diffusion are only seen in the decay tails in Fig. \ref{ZA30}c, with the less diffusive models 50pPm+ and 50pRa+ showing a slightly less steep decay than the other models. The simple form of the spectra implies that the time averaged energy $[K^\mathrm{ZS}]$ (the integral of the profiles along the frequency axis) scales as
\begin{equation}
[K^\mathrm{ZS}] \sim A^{-1}.\label{TOscaling}
\end{equation}
This means that the waves are able to draw an increasing amount of energy from the underlying convection as the separation between $\tau_{A}$ and $\tau_{U}$ increases. \rev{The leading contribution to this increase of $[K^\mathrm{ZS}]$ comes from the additional frequencies that are made available to wave motion as the fundamental Alfv�n frequency $f_{0}$ is increased. Resonant forcing by convection \citep[e.g.][]{Teed2019} does not appear to be the dominant excitation mechanism, because the gap widens along the path between the low and constant frequencies of thermal winds (again represented by the start of path model in Fig. \ref{ZA30}a) and the increasing frequency $f_{0}$. Significant energy levels are however preserved in the intermediate frequency range separating the two, where motion is neither the consequence of convection nor of waves, but rather results from a non-linear interaction between the two, with the dominant non-linearity for energy transfers being the Lorentz force in this case \citep{Teed2014,Aubert2017}. The observation of a broadening flat energy density profile in this interaction range is therefore supportive of a non-linear transfer of energy from convection to waves underlain by the Lorentz stresses.} Though the stabilising control of magnetic dissipation is not present at the axisymmetric scale, as we have shown above, it is expected to indirectly come from the non-axisymmetric contributions to these Lorentz stresses.  

\subsection{Non-axisymmetric waves.}

\begin{figure}
\centerline{\includegraphics[width=14cm]{fullvsfast-c.jpg}}
\caption{\label{fullfast}State of the 71p model at time 4749.8 yr of the simulation. Core surface Hammer projections (a,c) and partial equatorial plane views (b,d) of the azimuthal flow acceleration. In a,b, the total azimuthal acceleration $\dot{u}_\varphi$ is presented at native spatial and temporal resolution. In c,d, the fast and large-scale component of the equator-symmetric azimuthal acceleration $\dot{u}_\varphi^\mathrm{S}$ is presented. The fast component is obtained after removal of a 5-year running average. The large-scale component is obtained in c. by truncation after spherical harmonic degree 30, and in d. by lateral truncation after azimuthal wavenumber 30 and application of a running average of thickness 40 km in the radial direction. For clarity also, accelerations larger than $4\ut{km.yr^{-2}}$ are not represented in d. The partial equatorial views in b,d, are taken between the grey meridians delineated in a,c. In these equatorial views also, the density anomaly (green-brown, maximal values $\pm 0.5~\te{-4}\ut{kg/m^{3}}$) and radial magnetic field (orange-purple, maximal values $\pm 9.5 \ut{mT}$) are represented in a selectively transparent manner. Black arrows in c,d, denote the propagation direction of quasi-geostrophic Alfv�n (QGA) and Rossby waves. The QGA wave arrow in d. also marks the longitude selected for analysis in Fig. \ref{QGA71}.}
\end{figure}

Searching for non-axisymmetric waves is intrinsically more difficult as the signature of convection is stronger than for axisymmetric motion, and can attain short time scales at small spatial scales (see equation \ref{MACts}). The wave signature can therefore not be straightforwardly disentangled from that of convection, \rev{for instance} in native resolution snapshots of the azimuthal flow acceleration $\dot{u}_{\varphi}$ at the core surface (Fig. \ref{fullfast}a) and within the equatorial plane (Fig. \ref{fullfast}b). Focusing on the large-scale component (up to degree 30), where the acceleration is overwhelmingly equator-symmetric i.e. $\dot{u}_{\varphi}\approx \dot{u}_{\varphi}^\mathrm{S}$ (see section \ref{methodseries}) clarifies the picture by partly removing the convective signal originating at small spatial scales. For the purpose of illustration, in Fig. \ref{fullfast}c,d we further consider the rapid part of the large-scale signal, obtained after removal of a 5-year running average. This processing highlights \rev{two other classes}�of rapidly propagating features (located by labels in Fig. \ref{fullfast}c,d) in addition to the already described axisymmetric torsional waves\rev{: transverse quasi-geostrophic Alfv�n (QGA) waves and longitudinal Rossby waves.}

\subsubsection{Quasi-geostrophic Alfv�n waves.}
Non-axisymmetric, \rev{axially columnar} QGA waves propagate \rev{along magnetic field lines of arbitrary orientation perpendicular to the rotation axis. The typical distribution of field lines in the model \citep[see e.g. Fig. 8 in][]{Aubert2019b} mainly promotes cylindrical-radially propagating waves in the bulk of the fluid that are carried by the azimuthal flow $u_{\varphi}$ (similarly to torsional waves). When tracked in the equatorial plane (Fig. \ref{fullfast}d),} these are laterally limited by concentrations of radial magnetic field, as previously described in \cite{Aubert2018}. \rev{Near concentrations of azimuthal magnetic field found at low latitudes, the propagation direction can also acquire an azimuthal component (see e.g. Fig. \ref{fullfast}d near America).} While the QGA waves were previously mostly exhibited in the vicinity of magnetic acceleration pulse events, \rev{they are now significantly stronger in the 71p model (see section \ref{wavenerg}) and we can} confirm that they are ubiquitous and constantly sent out by the deep convection. 

\begin{figure}
\centerline{\includegraphics[width=14cm]{QGA71-c.jpg}}
\caption{\label{QGA71}Time-cylindrical radius diagrams of the non-axisymmetric, equator-symmetric core surface azimuthal flow acceleration $\dot{u}^\mathrm{S}_\varphi-\dot{u}^\mathrm{ZS}_\varphi$ at longitude $112.5^\mathrm{o}\mathrm{E}$ (located by arrows in Fig. \ref{fullfast}c,d) in the 71p model, presented at (a) native spatial and temporal resolution, (b) large-scale (spherical harmonic degree up to 30), and (c) large-scale for the fast component obtained after removal of a 5-year running average in time. The sets of slanted green lines denote advection at the one-dimensional convective velocity $D/\sqrt{3}\tau_{U}= 11 \ut{km/yr}$, and propagation at the one-dimensional Alfv�n wave velocity $D/\sqrt{3}\tau_{A}= 225 \ut{km/yr}$.}
\end{figure}

To better characterise the propagation of QGA wave features at the core surface in the 71p model, in Fig. \ref{QGA71} we now specifically focus on the non-axisymmetric, azimuthal and equator-symmetric flow acceleration $\dot{u}^\mathrm{S}_\varphi-\dot{u}^\mathrm{ZS}_\varphi$ and examine time-cylindrical radius diagrams at a specific longitude delineated by an arrow in Fig. \ref{fullfast}c,d. Representing this quantity at native spatial and temporal resolution (Fig. \ref{QGA71}a) mainly reveals the outwards advection of flow by convection at speeds commensurate with the one-dimensional convective velocity  $D/\sqrt{3}\tau_{U}= 11 \ut{km/yr}$. On this representation, however, faint signals propagating outwards at higher speeds can already be seen. In the large-scale component (Fig. \ref{QGA71}b) that removes the signature of fast convective signatures, we now observe together the slow convective and faster wave signals. Singling out these latter signals by again removing a 5-year running average in time (Fig. \ref{QGA71}c) reveals QGA waves with outward propagation speeds close to, but lower than the one-dimensional Alfv�n velocity $D/\sqrt{3}\tau_{A}= 225 \ut{km/yr}$. Comparing Figs. \ref{QGA71}c and \ref{TW71}c also shows that QGA waves can reach significantly smaller time scales and hence shorter radial wavelengths than torsional waves. 

While the Coriolis force identically vanishes from the magneto-inertial balance that drives axisymmetric torsional waves, it is necessarily present at the non-axisymmetric level and fundamentally modifies the wave equation \cite[e.g.][]{Finlay2008houches,Finlay2010}. This leads in particular to magneto-Coriolis waves with phase velocities much smaller than the Alfv�n velocity. These are furthermore dispersive, with the wave velocity increasing as the wavelength decreases. The effects of the Coriolis force can however be mitigated for axially-invariant waves of sufficiently small wavelength, that propagate in a direction perpendicular to the rotation vector. In this case, the wave velocity can approach the Alfv�n velocity from below \citep{Gerick2020}, as the influence of inertia is restored within the magneto-Coriolis balance. The axially columnar structure, propagation direction perpendicular to the rotation vector, velocities lower than $D/\sqrt{3}\tau_{A}$ and short radial wavelengths of the QGA waves observed here can also be understood within this framework. \rev{Our configuration however differs from that of \cite{Gerick2020} in the sense that the background magnetic field is highly complex, with relatively homogeneous regions surrounded by strongly heterogeneous field line concentrations corresponding to sharp gradients \citep[e.g. Fig. \ref{fullfast}b,d, see also Fig. 8 in][]{Aubert2019b}. This situation promotes a spatial segregation of the force balance \citep{Aubert2018}. The magneto-Coriolis part of this balance is mostly observed at the edges of the QGA wavefronts which correspond to the locations of strongest magnetic field heterogeneity. In the more magnetically homogeneous regions, however, the Coriolis force is mitigated to the point where wave motion becomes locally magneto-inertial again.} The residual \rev{influence} of the Coriolis force \rev{nevertheless tends to promote}  smaller radial length scales for QGA waves relative to torsional waves, which also rationalise the different behaviours of energy density spectra $\hat{K}(f)$ and $\hat{K}^\mathrm{ZS}(f)$ (compare Figs. \ref{psd}b,d,f and \ref{ZA30}) as regards the steepness of their high-frequency decay and the influence of bulk magnetic diffusion (or lack thereof) on this decay. \rev{We also expect this residual influence to increase as the waves approach the core surface at equatorial position, because of the increasing slope of the spherical boundary. This leads to additional wave slowdown compared to torsional waves and hence (the wave period being preserved) further reduction of the radial length scale (compare again Figs.  \ref{QGA71}c and \ref{TW71}c.)} 

\subsubsection{\label{RW}Rossby waves}
\rev{The Rossby waves observed in Fig. \ref{fullfast}c propagate eastwards in the vicinity of the equatorial plane. These are slow inertial waves in the sense} that their pulsation $\omega$ is much smaller than the rotation rate $\Omega$, thereby ensuring an evolution under a quasi-geostrophic force balance and an axially columnar structure \citep{Zhang2001,Busse2005,Canet2014}. \rev{From a geomagnetic standpoint, they are however fast in the sense that $\omega$ is larger than the typical pulsation $2\pi/\tau_{A}$ of Alfv�n waves. As a result, they are} only slightly modified by the presence of the magnetic field \citep[e.g.][]{Finlay2010} and typically feature magnetic to kinetic energy ratios smaller than unity \cite[e.g.][]{Gerick2020}. \rev{They hence do not} bear a significant signature in the magnetic acceleration signals of Fig. \ref{psd}, where a possible control from $\tau_{\Omega}$ is elusive. 

\begin{figure}
\centerline{\includegraphics[width=14cm]{rossbyvel.pdf}}
\caption{\label{Rossby}a: Frequency-domain energy density profiles of $\dot{u}_\varphi$ at the equator in a 130-year sequence of the 71p model. The acceleration signal is broken down into contributions from distinct azimuthal mode numbers $m$ and the energy is normalised relatively to the peak at $\omega/\Omega\approx0.0065$. Also reported at the top of the graph are the periods corresponding to each of the three identified peaks (located by colored arrows). b: Eastward propagation velocities (circles) identified on Radon-transformed time-longitude diagrams of equatorial azimuthal flow acceleration \citep[following the procedure described in][]{Finlay2005}, represented as a function of the mode number $m$ at each of the three normalised pulsations $\omega/\Omega\approx 0.0065, 0.011, 0.025$ corresponding to the peaks in panel a (see arrows of same color). Also reported as functions of $m$ are the closest matching phase velocities $c=\omega r_{o}/m$ (squares) obtained by adjusting the radial complexity number $N$ in equation (\ref{oO}). The grey line represents a $m^{-1}$ law.}
\end{figure}

In a full sphere \citep{Zhang2001} \rev{(a configuration that reasonably applies to our situation where the Rossby waves are confined at low to mid-latitudes, Fig. \ref{fullfast}c)}, and when $\omega/\Omega<<1$, the normalised pulsation $\omega/\Omega$ of \rev{hydrodynamic} Rossby waves can be approximated by the expression 
\begin{equation}
\dfrac{\omega}{\Omega}\approx\dfrac{2}{m+2}\left[\sqrt{1+\dfrac{m(m+2)}{N(2N+2m+1)}}-1\right],\label{oO}
\end{equation}
which involves the azimuthal mode number $m$ as well as a number $N$ describing their level of complexity in the radial direction. Fig. \ref{Rossby}a presents frequency-domain energy density profiles of the equatorial acceleration seen in Fig. \ref{fullfast}a, broken down into contributions from distinct azimuthal mode numbers $m$. The peaks that can be observed at various mode numbers are nearly synchronised in the vicinity of several distinct normalised pulsations. We focus on the three normalised pulsations $\omega/\Omega \approx 0.0065, 0.011, 0.025$, which contain significant energy across different values of $m$. The eastward propagation velocity of the corresponding waves can be determined by performing a Radon transform on time-longitude diagrams of the fast equatorial acceleration signal, again broken down by mode number $m$. At each value of $m$, Fig. \ref{Rossby}b reports the propagation velocities identified at distinct Radon energy peaks. Next to observed velocities, Fig. \ref{Rossby}b also reports theoretical phase velocities $c=\omega/k$, where $k=m/r_{o}$ and $\omega$ is determined from equation (\ref{oO}) by finding the radial complexity level $N$ that best matches the observed velocity. The agreement between observed and theoretical velocities is excellent throughout the range investigated for $\omega/\Omega$ and $m$, and provides an unambiguous characterisation of the Rossby waves seen in Fig. \ref{fullfast}a (and more clearly in Fig. \ref{fullfast}c after filtering out the low-frequency content). The synchronisation of $\omega/\Omega$ across distinct mode numbers $m$ is possible because despite their discrete character, the possible values given by equation (\ref{oO}) form a ensemble that is dense enough to offer $(m,N)$ couples yielding a pulsation close to $\omega/\Omega \approx 0.0065, 0.011, 0.025$. The synchronisation is then achieved by non-linear crosstalk between the waves, which is also necessary to ensure a saturation of their amplitude. Because of this synchronisation leading to nearly constant $\omega/\Omega$, the phase speed $c=\omega r_{o}/m$ of each wave category in Fig. \ref{Rossby}b naturally scales like $m^{-1}$. Unlike Alfv�n waves, Rossby waves are indeed highly dispersive in nature, with small-scale waves being significantly slower than large-scale waves. While all the waves observed here have periods within the interannual time scale range (see arrows in Fig. \ref{Rossby}a), we note that at the largest scales, their velocities up to $10^{4} \ut{km/yr}$ are the fastest observed in the 71p model. 

\subsection{\label{wavenerg}Wave energy scaling along the path.}
\begin{figure}
\centerline{\includegraphics[width=9cm]{velsenerg.pdf}}
\caption{\label{ve}a: Evolution with the path parameter $\epsilon$ of the time-averaged, total core surface flow acceleration energy $[K]$ up to spherical harmonic degree 30, plotted together with two diagnostics of the evolution of wave energy along the path (Earth's core conditions are towards the left of the graph). The energy of axisymmetric torsional waves is represented by the axisymmetric, azimuthal and equator-symmetric part $[K^\mathrm{ZS}]$, and the energy of non-axisymmetric waves is represented by the difference $[K]-[K_{29\%}]$ of $[K]$ to its value at 29 percent of the path. The grey lines mark the $\epsilon^{0.13}$ and $\epsilon^{0.25}$ power-law behaviours.}
\end{figure}

In Fig. \ref{ve} we present the evolution of flow acceleration energy along the parameter space path for the various waves that we have isolated. As measured by $[K^\mathrm{ZS}]$, the energy of torsional waves remains subdominant relatively to the total acceleration energy $[K]$, but gains two orders of magnitude along the path to reach $[K_{ZS}]/[K] \approx 0.1$ at 71 percent. At advanced path positions, the scaling $[K^\mathrm{ZS}] \sim A^{-1} \sim \epsilon^{-1/4}$ from equation (\ref{TOscaling}) is well approached by our results. in contrast,  $[K]$ asymptotically evolves less steeply (with $[K]\sim \epsilon^{-0.13}$ from our results) because it contains an invariant contribution from convection. This contribution is approximately removed by subtracting to $[K]$ the acceleration energy $[K_{29\%}]$ at the entry into the asymptotic regime, and $[K]-[K_{29\%}]$ may be seen as the total wave contribution that includes non-axisymmetric motion. The spectral form (\ref{Kscal}) suggests the scaling $[K]-[K_{29\%}] \sim S \rev{\sim A^{-1}Rm} \sim\epsilon^{-1/4}$, again in \rev{fair}  agreement \rev{(albeit being clearly validated by two points only)} with our numerical data at advanced path positions. At 71 percent of the path, the total wave contribution $[K]-[K_{29\%}]$ amounts to about half the total flow acceleration energy $[K]$, and is five times stronger than the energy $[K^\mathrm{ZS}]$ of axisymmetric torsional waves. If we denote as $\dot{U}_{W}$ the typical acceleration of waves in the total acceleration $\dot{U}$, in our advanced models this means that 
\begin{equation}
\dot{U}_{W}/\dot{U} \approx \left(\dfrac{[K]-[K_{29\%}]}{[K]}\right)^{1/2}=\mathcal{O} (1).\label{UdotWUdot}
\end{equation}

We terminate our analysis by estimating the contributions of waves to the core flow and magnetic field (and no longer to the time derivatives of these quantities, as we have done so far). Because these are relatively small, as we shall see, and because of the difficulties in disentangling the waves from convection that we have already alluded to, this cannot be straightforwardly achieved from the numerical model output and we need to take an alternative route. Assuming that the waves mainly evolve with time scale $\tau_{A}$, while the convection evolves with time scale $\tau_{U}$ (with $A=\tau_{A}/\tau_{U}$), and denoting again as $U_{W}$ the contribution of waves to the typical velocity field amplitude $U$, we estimate that
\begin{equation}
U_{W}/U=A \dot{U}_{W}/\dot{U}= \mathcal{O} (A).\label{UWU}
\end{equation}
We can further assume that the typical magnetic field amplitude $B_{W}$ carried by the Alfv�n waves obeys energy equipartition i.e. $B_{W}/U_{W}= \sqrt{\rho\mu}$. Using the definition $A=\sqrt{\rho\mu}U/B$, we then also estimate that
\begin{equation}
B_{W}/B=\dfrac{B_{W}}{U_{W}}\dfrac{U_{W}}{U}\dfrac{U}{B}=\mathcal{O}(A^{2})\label{BWB}
\end{equation}
This estimate is in principle valid at any altitude above the core-mantle boundary, if we assume that waves and convection share a similar length scale content. Equations (\ref{UWU},\ref{BWB}) show that the wave signatures in the total flow and magnetic fields are very subdominant since $A\ll 1$, and confirm that differentiating the velocity field once in time and the magnetic field twice in time is essential to highlighting these contributions. 

\section{\label{discu}Discussion}
\subsection{Waves and convection in the frequency domain}
In numerical models sampling the parameter space path introduced in \cite{Aubert2017}, dynamics of convective and wave origin occupy different, but overlapping frequency ranges, as seen for instance in spectral energy density profiles of the magnetic and flow acceleration (Fig. \ref{psd}). Of particular interest is the secular to decadal range located between the (approximately constant) overturn frequency $f_{U}=1/\tau_{U}$ and the cut-off frequency $f_{c}$, where energy density presents a plateau. This is where slow convection and rapid waves are in potential interplay. We have seen that slow convection accounts for the leftmost part of this plateau, the invariance of which indeed mirrors the kinematic invariance observed along the path. It is possible that this plateau relates with vorticity equivalence in the spatial domain \citep{Davidson2013,Aubert2019b}, which states that vorticity tends to be evenly distributed by magnetic turbulence in the range $[d_\mathrm{min},d_{\perp}]$ between the scale of magnetic dissipation and the dominant length scale at which convection powers the magnetic field. Assuming a simple linear correspondance between frequencies and length scales, this would indeed imply $u(f) \sim f^{-1}$ and $\dot{u}(f) \sim f^{0}$. This reasoning is appealing for explaining the leftmost end of this plateau but falls short of interpreting the rightmost end, the flattening of which along the path is a consequence of an elevating contribution coming primarily from hydromagnetic Alfv�n waves. This was confirmed in particular by the control on the cut-off frequency $f_{c}$ of the Lundquist number $S$ (equation \ref{cutoff}), which measures the number of Alfv�n wave periods occurring over the course of a magnetic diffusion time. The case of torsional waves (Fig. \ref{ZA30}) helped to illustrate the spectral broadening that can be expected as the time scale separation between the waves and convection increases, because of the higher wave frequencies that are made available and the non-linear wave-convection interactions underlain by Lorentz stresses. We hence conclude that the flat magnetic acceleration energy density profile in the range $[f_{U},f_{c}]$ \citep[corresponding to the $f^{-4}$ range observed in energy density spectra of the geomagnetic field,][]{DeSantis2003,Lesur2018} can be ascribed to the combined effect of non-linearly interacting slow convection and rapid Alfv�n waves. 

At higher frequencies $f \ge f_{c}$, most of the wave range is characterised by a $f^{-2}$ decay power law. In this range, the wave acceleration energy is controlled by the Lundquist number $S=\tau_{\eta}/\tau_{A}$ (equations \ref{Mscal},\ref{Kscal}), again highlighting the importance of time scale separation. This also underlines the stabilising control of magnetic diffusion felt by waves in the bulk of the fluid (and not at the core surface, Fig. \ref{psd}). Diffusion is essentially active at non-axisymmetric scales, where waves typically reach small radial length scales mitigating the influence of the Coriolis acceleration. In terms of length scales also, the dependence $f_{c}\sim \sqrt{S}$ (equation \ref{cutoff}) highlights the importance of the bulk magnetic diffusion length scale at the Alfv�n time scale $\delta=\sqrt{\eta\tau_{A}}=D/\sqrt{S}$. Waves at the largest scales such as axisymmetric torsional waves are immune to diffusion (Fig. \ref{ZA30}) but are nevertheless limited in amplitude because they are powered by non-linear couplings that involve non-axisymmetric scales where diffusion-limited Alfv�n waves are found. As we advance along the parameter space path, and despite the tightening constraints set by the QG-MAC balance, the availability of higher wave frequencies and the non-linear energy transfers cause an increase in the total wave acceleration energy (Fig. \ref{ve}). At 71 percent of the path we evaluate the total contribution from waves to the flow acceleration energy to be equivalent to that of convection when considering the signal up to spherical harmonic degree 30. At a fifth of the wave acceleration energy, the contribution from torsional waves is subdominant.

Using values $\tau_{\eta}=135000 \ut{yr}$, $\tau_U=130\ut{yr}$ and $\tau_{A}=2\ut{yr}$ (table \ref{outputs1}b), at Earth's core conditions we predict $S \approx 7~\te{4}$ and \rev{$f_{c} \approx 0.07 \ut{yr^{-1}}$} from the scaling (\ref{cutoff}). \rev{The $f^{0}$ range of interplay between waves and convection should therefore extend over a decade only between $f_{U}=8~\te{-3} \ut{yr^{-1}}$ and $f_{c}$. The Alfv�n frequency $1/\tau_{A}=0.5\ut{yr^{-1}}$ is predicted to lie well into the $f^{-2}$ range, at an acceleration energy density level of about $(f_{c}\tau_{A})^{2}\approx 1/50$ below the plateau (from equations \ref{Mscal},\ref{Kscal}). Assuming $Rm\approx 2000$ in the core (by doubling $\tau_{\eta}$) rather than the value $Rm\approx 1000$ adopted along the path shifts the cut-off frequency to $f_{c}\approx 0.1 \ut{yr^{-1}}$ and the relative attenuation at the Alfv�n frequency to $1/25$. These last results fall} short of accounting for the observed extent of the $f^{0}$ acceleration ($f^{-4}$ magnetic) range up to frequency $f \approx 1\ut{yr^{-1}}$ \citep{Lesur2018}, \rev{such that more fundamental modifications of the modelling set-up appear to be needed.} The path models are possibly underpowered at high frequencies because their design involves a neutrally buoyant core-mantle boundary. Exploring the effects of convective instability near the core surface on the high-frequency content of magnetic acceleration may therefore provide important geophysical constraints. It is unlikely that any degree of upper outer core stratification would help to bring the numerical results close to the geomagnetic observation, as this would further hinder the short-timescale dynamics \citep{Aubert2019}. The stratification would also degrade the morphological resemblance of the model core surface magnetic field to the present-day field \citep{Gastine2020}. From the observational standpoint, this discussion also highlights the importance of efforts aiming at cleaning the geomagnetic acceleration signal from external contributions close to annual frequencies \citep[see e.g.][]{Finlay2017}. 

\subsection{Detectability of hydromagnetic waves in geomagnetic observations.}
Equation (\ref{BWB}) suggests that the relative contribution $B_{W}$ from waves in the magnetic field amplitude $B$ is $B_{W}/B=\mathcal{O}(A^{2})$ i.e. $B_{W}\approx 8\ut{nT}$ at Earth's surface and at the physical condition $A=1.5~\te{-2}$ of the core. Though this may appear extremely weak, it remains within the typical resolution of satellite-based observations \citep[see e.g.][]{Finlay2016b}, and we have seen (Figs. \ref{psd},\ref{ve}, equation \ref{UdotWUdot}) that differentiating the magnetic field twice in time, or the velocity field once in time, leads to sizeable wave contributions to the total acceleration energy. This underlines the crucial importance of extracting the geomagnetic acceleration from ground observatory and satellite data at a good level of spatial and temporal resolution. This also motivates research towards elaborate approaches aiming at extracting a reliable flow acceleration from the magnetic acceleration signal \citep[see a recent review in][]{Gillet2019b}. Furthermore, the increase of wave energy along the path (Fig. \ref{ve}), the ubiquitous character of waves (Figs. \ref{fullfast},\ref{QGA71}) as well as the large-scale content of torsional waves (Fig. \ref{TW71}) appear to promote some optimism as regards the detectability of waves in the geomagnetic signal emanating from Earth's core.

Among the signal caused by waves in the magnetic acceleration, hydromagnetic Alfv�n waves are dominant because (unlike high-frequency Rossby waves) they achieve equipartition between the kinetic and magnetic energies that they carry (Fig. \ref{psd}). These should hence be most straightforwardly detectable in the geomagnetic acceleration signal. Concerning the typical flow amplitude $U^\mathrm{ZS}$ of torsional waves, following the estimation strategy leading to equation (\ref{UWU}) we infer $U^{ZS}/U \approx A \sqrt{[K^\mathrm{ZS}]/[K]}$, with an extrapolation to the end of the path yielding $[K^\mathrm{ZS}]/[K] \approx 0.17$. Using $U=D/\tau_{U} \approx 17 \ut{km/yr}$ and $A=1.5 ~\te{-2}$, this finally leads to $U^\mathrm{ZS} \approx 0.1 \ut{km/yr}$, somewhat smaller than (but of the same order of magnitude as) the value $\approx 0.3 \ut{km/yr}$ obtained from modelling of the rapidly evolving core flow \citep[see Fig. 13 in][]{Gillet2015}. Likewise, at the end of the path the total wave amplitude $U_{W}$ including axisymmetric and non-axisymmetric contributions should be higher. From equations (\ref{UdotWUdot},\ref{UWU}) we infer $U_{W}/U \approx A \sqrt{([K]-[K_\mathrm{29\%}])/[K]}\approx A$ and therefore $U_{W} \approx 0.25 \ut{km/yr}$, again comparable to the value $\approx 0.6 \ut{km/yr}$ obtained by \cite{Gillet2015} for the non-zonal flow. We finally note that the value $[K^\mathrm{ZS}]/([K]-[K^\mathrm{ZS}]) \approx 0.2$ that we predict at the end of the path for the ratio of zonal to non-zonal power in the core flows is in fair agreement with that retrieved by \cite{Gillet2015} at interannual frequencies (their Fig. 9). Our best chances to characterise the signature of non-axisymmetric Alfv�n waves still rests in the analysis of the geomagnetic jerks that they cause, because of the associated geometrical wave amplification effects \citep{Aubert2019}. We have found stronger and more frequent jerks in the 71p model than at earlier path positions, though some jerks events may become too fast for being noticeable in determinations of the geomagnetic acceleration with limited temporal resolution (Figs. \ref{SVSAmorph},\ref{EJ}). Previously, we had ascribed the increase of jerk energy $E_\mathrm{J}$ along the path to an increased level of wave radial shoaling, but the present results rather incite us to simply associate it with the linear increase of wave acceleration energy with $S$ that we have documented in this study.

The case for detectability of hydrodynamic Rossby waves in the geomagnetic signal appears considerably less obvious, as we did not find a conclusive influence of the rotational time scale $\tau_{\Omega}$ in the magnetic acceleration energy spectra of our models (Fig. \ref{psd}). Only the slowest Rossby modes with periods approaching the Alfv�n time scale $\tau_{A}$ can in principle be detected from geomagnetic observations, because faster modes carry less magnetic than kinetic energy \citep[e.g.][]{Gerick2020}. Although these modes also feature the slowest eastward propagation speeds (Fig. \ref{Rossby}), these speeds are still up to several thousands of kilometers per year in the 71p model and should even be ten times faster in the core as they scale linearly with $1/\tau_{\Omega}$ (equation \ref{oO}). Seen from the standpoint of typical geomagnetic acceleration timescales, these would therefore amount to almost instantaneous signals and would hence be very hard to isolate as propagating features, unless the signal is considered at the smallest spatial scales where the velocity of these dispersive waves is considerably slower. \rev{Eastward-propagating, equatorial} geomagnetic signals at speeds \rev{in the range} $500-1000\ut{km/yr}$ \rev{and wavenumbers $m=3-7$} have recently been inferred from geomagnetic acceleration records \citep{Chulliat2015,ChiDuran2020}. \rev{According to our analysis, at Earth's core conditions these could be explained in terms of Rossby waves only if the spatial complexity level $N$ (equation \ref{oO}) was allowed to reach high values $N> 60$, which is beyond the latitudinal resolution available for geomagnetic acceleration.}

\subsection{The path theory in the light of the 71p model and future prospects towards reaching Earth's core conditions}
Following the path theory introduced in \cite{Aubert2017}, this study has introduced a model located at 71 percent of this path. This has considerably enlarged the asymptotic portion (beyond 29 percent) where similar models are available, and the 71p model could again provide a complete validation to this theory. The leading order QG and first-order MAC force balances are stable, while the amplitude of inertia and viscosity continually decrease along the path \rev{\citep[compare Fig. \ref{forcebal} to Fig. 1 of][]{Aubert2018}}. Power-driven, diffusivity-free scaling laws proposed in \cite{Aubert2017} could be confirmed (Fig. \ref{scalings}). In the 71p model this leads to a state where an overwhelming fraction of the injected convective power is Ohmically dissipated, and where the Taylor constraint is enforced at a high level (Table \ref{outputs2}). The dynamo is also in a strong-field state, with the ratio of magnetic to kinetic energy being directly given by $1/A^{2}=416$, now just an order of magnitude away from Earth's core value. The statics (main field morphology), kinematics (convective core flows, magnetic secular variation), as well as the dynamics at time scales shorter than the convective overturn time $\tau_{U}$ are still invariant and carried over from the start of path, while the short-timescale dynamics is gradually enriched in a way that has been documented here in detail (Fig. \ref{SVSAmorph},\ref{psd}). Here we have demonstrated that most, and therefore probably all of the parameter space path is devoid of abrupt physical transitions. This further rationalises the relevance of earlier dynamo models located close to the start of the path to describe the geodynamo, and this also further strengthens the likeliness of core dynamics being in a similar dynamical regime as that observed at 71 percent of the path. 

With a computation carried out over the course of two years, involving 246 million time steps and 15 million single-core CPU hours, the model at 71 percent of the path may be seen as an extreme endeavour that apparently obscures the prospect of being able to terminate the exploration of this path. A positive note is that the computation of this model provided the opportunity to perform several low-level optimisations in the numerical code towards a faster execution at given number of cores and also towards the possibility to use more cores while maintaining a good strong parallel scaling. Together with an improved generation of supercomputers provided by GENCI in France, we could achieve at least a fivefold increase in computation speed for the path models. This was used to increase the spatial resolution and decrease the hyperdiffusivity at which the 71p model runs, and also 
opened the way to an exploration of cross-path models at 50 percent of the path in a way that could not have been feasible only two years ago, at the time of our earlier study \citep{Aubert2018}. We have also seen that it is no longer necessary to advance in half-decades of $\epsilon$ along the path, and that much larger leaps can be achieved through a simple re-scaling procedure of checkpoint files. The next stop along the road is therefore most probably the final one, i.e. being able to simulate the geodynamo exactly in Earth's core conditions. This will presumably imply another round of optimisations and another generation of Tier-1 supercomputers, but we can in principle foresee the completion of this challenge in the coming decade.

\section*{Acknowledgements}
The authors thank two anonymous referees for comments and Dominique Jault, Nathana�l Schaeffer and Thomas Gastine for discussions and help in code optimisation. JA acknowledges support from the Fondation Simone et Cino Del Duca of Institut de France (2017 Research Grant). This project has also been funded by ESA in the framework of EO Science for Society, through contract 4000127193/19/NL/IA (SWARM + 4D Deep Earth: Core). NG was partially supported by the French Centre National d�Etudes Spatiales (CNES) for the study of Earth�s core dynamics in the context of the Swarm mission of ESA. Numerical computations were performed at S-CAPAD, IPGP and using HPC resources from GENCI-TGCC and GENCI-CINES (Grant numbers A0060402122 and A0080402122).

\section*{Data availability}
The numerical code and simulation data analysed in this study are available from the corresponding author upon reasonable request. The core surface data from the 71 percent of path model is also available online at the URL \\
https://4d-earth-swarm.univ-grenoble-alpes.fr/data. 

\bibliographystyle{gji}
\bibliography{Biblio}

\end{document}
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@article{Schwaiger2021,
	abstract = {{In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are simultaneously representative of the energy contained in the solution (energetically relevant) and also indicative of the established force balance (dynamically relevant). In the case of numerical simulations of rotating convection and magnetohydrodynamic dynamos in spherical shells, it has remained difficult to measure length scales that are both energetically and dynamically relevant, a situation that has led to conflicting interpretations, and sometimes misrepresentations of the underlying force balance. By analysing an extensive set of magnetic and non-magnetic models, we focus on two length scales that achieve both energetic and dynamical relevance. The first one is the peak of the poloidal kinetic energy spectrum, which we successfully compare to crossover points on spectral representations of the force balance. In most dynamo models, this result confirms that the dominant length scale of the system is controlled by a previously proposed quasi-geostrophic (QG-) MAC (Magneto-Archimedean-Coriolis) balance. In non-magnetic convection models, the analysis generally favours a QG-CIA (Coriolis-Inertia-Archimedean) balance. Viscosity, which is typically a minor contributor to the force balance, does not control the dominant length scale at high convective supercriticalities in the non-magnetic case, and in the dynamo case, once the generated magnetic energy largely exceeds the kinetic energy. In dynamo models, we introduce a second energetically relevant length scale associated with the loss of axial invariance in the flow. We again relate this length scale to another crossover point in scale-dependent force balance diagrams, which marks the transition between large-scale geostrophy (the equilibrium of Coriolis and pressure forces) and small-scale magnetostrophy, where the Lorentz force overtakes the Coriolis force. Scaling analysis of these two energetically and dynamically relevant length scales suggests that the Earth's dynamo is controlled by a QG-MAC balance at a dominant scale of about \\$200 \\, \\mathrm\\{km\\}\\$, while magnetostrophic effects are deferred to scales smaller than \\$50 \\, \\mathrm\\{km\\}\\$.}},
	author = {Schwaiger, T and Gastine, T and Aubert, J},
	date-added = {2021-02-03 12:01:25 +0100},
	date-modified = {2021-02-03 12:02:46 +0100},
	doi = {10.1093/gji/ggaa545},
	journal = {Geophys. J. Int.},
	month = {11},
	number = {3},
	pages = {1890-1904},
	title = {{Relating force balances and flow length scales in geodynamo simulations}},
	volume = {224},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggaa545}}

@incollection{Finlay2008houches,
	abstract = {Publisher Summary This chapter discusses the laboratory experiments studying the influence of rotation and magnetic fields on electrically conducting fluids dramatically demonstrate the intrinsic stability that these influences can impart to the fluids. Waves occurring as a result of the stability imparted by fluid rotation are known as inertial waves. They are observed in natural rotating fluid systems such as Earth's ocean. Waves in electrically conducting fluids occurring as a result of the stability imparted by magnetic fields is known as hydromagnetic or Alfv{\'e}n waves. They are found in plasmas or fluids with high electrical conductivity, such as the solar corona and Earth's magnetosphere and core. It is therefore a matter of considerable geophysical and astrophysical importance to understand and be able to quantitatively model such waves and their generalizations that occur when both magnetic fields and rotation are present. The chapter reviews that waves properties, particularly their dispersion, and how these vary with location and time depend on the nature of the system supporting the waves. Study of waves thus allows underlying physical properties of often inaccessible geophysical and astrophysical systems to be investigated. Furthermore, waves are a mechanism by which energy and momentum can be transported; observations of waves can therefore discuss much about how the underlying system is operating and evolving.},
	author = {Finlay, C. C.},
	booktitle = {{Lecture notes on Les Houches Summer School: Dynamos}},
	booktitle1 = {Les Houches},
	chapter = {8},
	da = {2008/01/01/},
	date-added = {2021-01-28 10:45:03 +0100},
	date-modified = {2021-01-28 15:04:51 +0100},
	doi = {https://doi.org/10.1016/S0924-8099(08)80012-1},
	editor = {Cardin, P. and Cugliandolo, L. F.},
	pages = {403--450},
	publisher = {Elsevier},
	title = {Waves in the presence of magnetic fields, rotation and convection},
	volume = {88},
	year = {2008},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0924809908800121},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0924-8099(08)80012-1}}

@inbook{Alfven1963,
	author = {Alfv{\'e}n, H. and F{\"a}lthammar, C.G.},
	chapter = {3.4.5},
	date-added = {2021-01-28 10:13:02 +0100},
	date-modified = {2021-01-28 10:15:57 +0100},
	edition = {2nd ed.},
	publisher = {Oxford Univ. Press},
	title = {Cosmical Electrodynamics},
	year = {1963}}

@article{Teed2019,
	abstract = {{Turbulence and waves in Earth's iron-rich liquid outer core are believed to be responsible for the generation of the geomagnetic field via dynamo action. When waves break upon the mantle they cause a shift in the rotation rate of Earth's solid exterior and contribute to variations in the length-of-day on a ∼6-yr timescale. Though the outer core cannot be probed by direct observation, such torsional waves are believed to propagate along Earth's radial magnetic field, but as yet no self-consistent mechanism for their generation has been determined. Here we provide evidence of a realistic physical excitation mechanism for torsional waves observed in numerical simulations. We find that inefficient convection above and below the solid inner core traps buoyant fluid forming a density gradient between pole and equator, similar to that observed in Earth's atmosphere. Consequently, a shearing jet stream---a `thermal wind'---is formed near the inner core; evidence of such a jet has recently been found. Owing to the sharp density gradient and influence of magnetic field, convection at this location is able to operate with the turnover frequency required to generate waves. Amplified by the jet it then triggers a train of oscillations. Our results demonstrate a plausible mechanism for generating torsional waves under Earth-like conditions and thus further cement their importance for Earth's core dynamics.}},
	author = {Teed, R J and Jones, C A and Tobias, S M},
	date-added = {2021-01-25 14:56:35 +0100},
	date-modified = {2021-01-25 14:57:30 +0100},
	doi = {10.1093/gji/ggy416},
	journal = {Geophys. J. Int.},
	month = {10},
	number = {1},
	pages = {123-129},
	title = {{Torsional waves driven by convection and jets in Earth's liquid core}},
	volume = {216},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggy416}}

@article{Gerick2020,
	abstract = {AbstractFast changes of Earth's magnetic field could be explained by inviscid and diffusion-less quasi-geostrophic (QG) Magneto-Coriolis modes. We present a hybrid QG model with columnar flows and three-dimensional magnetic fields and find modes with periods of a few years at parameters relevant to Earth's core. For the simple poloidal magnetic field that we consider here they show a localization of kinetic and magnetic energy in the equatorial region. This concentration of energy near the equator and the high frequency make them a plausible mechanism to explain similar features observed in recent geomagnetic field observations. Our model potentially opens a way to probe the otherwise inaccessible magnetic field structure in the Earth's outer coreThis article is protected by copyright. All rights reserved.},
	author = {Gerick, F. and Jault, D. and Noir, J.},
	date-added = {2021-01-13 13:35:50 +0100},
	date-modified = {2021-02-03 12:05:04 +0100},
	journal = {Geophys. Res. Lett.},
	keywords = {Magneto-Coriolis modes, core dynamics, secular variations, MHD modes},
	note = {doi: 10.1029/2020GL090803},
	pages = {2020GL090803},
	title = {{Fast Quasi-Geostrophic Magneto-Coriolis Modes in the Earth's core}},
	volume = {47},
	year = {2020},
	Bdsk-Url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020GL090803},
	Bdsk-Url-2 = {https://doi.org/10.1029/2020GL090803}}

@article{Christensen2002,
	author = {Christensen, U. R.},
	date-added = {2020-12-02 10:12:47 +0100},
	date-modified = {2020-12-02 10:12:47 +0100},
	journal = {J. Fluid. Mech.},
	pages = {115-133},
	title = {Zonal flow driven by strongly supercritical convection in rotating spherical shells},
	volume = {470},
	year = {2002}}

@article{Finlay2017,
	abstract = {Measurements of the Earth's magnetic field collected by low-Earth-orbit satellites such as Swarm and CHAMP, as well as at ground observatories, are dominated by sources in the Earth's interior. However these measurements also contain significant contributions from more rapidly-varying current systems in the ionosphere and magnetosphere. In order to fully exploit magnetic data to probe the physical properties and dynamics of the Earth's interior, field models with suitable treatments of external sources, and their associated induced signals, are essential. Here we review the methods presently used to construct models of the internal field, focusing on techniques to handle magnetospheric and ionospheric signals. Shortcomings of these techniques often limit the quality, as well as spatial and temporal resolution, of internal field models. We document difficulties in using track-by-track analysis to characterize magnetospheric field fluctuations, differences in internal field models that result from alternative treatments of the quiet-time ionospheric field, and challenges associated with rapidly changing, but spatially correlated, magnetic signatures of polar cap current systems. Possible strategies for improving internal field models are discussed, many of which are described in more detail elsewhere in this volume.},
	author = {Finlay, C. C. and Lesur, V. and Th{\'e}bault, E. and Vervelidou, F. and Morschhauser, A. and Shore, R.},
	da = {2017/03/01},
	date-added = {2020-11-10 12:00:05 +0100},
	date-modified = {2020-11-10 12:00:21 +0100},
	doi = {10.1007/s11214-016-0285-9},
	id = {Finlay2017},
	isbn = {1572-9672},
	journal = {Space. Sci. Rev.},
	number = {1},
	pages = {157--189},
	title = {Challenges Handling Magnetospheric and Ionospheric Signals in Internal Geomagnetic Field Modelling},
	ty = {JOUR},
	volume = {206},
	year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1007/s11214-016-0285-9}}

@article{Gastine2020,
	abstract = {{The existence of a stably stratified layer underneath the core--mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally subadiabatic. The exact properties of this stably stratified layer, namely its size \\$\\mathcal \\{H\\}\_s\\$ and the degree of its stratification characterized by the Brunt--V{\"a}is{\"a}l{\"a} frequency N, are however uncertain and highly debated. A stable layer underneath the CMB can have crucial dynamical impacts on the geodynamo. Because of the inhibition of the convective motions, a stable layer is expected to primarily act as a low-pass filter on the magnetic field, smoothing out the rapidly varying and small-scale features by skin effect. To investigate this effect more systematically, we compute 70 global geodynamo models varying the size of the stably stratified layer from 0 to 300 km and its amplitude from N/Ω = 0 to N/Ω ≃ 50, Ω being the rotation rate. We show that the penetration of the convective flow in the stably stratified layer is controlled by the typical size of the convective eddies and by the local variations of the ratio N/Ω. Using quantitative measures of the degree of morphological semblance between the magnetic field obtained in numerical models and the geomagnetic field at the CMB, we establish an upper bound for the stable layer thickness \\$\\mathcal \\{H\\}\_s\\lt (N/\\Omega )^\\{-1\\} \\mathcal \\{L\\}\_s\\$, \\$\\mathcal \\{L\\}\_s\\$ being the horizontal size of the convective flow at the base of the stable layer. This defines a strong geomagnetic constraint on the properties of a stably stratified layer beneath the CMB. Unless unaccounted double-diffusive effects could drastically modify the dynamics of the stable layer, our numerical geodynamo models hence favour no stable stratification atop the core.}},
	author = {Gastine, Thomas and Aubert, Julien and Fournier, Alexandre},
	date-added = {2020-11-10 11:57:03 +0100},
	date-modified = {2020-11-10 11:58:42 +0100},
	doi = {10.1093/gji/ggaa250},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {05},
	number = {2},
	pages = {1433-1448},
	title = {{Dynamo-based limit to the extent of a stable layer atop Earth's core}},
	volume = {222},
	year = {2020},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggaa250}}

@article{Lesur2010b,
	abstract = {Two recent magnetic field models, GRIMM and xCHAOS, describe core field accelerations with similar behavior up to Spherical Harmonic (SH) degree 5, but which differ significantly for higher degrees. These discrepancies, due to different approaches in smoothing rapid time variations of the core field, have strong implications for the interpretation of the secular variation. Furthermore, the amount of smoothing applied to the highest SH degrees is essentially the modeler's choice. We therefore investigate new ways of regularizing core magnetic field models. Here we propose to constrain field models to be consistent with the frozen flux induction equation by co-estimating a core magnetic field model and a flow model at the top of the outer core. The flow model is required to have smooth spatial and temporal behavior. The implementation of such constraints and their effects on a magnetic field model built from one year of CHAMP satellite and observatory data, are presented. In particular, it is shown that the chosen constraints are efficient and can be used to build reliable core magnetic field secular variation and acceleration model components.},
	author = {Lesur, V. and Wardinski, I. and Asari, S. and Minchev, B. and Mandea, M.},
	da = {2010/06/01},
	date-added = {2020-11-09 13:31:26 +0100},
	date-modified = {2020-11-09 13:31:54 +0100},
	doi = {10.5047/eps.2010.02.010},
	id = {Lesur2010},
	isbn = {1880-5981},
	journal = {Earth, Plan. Space},
	number = {6},
	pages = {503--516},
	title = {Modelling the Earth's core magnetic field under flow constraints},
	ty = {JOUR},
	volume = {62},
	year = {2010},
	Bdsk-Url-1 = {https://doi.org/10.5047/eps.2010.02.010}}

@article{Landeau2017,
	abstract = {Abstract Energy considerations indicate that the power delivered to the present-day geodynamo comes mainly from the growth of the solid inner core, through light element and latent heat releases. The nucleation of the inner core was, therefore, a major transition for the geodynamo. Here, we use numerical dynamo simulations linked by thermochemical evolution of the core to investigate the effects of inner-core nucleation (ICN) on the geodynamo, and identify possible \{ICN\} footprints in the palaeomagnetic field. Our results suggest that a strong-field dipole-dominated dynamo prior and after \{ICN\} (the uniformitarian scenario) is most likely. We predict little footprint of \{ICN\} on the surface field intensity, consistent with the observed lack of a long-term trend in paleointensity data. Instead, we find that the best proxy for inner-core growth is an increase in axial octupole strength with age, from present-day to ICN, which might be resolvable in the palaeomagnetic record. We confirm the existence of weak-field, multipolar dynamos prior to ICN, suggesting the dynamo might have transiently reached a weak-field state (the catastrophic scenario). The narrow stability domain of these weak-field dynamos implies that the catastrophic scenario is less probable than the uniformitarian scenario. },
	author = {Maylis Landeau and Julien Aubert and Peter Olson},
	date-added = {2020-10-13 18:24:20 +0200},
	date-modified = {2020-10-13 18:24:36 +0200},
	doi = {http://doi.org/10.1016/j.epsl.2017.02.004},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {Geocentric Axial Dipole},
	pages = {193 - 204},
	title = {The signature of inner-core nucleation on the geodynamo},
	volume = {465},
	year = {2017},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X1730064X},
	Bdsk-Url-2 = {http://doi.org/10.1016/j.epsl.2017.02.004}}

@article{ChiDuran2020,
	abstract = {Abstract Satellite observations reveal short pulses in the second time derivative of the geomagnetic field. We seek to interpret these signals using complex empirical orthogonal functions (CEOFs). This methodology decomposes the signal into traveling waves, permitting estimates for the period, angular wave number, and phase velocity. We recover CEOFs from the CHAOS-6 model, focusing on three geographic regions with strong secular acceleration. Two regions are confined to the equator, while the third is located under Alaska. We find evidence for both eastward and westward traveling waves with periods between 7 and 20 years. There is also evidence for weaker standing waves with complex spatial patterns. Two of the three regions have waves that are compatible with predictions for waves in a stratified fluid. Our results yield estimates for the structure of fluid stratification at the top of the core.},
	author = {Chi-Dur{\'a}n, Rodrigo and Avery, Margaret S. and Knezek, Nicholas and Buffett, Bruce A.},
	date-added = {2020-10-01 14:33:03 +0200},
	date-modified = {2020-10-01 14:33:20 +0200},
	doi = {10.1029/2020GL087940},
	eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020GL087940},
	journal = {Geophys. Res. Lett.},
	note = {e2020GL087940 10.1029/2020GL087940},
	number = {17},
	pages = {e2020GL087940},
	title = {Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions},
	volume = {47},
	year = {2020},
	Bdsk-Url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020GL087940},
	Bdsk-Url-2 = {https://doi.org/10.1029/2020GL087940}}

@incollection{Gillet2019b,
	author = {Gillet, N.},
	booktitle = {Geomagnetism, Aeronomy and Space Weather : a Journey from the Earth's Core to the Sun},
	chapter = {9},
	date-added = {2020-10-01 12:29:32 +0200},
	date-modified = {2020-10-01 12:30:30 +0200},
	editor = {Mandea, M. and Korte, M. and Petrovsky, E. and Yau, A},
	publisher = {International Association of Geomagnetism and Aeronomy},
	title = {Spatial and temporal changes of the geomagnetic field : insights from forward and inverse core field models},
	year = {2019}}

@article{Buffett2015,
	abstract = {We use stochastic models for fluctuations in the dipole moment to derive a geomagnetic power spectrum. The theoretical spectrum is represented as a function of frequency f in the general form Af−n with smooth transitions between changes in the exponent n. A flat spectrum (n=0) at low frequencies changes to n=2 at intermediate frequencies. We attribute the transition frequency to the decay time of dipole fluctuations. Accounting for correlated noise in the stochastic model introduces another transition from n=2 to 4, where the transition frequency is set by the correlation time of the noise. Numerical geodynamo models suggest that the correlation time is less than the convective overturn time and may be related to the lifetime of helical eddies. Applying these results to paleomagnetic estimates of the power spectrum yields a correlation time of 100 to 200 yrs. Evidence for a transition between n=0 and n=2 in paleomagnetic power spectra is interpreted as a constraint on the electrical conductivity of the core. Additional correlation times in the noise model are expected to produce a transition to n=6, possibly associated with diffusion of the dipole field through a magnetic boundary layer at the top of the core.},
	author = {Bruce Buffett and Hiroaki Matsui},
	date-added = {2020-09-23 17:37:45 +0200},
	date-modified = {2020-09-23 17:38:10 +0200},
	doi = {https://doi.org/10.1016/j.epsl.2014.11.045},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {geodynamo, geomagnetic spectrum, stochastic model},
	pages = {20 - 26},
	title = {A power spectrum for the geomagnetic dipole moment},
	volume = {411},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X14007456},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.epsl.2014.11.045}}

@article{Lehnert1954,
	adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	adsurl = {https://ui.adsabs.harvard.edu/abs/1955ApJ...121..481L},
	author = {{Lehnert}, B.},
	date-added = {2020-09-22 13:55:41 +0200},
	date-modified = {2020-09-22 13:59:55 +0200},
	doi = {10.1086/146009},
	journal = {Ap. J.},
	pages = {647},
	title = {{Magnetohydrodynamic Waves Under the Action of the Coriolis Force.}},
	volume = {119},
	year = 1954,
	Bdsk-Url-1 = {https://doi.org/10.1086/146009}}

@article{Constable2005,
	abstract = {We construct a power spectrum of geomagnetic dipole moment variations or their proxies that spans the period range from some tens of million down to about 100 years. Empirical estimates of the spectrum are derived from the magnetostratigraphic time scale, from marine sediment relative paleointensity records, and from a time varying paleomagnetic field model for the past 7 kyr. The spectrum has the most power at long periods, reflecting the influence of geomagnetic reversals and in general decreases with increasing frequency (decreasing period). The empirical spectrum is compared with predictions from simple models. Discrepancies between the observed and predicted spectra are discussed in the context of: (i) changes in reversal rate, (ii) overall average reversal rate, (iii) cryptochrons, (iv) the time taken for a reversal to occur, and (v) long term paleosecular variations and average estimates of the field strength and variance from other sources.},
	author = {Catherine Constable and Catherine Johnson},
	date-added = {2020-09-18 13:32:59 +0200},
	date-modified = {2020-09-18 13:33:10 +0200},
	doi = {https://doi.org/10.1016/j.pepi.2005.03.015},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Geomagnetism, Paleomagnetism, Paleomagnetic power spectrum, Paleosecular variations},
	note = {Studies of the Earth's Deep Interior},
	number = {1},
	pages = {61 - 73},
	title = {A paleomagnetic power spectrum},
	url = {http://www.sciencedirect.com/science/article/pii/S003192010500169X},
	volume = {153},
	year = {2005},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S003192010500169X},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2005.03.015}}

@article{Panovska2013,
	abstract = {In order to understand mechanisms that maintain and drive the evolution of the Earthʼs magnetic field, a characterization of its behavior on time scales of centuries to millennia is required. We have conducted a search for periodicities in Holocene sediment magnetic records, by applying three techniques: multitaper spectral estimation, wavelet analysis and empirical mode decomposition. When records are grouped according to their geographical locations, we find encouraging consistency amongst the observed periods, especially in nearby inclination records. No evidence was obtained for discrete, globally observed, periods. Rather we find a continuous broadband spectrum, with a slope corresponding to a power law with exponent of −2.3$\pm$0.6 for the period range between 300 and 4000 yr. This is consistent with the hypothesis that chaotic convection in the outer core drives the majority of secular variation.},
	author = {S. Panovska and C.C. Finlay and A.M. Hirt},
	date-added = {2020-09-18 13:32:26 +0200},
	date-modified = {2020-09-18 13:32:49 +0200},
	doi = {https://doi.org/10.1016/j.epsl.2013.08.010},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {paleomagnetism, geomagnetism, paleosecular variation, lake sediments, paleomagnetic spectrum, periodicity},
	pages = {88 - 94},
	title = {Observed periodicities and the spectrum of field variations in Holocene magnetic records},
	volume = {379},
	year = {2013},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X13004366},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.epsl.2013.08.010}}

@article{DeSantis2003,
	abstract = {Many natural phenomena show a relationship between their spatial and temporal Fourier spectra. This paper discusses such a connection for the geomagnetic field, when some assumptions are made about the (exponential or power-law) behaviour of the spatial power spectrum of the field itself and that of its time derivative (the spatial spectrum of the secular variation) as estimated from global geomagnetic field models. It is shown that, under either assumption, the temporal spectrum of the geomagnetic field computed at the core--mantle boundary (CMB) would have a power-law behaviour with a negative spectral exponent of about 0.5. At the Earth's surface, although the temporal spectrum obtained from the power-law spatial model assumes a slightly more complicated form, it can be practically approximated with a power law with a negative exponent of about 3.6. Analysis of magnetic observatory data confirms these results and that the starting hypotheses are reasonable, especially in view of the possibly chaotic state of the dynamical processes underlying the generation and maintenance of the geomagnetic field.},
	author = {A. {De Santis} and D.R. Barraclough and R. Tozzi},
	date-added = {2020-09-18 13:32:02 +0200},
	date-modified = {2020-09-18 13:33:40 +0200},
	doi = {https://doi.org/10.1016/S0031-9201(02)00211-X},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Geomagnetic field spectra, Secular variation, Persistence times},
	note = {Magnetic Field Modelling},
	number = {2},
	pages = {125 - 134},
	title = {Spatial and temporal spectra of the geomagnetic field and their scaling properties},
	volume = {135},
	year = {2003},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S003192010200211X},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0031-9201(02)00211-X}}

@article{Meduri2016,
	abstract = {Earth's axial dipole field changes in a complex fashion on many different time scales ranging from less than a year to tens of million years. Documenting, analysing, and replicating this intricate signal is a challenge for data acquisition, theoretical interpretation, and dynamo modeling alike. Here we explore whether axial dipole variations can be described by the superposition of a slow deterministic drift and fast stochastic fluctuations, i.e. by a Langevin-type system. The drift term describes the time averaged behavior of the axial dipole variations, whereas the stochastic part mimics complex flow interactions. The statistical behavior of the system is described by a Fokker-Planck equation which allows useful predictions, including the average rates of dipole reversals and excursions. We analyze several numerical dynamo simulations, most of which have been integrated particularly long in time, and also the palaeomagnetic model PADM2M which covers the past 2Myr. The results show that the Langevin description provides a viable statistical model of the axial dipole variations on time scales longer than about 1kyr. For example, the axial dipole probability distribution and the average reversal rate are successfully predicted. The exception is PADM2M where the stochastic model reversal rate seems too low. The dependence of the drift on the axial dipole moment reveals the nonlinear interactions that establish the dynamo balance. A separate analysis of inductive and diffusive magnetic effects in three dynamo simulations suggests that the classical quadratic quenching of induction predicted by mean-field theory seems at work.},
	author = {Meduri, Domenico G. and Wicht, Johannes},
	date-added = {2020-09-18 13:31:23 +0200},
	date-modified = {2020-09-18 13:31:55 +0200},
	doi = {10.3389/feart.2016.00038},
	issn = {2296-6463},
	journal = {Front. Earth. Sci.},
	pages = {38},
	title = {A Simple Stochastic Model for Dipole Moment Fluctuations in Numerical Dynamo Simulations},
	volume = {4},
	year = {2016},
	Bdsk-Url-1 = {https://www.frontiersin.org/article/10.3389/feart.2016.00038},
	Bdsk-Url-2 = {https://doi.org/10.3389/feart.2016.00038}}

@article{Canet2014,
	abstract = {The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic (QG) eigenmodes: fast, primarily hydrodynamic, inertial modes with period related to the rotation time scale and slow, primarily magnetic, magnetostrophic modes with much longer periods. Here, we investigate the properties of these hydromagnetic quasi-geostrophic modes as a function of non-dimensional parameters controlling the strength of the background magnetic field, the planetary rotation rate, and the amount of magnetic dissipation. We first present analytic solutions that illustrate the essential parameter dependences of the modes and provide a convenient benchmark for our numerical scheme. A comparison between known three-dimensional inertial modes in a sphere and our axially invariant QG modes shows encouraging agreement at low azimuthal wavenumbers, particularly for the slowest modes. The container geometry and background magnetic field structure are found to influence the radial structure of the modes, but not the scaling of their frequency with the control parameters. When the background magnetic field decreases toward the outer boundary in a spherical shell, QG modes tend to be compressed towards the outer boundary. Including magnetic dissipation, we find a continuous transition from diffusionless slow magnetic modes into quasi-free decay magnetic modes. During that transition (which is controlled by the magnitude of the Elsasser number), we find that slow magnetic modes weakly modified by diffusion exhibit a distinctive spiralling planform. When magnetic diffusion is significant (Elsasser number much smaller than unity), we find quasi-free decay slow magnetic modes whose decay time scale is comparable to, or shorter than, their oscillation time scale. Based on our analysis, we expect Mercury to be in a regime where the slow magnetic modes are of quasi-free decay type. Earth and possibly Ganymede, with their larger Elsasser numbers, may possess slow modes that are in the transition regime of weak diffusion, depending on the details of their poorly known internal magnetic fields. Fast QG modes, that are almost unaffected by the background magnetic field, are expected in the cores of all three bodies.},
	author = {E. Canet and C.C. Finlay and A. Fournier},
	date-added = {2020-09-01 11:56:35 +0200},
	date-modified = {2020-09-01 11:57:15 +0200},
	doi = {https://doi.org/10.1016/j.pepi.2013.12.006},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Core dynamics, Planetary magnetic fields, Ganymede, Mercury, Earth},
	pages = {1 - 15},
	title = {Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores},
	volume = {229},
	year = {2014},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920113001970},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2013.12.006}}

@article{Busse2005,
	abstract = {The problem of inertial modes in the solar convection zone is considered. Of particular interest from the point of view of observations are slow, nearly geostrophic modes, for which approximate explicit dispersion relationships are given. Typical properties of these modes are discussed, and their relationship to Rossby waves is clarified. Possible applications to solar phenomena are mentioned.},
	author = {F. H. Busse and K. Zhang and X. Liao},
	date-added = {2020-09-01 11:54:54 +0200},
	date-modified = {2020-09-01 11:55:19 +0200},
	doi = {10.1086/497300},
	journal = {Ap. J.},
	month = {sep},
	number = {2},
	pages = {L171--L174},
	publisher = {{IOP} Publishing},
	title = {On Slow Inertial Waves in the Solar Convection Zone},
	url = {https://doi.org/10.1086%2F497300},
	volume = {631},
	year = 2005,
	Bdsk-Url-1 = {https://doi.org/10.1086%2F497300},
	Bdsk-Url-2 = {https://doi.org/10.1086/497300}}

@article{Zhang2001,
	author = {Zhang, K. and Earnshaw, P. and Liao, X and Busse, F. H., F. H.},
	date-added = {2020-09-01 11:52:27 +0200},
	date-modified = {2020-09-01 11:53:23 +0200},
	doi = {10.1017/S0022112001004049},
	journal = {Journal of Fluid Mechanics},
	pages = {103--119},
	publisher = {Cambridge University Press},
	title = {On inertial waves in a rotating fluid sphere},
	volume = {437},
	year = {2001},
	Bdsk-Url-1 = {https://doi.org/10.1017/S0022112001004049}}

@article{Hide1966,
	abstract = { Free hydromagnetic oscillations of a rotating spherical shell of an incompressible fluid are investigated by means of a simple theoretical model. For each spatial harmonic, rotation gives rise to two distinct modes of oscillation, `magnetic' and `inertial', which propagate with different velocities. As an application of the theory, it is shown that if the strength of the toroidal magnetic field in the Earth's core is 100 Oe, then many of the properties of the observed secular changes, including the slow westward drift, of the main geomagnetic field at the Earth's surface can be accounted for in terms of the interaction of magnetic modes in the core with the Earth's poloidal magnetic field. Concomitant magnetic variations due to inertial modes in the core would, owing to their relatively short periods (several days), fail to penetrate to the surface of the Earth, although the eddy currents induced in the lower mantle by these modes might affect the mechanical coupling between the mantle and the core. },
	author = {Hide, Raymond},
	date-added = {2020-09-01 11:48:37 +0200},
	date-modified = {2020-09-01 11:51:01 +0200},
	doi = {10.1098/rsta.1966.0026},
	journal = {Phil. Trans. Roy. Soc. A},
	number = {1107},
	pages = {615-647},
	title = {Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation},
	volume = {259},
	year = {1966},
	Bdsk-Url-1 = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.1966.0026},
	Bdsk-Url-2 = {https://doi.org/10.1098/rsta.1966.0026}}

@article{Rieutord1997,
	author = {Rieutord, M. and Valdettaro, L.},
	date-added = {2020-09-01 11:46:13 +0200},
	date-modified = {2020-09-01 11:46:44 +0200},
	doi = {10.1017/S0022112097005491},
	journal = {Journal of Fluid Mechanics},
	pages = {77--99},
	publisher = {Cambridge University Press},
	title = {Inertial waves in a rotating spherical shell},
	volume = {341},
	year = {1997},
	Bdsk-Url-1 = {https://doi.org/10.1017/S0022112097005491}}

@incollection{Jones2015,
	abstract = {The Earth's liquid outer core is stirred by thermal and compositional convection. In thermal convection, the buoyancy is due to temperature fluctuations, while in compositional convection, it is produced by light material released at the inner core boundary. Convection in the core is strongly supercritical and is greatly affected by rotation and magnetic field. In this chapter, we focus on the issues of how fast the convective motions are, what is their morphology, and how this relates to the heat transport. Core convection is believed to be a primary source of dynamo action, and so it is responsible for the Earth's magnetic field. We therefore also consider how the morphology of core convection affects the magnetic field generated. In `Introduction to Core Convection,' the basic physical principles of core convection are discussed and how core flow relates to the secular variation of the magnetic field. In Section 8.05.2, the basic equations governing core convection are discussed. The relationship between compressible convection and Boussinesq convection is a key issue here. We also consider whether the core is convecting everywhere or whether some regions may be stably stratified. In Section 8.05.3, high Rayleigh number and nonmagnetic and nonrotating thermal convection and compositional convection are considered, and the possibility of a translating inner core is discussed. Section 8.05.4 describes the effect of rotation on convection. The now well-understood problem of the onset of rapidly rotating convection is reviewed, and techniques and results for strongly nonlinear rotating convection are described. Section 8.05.5 reviews the dynamical effects of a magnetic field on the onset and pattern of convection. It also describes some aspects of convection-driven dynamo models. In Section 8.05.6, the interesting effects of heterogeneous boundary conditions on core convection are considered. This problem is connected with the issue of whether core convection is affected by mantle convection. The final section summarizes the current position and considers the future prospects for expanding our knowledge of core convection.},
	address = {Oxford},
	author = {C.A. Jones},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2020-08-28 14:52:18 +0200},
	date-modified = {2020-08-28 14:52:36 +0200},
	doi = {https://doi.org/10.1016/B978-0-444-53802-4.00141-X},
	edition = {Second Edition},
	editor = {Gerald Schubert},
	isbn = {978-0-444-53803-1},
	keywords = {Core convection, Core dynamics, Earth's core, Geodynamo, Magnetoconvection, Rotating convection},
	pages = {115 - 159},
	publisher = {Elsevier},
	title = {8.05 - Thermal and Compositional Convection in the Outer Core},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B978044453802400141X},
	Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-444-53802-4.00141-X}}

@article{Aubert2020,
	abstract = {{The nature of the force balance that governs the geodynamo is debated. Recent theoretical analyses and numerical simulations support a quasigeotrophic (QG), magneto-Archimedes-Coriolis (MAC) balance in Earth's core, where the Coriolis and pressure forces equilibrate at leading order in amplitude, and where the buoyancy, Lorentz and ageostrophic Coriolis forces equilibrate at the next order. In contrast, earlier theoretical expectations have favoured a magnetostrophic regime where the Lorentz force would reach leading order at the system scale. The dominant driver (buoyant or magnetic) for the general circulation in Earth's core is equally debated. In this study, these questions are explored in the light of the high-quality geomagnetic data recently acquired by satellites and at magnetic ground observatories. The analysis involves inverse geodynamo modelling, a method that uses multivariate statistics extracted from a numerical geodynamo model to infer the state of Earth's core from a geomagnetic field model interpretation of the main field and secular variation data. To test the QG-MAC dynamic hypothesis against the data, the framework is extended in order to explicitly prescribe this force balance into the inverse problem solved at the core surface. The resulting inverse solutions achieve a quantitatively adequate fit to the data while ensuring deviations from the QG-MAC balance (which amount to an inertial driving of the flow) lower than each of the leading forces. The general circulation imaged within the core over the past two decades confirms the existence of a planetary-scale, eccentric, axially columnar gyre that comprises an intense, equatorially symmetric jet at high latitudes in the Pacific hemisphere. The dominant driver of this circulation is shown to be of buoyant nature, through a thermal wind balance with a longitudinally hemispheric buoyancy anomaly distribution. Geomagnetic forecasts initiated with the inverted core states are systematically more accurate against the true interannual geomagnetic field evolution when enforcing the QG-MAC constraint. This force balance is therefore consistent with the geomagnetic data at the large scales of Earth's core that can be imaged by the method.}},
	author = {Aubert, Julien},
	date-added = {2020-08-28 13:50:52 +0200},
	date-modified = {2020-08-28 13:51:05 +0200},
	doi = {10.1093/gji/ggaa007},
	eprint = {https://academic.oup.com/gji/article-pdf/221/1/378/32369192/ggaa007.pdf},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {01},
	number = {1},
	pages = {378-393},
	title = {{Recent geomagnetic variations and the force balance in Earth's core}},
	volume = {221},
	year = {2020},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggaa007}}

@article{Wicht2019,
	author = {Johannes Wicht and Sabrina Sanchez},
	date-added = {2020-08-28 13:38:37 +0200},
	date-modified = {2020-08-28 13:39:06 +0200},
	doi = {10.1080/03091929.2019.1597074},
	eprint = {https://doi.org/10.1080/03091929.2019.1597074},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {1-2},
	pages = {2-50},
	publisher = {Taylor & Francis},
	title = {Advances in geodynamo modelling},
	volume = {113},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1080/03091929.2019.1597074}}

@incollection{Olson2015,
	abstract = {This is an account of the dynamics at the heart of the Earth, a comprehensive survey of the physical and chemical processes that have shaped our planet's partly liquid, partly solid, metallic core. In emphasizing the dynamics of the core, this volume is unique in geophysics. There has been more than a century of investigations into the structure and composition of the core, whereas the dynamics of the core has received widespread scientific attention only in the past few decades. Fueled by advances in related disciplines, including seismic and magnetic imaging of the core and high-pressure experiments on core materials, the past two decades have witnessed an explosion of core dynamics research. Progress includes self-consistent numerical dynamo models, innovative fluid dynamics experiments, new concepts about the core composition and its evolution, and the manner in which the core interacts with other parts of the Earth. The improved observational constraints, in conjunction with the more powerful modeling tools, have shed new light on how the core has evolved, what drives the geodynamo, and other long-standing Earth science problems. These advances, along with the new questions they have raised, are the subjects of this volume. Nineteen experts review our current understanding of the energetics and structure of the core; the global circulation within the molten outer core; the dynamics of the solid inner core; the convection, turbulence, and rotational instabilities in the outer core; geodynamo theory; numerical geodynamo models; geomagnetic polarity reversals; laboratory experiments on the core; and the interactions between the core and the mantle.},
	address = {Oxford},
	author = {P. Olson},
	booktitle = {{Treatise on Geophysics (Second Edition)}},
	date-added = {2020-08-28 13:19:51 +0200},
	date-modified = {2020-08-28 13:20:11 +0200},
	doi = {https://doi.org/10.1016/B978-0-444-53802-4.00137-8},
	edition = {Second Edition},
	editor = {Gerald Schubert},
	isbn = {978-0-444-53803-1},
	keywords = {Convection, Core dynamics, Core--mantle boundary, Core--mantle interactions, Dynamo theory, Earth's core, Earth's mantle, Energetics, Fluid experiments, Geomagnetic field, Inner core boundary, Magnetohydrodynamics, Numerical models, Paleomagnetic field, Precession, Rotation, Turbulence},
	pages = {1 - 25},
	publisher = {Elsevier},
	title = {8.01 - Core Dynamics: An Introduction and Overview},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B9780444538024001378},
	Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-444-53802-4.00137-8}}

@book{Greenspan1968,
	author = {Greenspan, H. P.},
	date-added = {2019-12-16 16:20:22 +0100},
	date-modified = {2019-12-16 16:20:22 +0100},
	publisher = {Breukelen Press},
	title = {The theory of rotating fluids},
	year = {1968}}

@article{Schwaiger2019,
	abstract = {{Dynamo action in the Earth's outer core is expected to be controlled by a balance between pressure, Coriolis, buoyancy and Lorentz forces, with marginal contributions from inertia and viscous forces. Current numerical simulations of the geodynamo, however, operate at much larger inertia and viscosity because of computational limitations. This casts some doubt on the physical relevance of these models.Our work aims at finding dynamo models in a moderate computational regime which reproduce the leading-order force balance of the Earth. By performing a systematic parameter space survey with Ekman numbers in the range 10−6 ≤ E ≤ 10−4, we study the variations of the force balance when changing the forcing (Rayleigh number, Ra) and the ratio between viscous and magnetic diffusivities (magnetic Prandtl number, Pm). For dipole-dominated dynamos, we observe that the force balance is structurally robust throughout the investigated parameter space, exhibiting a quasi-geostrophic (QG) balance (balance between Coriolis and pressure forces) at zeroth order, followed by a first-order Magneto-Archimedean-Coriolis (MAC) balance between the ageostrophic Coriolis, buoyancy and Lorentz forces. At second order, this balance is disturbed by contributions from inertia and viscous forces. Dynamos with a different sequence of the forces, where inertia and/or viscosity replace the Lorentz force in the first-order force balance, can only be found close to the onset of dynamo action and in the multipolar regime. To assess the agreement of the model force balance with that expected in the Earth's core, we introduce a parameter quantifying the distance between the first- and second-order forces. Analysis of this parameter shows that the strongest-field dynamos can be obtained close to the onset of convection (Ra close to critical) and in situations of reduced magnetic diffusivity (high Pm). Decreasing the Ekman number gradually expands this regime towards higher supercriticalities and lower values of Pm.Our study illustrates that most classical numerical dynamos are controlled by a QG-MAC balance, while cases where viscosity and inertia play a dominant role are the exception rather than the norm.}},
	author = {Schwaiger, T and Gastine, T and Aubert, J},
	date-added = {2019-09-20 15:43:27 +0200},
	date-modified = {2019-09-20 15:44:24 +0200},
	doi = {10.1093/gji/ggz192},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {04},
	number = {S1},
	pages = {S101-S114},
	title = {{Force balance in numerical geodynamo simulations: a systematic study}},
	volume = {219},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggz192}}

@article{Aubert2019b,
	abstract = {{The geodynamo features a broad separation between the large scale at which Earth's magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer core. Here, the properties of this scale separation are analysed using high-resolution numerical simulations that approach closer to Earth's core conditions than earlier models. The new simulations are obtained by increasing the resolution and gradually relaxing the hyperdiffusive approximation of previously published low-resolution cases. This upsizing process does not perturb the previously obtained large-scale, leading-order quasi-geostrophic (QG) and first-order magneto-Archimedes-Coriolis (MAC) force balances. As a result, upsizing causes only weak transients typically lasting a fraction of a convective overturn time, thereby demonstrating the efficiency of this approach to reach extreme conditions at reduced computational cost. As Earth's core conditions are approached in the upsized simulations, Ohmic losses dissipate up to 97 per cent of the injected convective power. Kinetic energy spectra feature a gradually broadening self-similar, power-law spectral range extending over more than a decade in length scale. In this range, the spectral energy density profile of vorticity is shown to be approximately flat between the large scale at which the magnetic field draws its energy from convection through the QG-MAC force balance and the small scale at which this energy is dissipated. The resulting velocity and density anomaly planforms in the physical space consist in large-scale columnar sheets and plumes, respectively, co-existing with small-scale vorticity filaments and density anomaly ramifications. In contrast, magnetic field planforms keep their large-scale structure after upsizing. The small-scale vorticity filaments are aligned with the large-scale magnetic field lines, thereby minimizing the dynamical influence of the Lorentz force. The diagnostic outputs of the upsized simulations are more consistent with the asymptotic QG-MAC theory than those of the low-resolution cases that they originate from, but still feature small residual deviations that may call for further theoretical refinements to account for the structuring constraints of the magnetic field on the flow.}},
	author = {Aubert, Julien},
	date-added = {2019-09-20 15:42:32 +0200},
	date-modified = {2019-09-20 15:44:36 +0200},
	doi = {10.1093/gji/ggz232},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {05},
	number = {S1},
	pages = {S137-S151},
	title = {{Approaching Earth's core conditions in high-resolution geodynamo simulations}},
	volume = {219},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggz232}}

@article{Gillet2019,
	abstract = {{We make use of recent geodynamo simulations to propose a reduced stochastic model of the dynamics at the surface of Earth's core. On decadal and longer periods, this model replicates the most energetic eigen directions of the geodynamo computation. Towards shorter timescales, it proposes a compensation for weaknesses of these simulations. This model furthermore accounts for the signature, in the geomagnetic secular variation, of errors of representativeness associated with unresolved processes. We incorporate the reduced stochastic model into a geomagnetic data assimilation algorithm---an augmented state ensemble Kalman filter---and apply it to re-analyse magnetic field changes over the period 1880--2015. Errors of representativeness appear to be responsible for an important fraction of the observed changes in the secular variation, as it is the case in the dynamo simulation.Recovered core surface motions are primarily symmetric with respect to the equator. We observe the persistence of the eccentric westward gyre over the whole studied era and vortices that partly follow isocontours of the radial magnetic field at the core surface. Our flow models provide a good fit to decadal changes in the length-of-day and predict its interannual variations over the period 1940--2005. The largest core flow acceleration patterns are found in an equatorial belt below 10$\,^{\circ}$ in latitude and are associated with non-axisymmetric features. No systematic longitudinal drift of acceleration patterns is found, even over the past decades where satellite data are available. The acceleration of the high-latitude westward jet in the Pacific hemisphere is, during the satellite era, a factor 5 smaller than previously reported and its structure shows some evidence for equatorial asymmetry. The era of continuous satellite records provides enhanced contrast on the rapid core flow variations. The proposed assimilation algorithm offers the prospect of evaluating Earth-likeness of geodynamo simulations.}},
	author = {Gillet, N and Huder, L and Aubert, J},
	date-added = {2019-09-20 15:41:47 +0200},
	date-modified = {2019-09-20 15:42:24 +0200},
	doi = {10.1093/gji/ggz313},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {07},
	number = {1},
	pages = {522-539},
	title = {{A reduced stochastic model of core surface dynamics based on geodynamo simulations}},
	volume = {219},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggz313}}

@inbook{Bizouard2009,
	abstract = {The Earth Orientation Center of the IERS, located at Paris Observatory, SYRTE, has the task to provide to the scientific community the international reference time series for the Earth Orientation Parameters (EOP), referred as ''IERS C04'' (Combined 04), resulting from a combination of operational EOP series, each of them associated with a given geodetic technique. The procedure developed to derive the C04 solution was recently upgraded for several reasons: first we have implemented the new IAU2000 conventions; secondly it has been necessary to re-align the solution to improve its consistency with respect to the ITRF. Due to the separate determination of both celestial and terrestrial reference frames and EOP, there has been a slow degradation of the overall consistency and discrepancies at the level of 300 micro-arc-seconds were existing between the current IERS C04 and the ITRF realization. We have taken this opportunity to upgrade the numerical combination procedure; improvements concern in particular routines, tables dimensions, generalized double precisions. Using the combined polar motion solution associated with the newly release International Terrestrial Reference Frame 2005 (ITRF 2005), we produce a better solution including estimates of the errors of combined values. Individual EOP series have been reprocessed since 1984. Pole coordinates are now fully consistent with ITRF. The nutation offsets and UT1 are made consistent with the International Celestial Reference Frame (ICRF). The new C04 solution, referred as 05 C04, updated two times per week became the offcial C04 solution since October 2007.},
	address = {Berlin, Heidelberg},
	author = {Bizouard, Christian and Gambis, Daniel},
	booktitle = {Geodetic Reference Frames: IAG Symposium Munich, Germany, 9-14 October 2006},
	date-added = {2019-06-11 12:20:07 +0200},
	date-modified = {2019-06-11 12:20:07 +0200},
	doi = {10.1007/978-3-642-00860-3_41},
	editor = {Drewes, Hermann},
	isbn = {978-3-642-00860-3},
	pages = {265--270},
	publisher = {Springer Berlin Heidelberg},
	title = {The Combined Solution C04 for Earth Orientation Parameters Consistent with International Terrestrial Reference Frame 2005},
	url = {https://doi.org/10.1007/978-3-642-00860-3_41},
	year = {2009},
	Bdsk-Url-1 = {https://doi.org/10.1007/978-3-642-00860-3_41}}

@article{Deguen2018,
	abstract = {{The hemispherical asymmetry of the inner core has been interpreted as resulting from a high-viscosity mode of inner core convection, consisting in a translation of the inner core. A thermally driven translation, as originally proposed, is unlikely if the currently favoured high values of the thermal conductivity of iron at core conditions are correct. We consider here the possibility that inner core translation results from an unstable compositional gradient, which would develop either because the light elements present in the core become increasingly incompatible as the inner core grows, or because of a possibly positive feedback of the development of the F-layer on inner core convection. Though the magnitude of the destabilizing effect of the compositional field is predicted to be similar to or smaller than the stabilizing effect of the thermal field, the huge difference between thermal and chemical diffusivities implies that double-diffusive instabilities can still arise even if the net buoyancy increases upward. Using linear stability analysis and numerical simulations, we demonstrate that a translation mode can indeed exist if the compositional field is destabilizing, even if the temperature profile is subadiabatic, and irrespectively of the relative magnitudes of the composition and potential temperature gradients. The existence of this double diffusive mode of translation requires that the following conditions are met: (i) the compositional profile within the inner core is destabilizing, and remains so for a duration longer than the destabilization timescale (on the order of 200 Myr, but strongly dependent on the magnitude of the initial perturbation); and (ii) the inner core viscosity is sufficiently large, the required value being a strongly increasing function of the inner core size (e.g. 1017 Pa s when the inner core was 200 km in radius, and ≃3 × 1021 Pa s at the current inner core size). If these conditions are met, the predicted inner core translation rate is found to be similar to the inner core growth rate, which is more consistent with inferences from the geomagnetic field morphology and secular variation than the higher translation rate predicted for a thermally driven translation.}},
	author = {Deguen, R and Alboussi{\`e}re, T and Labrosse, S},
	date-added = {2019-06-06 13:52:40 +0200},
	date-modified = {2019-06-06 13:53:01 +0200},
	doi = {10.1093/gji/ggy120},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {03},
	number = {1},
	pages = {88-107},
	title = {{Double-diffusive translation of Earth's inner core}},
	volume = {214},
	year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggy120}}

@article{Beggan2010,
	abstract = {Over the past ten years satellite measurements in combination with data from ground-based observatories have allowed very detailed models of the secular variation (SV) of the Earth's magnetic field to be constructed. However, forecasting the change of the main field still remains a challenge, primarily because the core processes controlling SV are not sufficiently well understood. Hence, most forecasts do not appeal to any physical modelling constraints but use, for example, polynomial extrapolation from previous measurements. We attempt to apply a physical model to forecast the average SV during 2010--2015 by developing a core flow model. This steady flow model, derived from SV data during 2004.5 to 2009.5, generates a set of Gauss SV coefficients which are used to advect the large scale magnetic field forwards in time. Although this model has not been submitted as a candidate for IGRF-11, we present our SV prediction model and compare it to other candidate IGRF-11 SV models. In addition, we examine the use of the Ensemble Kalman filter to optimally assimilate field models derived from (1) forecast methods and (2) noisy data measurements. Such a scenario might conceivably arise if high quality satellite data with global coverage are not available for a significant period of time. We show that the overall misfit of the assimilated model to the actual field can be lower than the individual misfits of the input models, provided the uncertainties of each model are reasonably well known.},
	author = {Beggan, Ciar{\'a}n and Whaler, Kathy},
	date-added = {2019-06-04 15:37:20 +0200},
	date-modified = {2019-06-04 15:37:26 +0200},
	day = {31},
	doi = {10.5047/eps.2010.07.004},
	issn = {1880-5981},
	journal = {Earth, Planets and Space},
	month = {Dec},
	number = {10},
	pages = {11},
	title = {Forecasting secular variation using core flows},
	volume = {62},
	year = {2010},
	Bdsk-Url-1 = {https://doi.org/10.5047/eps.2010.07.004}}

@article{Whaler2015,
	abstract = {{Improving forecasts of the temporal and spatial changes of the Earth's
   main magnetic field over periods of less than 5 years has important
   scientific and economic benefits. Various methods for forecasting the
   rate of change, or secular variation, have been tried over the past few
   decades, ranging from the extrapolation of trends in ground observatory
   measurements to computational geodynamo modeling with data assimilation
   from historical magnetic field models. We examine the utility of an
   intermediate approach, using temporally varying core surface flow models
   derived from relatively short periods of magnetic field data to produce,
   by advection, secular variation estimates valid for the Earth's surface.
   We describe a new method to compute a core flow changing linearly with
   time from magnetic secular variation and acceleration data. We invert a
   combination of data from the CHAMP satellite mission and ground
   observatories over the period 2001.0 to 2010.0 for a series of such
   models. We assess their ability to forecast magnetic field changes by
   comparing them to CHAOS-4, a state-of-the-art model using data from 1997
   to 2014.5. We show that the magnetic field predictions tend to have a
   lower root-mean-square difference from CHAOS-4 than the International
   Geomagnetic Reference Field or World Magnetic Map series of secular
   variation models.}},
	author = {Whaler, K. A. and Beggan, C. D.},
	date-added = {2019-06-04 15:33:34 +0200},
	date-modified = {2019-06-04 15:33:34 +0200},
	doi = {{10.1002/2014JB011697}},
	eissn = {{2169-9356}},
	issn = {{2169-9313}},
	journal = {J. Geophys. Res.},
	month = {{MAR}},
	number = {{3}},
	pages = {{1400-1414}},
	title = {{Derivation and use of core surface flows for forecasting secular variation}},
	unique-id = {{ISI:000353160200002}},
	volume = {{120}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/2014JB011697%7D}}

@article{Evensen2003,
	author = {Evensen, G.},
	date-added = {2019-05-24 11:20:18 +0200},
	date-modified = {2019-05-24 11:20:18 +0200},
	doi = {10.1007/s10236-003-0036-9},
	journal = {Ocean Dyn.},
	pages = {343-367},
	title = {{The Ensemble Kalman Filter: theoretical formulation And Practical Implementation}},
	volume = {53},
	year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10236-003-0036-9}}

@phdthesis{Dormy1997,
	author = {Dormy, E.},
	date-added = {2019-05-23 15:01:19 +0200},
	date-modified = {2019-12-17 14:45:49 +0100},
	note = {http://www.math.ens.fr/$\sim$dormy/Publications/doubleTh.html, see also Errata},
	school = {Institut de Physique du Globe de Paris},
	title = {Mod\'elisation num{\'e}rique de la dynamo terrestre},
	year = {1997}}

@article{Kloss2019,
	abstract = {{We present a new model of time-dependent flow at low latitudes in the Earth's core between 2000 and 2018 derived from magnetic field measurements made on board the Swarm and CHAMP satellites and at ground magnetic observatories. The model, called CoreFlo-LL.1, consists of a steady background flow without imposed symmetry plus a time-dependent flow that is dominated by geostrophic and quasi-geostrophic components but also allows weak departures from equatorial symmetry. Core flow mode amplitudes are determined at 4-month intervals by a robust least-squares fit to ground and satellite secular variation data. The l1 norm of the square root of geostrophic and inertial mode enstrophies, and the l2 norm of the flow acceleration, are minimized during the inversion procedure. We find that the equatorial region beneath the core--mantle boundary is a place of vigorous, localized, fluid motions; time-dependent flow focused at low latitudes close to the core surface is able to reproduce rapid field variations observed at non-polar latitudes at and above Earth's surface. Magnetic field acceleration pulses are produced by alternating bursts of non-zonal azimuthal flow acceleration in this region. Such bursts are prominent in the longitudinal sectors from 80--130$\,^{\circ}$E and 60--100$\,^{\circ}$W throughout the period studied, but are also evident under the equatorial Pacific from 130$\,^{\circ}$E to 150$\,^{\circ}$W after 2012. We find a distinctive interannual alternation in the sign of the non-zonal azimuthal flow acceleration at some locations involving a rapid crossover between flow acceleration convergence and divergence. Such acceleration sign changes can occur within a year or less and, when the structures involved are of large spatial extent, they can give rise to geomagnetic jerks at the Earth's surface. For example, in 2014, we find a change in the sign of the non-zonal azimuthal flow acceleration under the equatorial Pacific as a region of flow acceleration divergence near 130$\,^{\circ}$E changes to a region of flow acceleration convergence. This occurs at a maximum in the amplitude of the time-varying azimuthal flow under the equatorial Pacific and corresponds to a geomagnetic jerk at the Earth's surface.}},
	author = {Kloss, Clemens and Finlay, Christopher C},
	date-added = {2019-05-17 14:32:04 +0200},
	date-modified = {2019-05-17 14:32:15 +0200},
	doi = {10.1093/gji/ggy545},
	eprint = {http://oup.prod.sis.lan/gji/article-pdf/217/1/140/27662198/ggy545.pdf},
	issn = {0956-540X},
	journal = {Geoph. J. Int.},
	month = {01},
	number = {1},
	pages = {140-168},
	title = {{Time-dependent low-latitude core flow and geomagnetic field acceleration pulses}},
	volume = {217},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggy545}}

@article{Barrois2017,
	abstract = {{We invert for motions at the surface of Earth's core under spatial and temporal constraints that depart from the mathematical smoothings usually employed to ensure spectral convergence of the flow solutions. Our spatial constraints are derived from geodynamo simulations. The model is advected in time using stochastic differential equations coherent with the occurrence of geomagnetic jerks. Together with a Kalman filter, these spatial and temporal constraints enable the estimation of core flows as a function of length and time-scales. From synthetic experiments, we find it crucial to account for subgrid errors to obtain an unbiased reconstruction. This is achieved through an augmented state approach. We show that a significant contribution from diffusion to the geomagnetic secular variation should be considered even on short periods, because diffusion is dynamically related to the rapidly changing flow below the core surface. Our method, applied to geophysical observations over the period 1950--2015, gives access to reasonable solutions in terms of misfit to the data. We highlight an important signature of diffusion in the Eastern equatorial area, where the eccentric westward gyre reaches low latitudes, in relation with important up/downwellings. Our results also confirm that the dipole decay, observed over the past decades, is primarily driven by advection processes. Our method allows us to provide probability densities for forecasts of the core flow and the secular variation.}},
	author = {Barrois, O. and Gillet, N. and Aubert, J.},
	date-added = {2019-05-17 14:26:53 +0200},
	date-modified = {2019-05-17 14:27:06 +0200},
	doi = {10.1093/gji/ggx280},
	eprint = {http://oup.prod.sis.lan/gji/article-pdf/211/1/50/19443412/ggx280.pdf},
	issn = {0956-540X},
	journal = {Geoph. J. Int.},
	month = {07},
	number = {1},
	pages = {50-68},
	title = {{Contributions to the geomagnetic secular variation from a reanalysis of core surface dynamics}},
	volume = {211},
	year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggx280}}

@article{Baerenzung2018,
	abstract = {Abstract We propose a reduced dynamical system describing the coupled evolution of fluid flow and magnetic field at the top of the Earth's core between the years 1900 and 2014. The flow evolution is modeled with a first-order autoregressive process, while the magnetic field obeys the classical frozen flux equation. An ensemble Kalman filter algorithm serves to constrain the dynamics with the geomagnetic field and its secular variation given by the COV-OBS.x1 model. Using a large ensemble with 40,000 members provides meaningful statistics including reliable error estimates. The model highlights two distinct flow scales. Slowly varying large-scale elements include the already documented eccentric gyre. Localized short-lived structures include distinctly ageostophic features like the high-latitude polar jet on the Northern Hemisphere. Comparisons with independent observations of the length-of-day variations not only validate the flow estimates but also suggest an acceleration of the geostrophic flows over the last century. Hindcasting tests show that our model outperforms simpler predictions bases (linear extrapolation and stationary flow). The predictability limit, of about 2,000 years for the magnetic dipole component, is mostly determined by the random fast varying dynamics of the flow and much less by the geomagnetic data quality or lack of small-scale information.},
	author = {B{\"a}renzung, Julien and Holschneider, Matthias and Wicht, Johannes and Sanchez, Sabrina and Lesur, Vincent},
	date-added = {2019-05-17 14:23:46 +0200},
	date-modified = {2019-05-17 14:24:01 +0200},
	doi = {10.1029/2017JB015115},
	eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2017JB015115},
	journal = {{J. Geophys. Res.}},
	keywords = {core flow, assimilation, prediction, length of day},
	number = {6},
	pages = {4539-4560},
	title = {Modeling and Predicting the Short-Term Evolution of the Geomagnetic Field},
	volume = {123},
	year = {2018},
	Bdsk-Url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2017JB015115},
	Bdsk-Url-2 = {https://doi.org/10.1029/2017JB015115}}

@article{:aa,
	date-added = {2019-05-17 14:23:32 +0200},
	date-modified = {2019-05-17 14:23:32 +0200},
	Bdsk-File-1 = {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}}

@article{Amit2013,
	abstract = {{Core flows inverted from time-dependent geomagnetic field models image the geodynamo at the top of its generation region, the Earth's outer core. Physical assumptions incorporated in these inversions affect the resulting flows. Based on rapid rotation dominance, two assumptions similar in form yet different in essence have been proposed: tangential geostrophy (TG, LeMou{\"e}l 1984) and columnar flow (CF, Amit \\&amp; Olson 2004). We recall that CF is theoretically consistent with the quasi-geostrophy (QG) theory for an incompressible fluid with spherical solid boundaries whereas TG is not. As such, we highlight the importance of applying the CF assumption when inverting geomagnetic data for interior core (columnar) flows that can be used in kinematic dynamo and thermal convection models in the Boussinesq approximation. Next we evaluate the non-uniqueness associated with CF flows. The areas of ambiguous patches at the core surface where invisible TG or CF flows reside are roughly comparable. The spatial distribution of ambiguous patches for both TG and CF is quite asymmetric about the equator, so assuming equatorial symmetry is expected to reduce the non-uniqueness significantly. In fact, for assumed equatorial symmetry, the only possible non-unique flows will be those along hypothetical ζ-contours in the opposite hemispheres that their equatorial plane projections are parallel. TG flows exhibit a strong Atlantic/Pacific hemispheric dichotomy and a well-defined eccentric gyre whereas in CF flows the dichotomy between these two hemispheres is weaker and the gyre is less clear suggesting that the eccentric gyre might not conserve mass. Both TG and CF upwelling/downwelling patterns are strongly localized in the equatorial region. In addition, in both cases upwelling/downwelling is correlated with equatorward/poleward flow respectively, as expected for QG convection. CF upwelling is more intense than TG upwelling but the magnitude ratio is smaller than the factor 2 distinguishing the analytical expressions of the two assumptions. This smaller magnitude ratio is due to the fact that presently observed geomagnetic secular variation features are mostly explained by magnetic field advection by toroidal core flow in the frozen-flux approximation. Robust upwelling features below India/Indonesia may be viewed as geomagnetic evidence for whole core convection.}},
	author = {Amit, Hagay and Pais, Maria Alexandra},
	date-added = {2019-05-17 13:57:27 +0200},
	date-modified = {2019-05-17 13:57:43 +0200},
	doi = {10.1093/gji/ggt077},
	eprint = {http://oup.prod.sis.lan/gji/article-pdf/194/1/145/9806043/ggt077.pdf},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {04},
	number = {1},
	pages = {145-157},
	title = {{Differences between tangential geostrophy and columnar flow}},
	volume = {194},
	year = {2013},
	Bdsk-Url-1 = {https://doi.org/10.1093/gji/ggt077}}

@article{Pais2004,
	abstract = {The task of finding a flow at the top of the core that fits geomagnetic observations at the Earth's surface is an underdetermined problem. Weighted regularized least squares together with the tangential geostrophy hypothesis strongly constrain the flow, inhibiting both medium- to small-scale flow features from emerging and low-latitude currents from crossing the geographic equator. In this study, we solve the inverse problem in the frozen flux approximation, using a weak regularization and alleviating the tangential geostrophy constraint. Two classes of solutions are found (I and II), both fitting the data within the errors but nonetheless showing very distinct features. Using, as a further criterion, the ability of the flow solutions to reproduce the decade variations of the length of day does not allow us, in general, to give a clear preference to one class over another. For typical flows from the whole set of solutions described above, we identify the regions on the core-mantle boundary (CMB) where tangential geostrophy is violated, and we quantify those deviations. Assuming that they are due to Lorentz forces acting on the fluid, we compute preliminary charts of electrical density currents (J) on the CMB, consistent with the frozen flux and insulating mantle hypotheses. The most pronounced features in these charts are concentrated over the hemisphere roughly centered beneath the Atlantic Ocean. In light of thermodynamical arguments, class II flows seem closer to real surface core flows. We compute an upper limit JRMS ≈ 0.4 A/m2 for geomagnetically ``visible'' density currents related to these flows.},
	author = {Pais, M. A. and Oliveira, O. and Nogueira, F.},
	date-added = {2019-05-17 13:48:17 +0200},
	date-modified = {2019-05-17 13:48:31 +0200},
	doi = {10.1029/2004JB003012},
	eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004JB003012},
	journal = {{J. Geophys. Res.}},
	keywords = {CMB flows, tangential geostrophy, CMB electrical density currents},
	number = {B8},
	title = {Nonuniqueness of inverted core-mantle boundary flows and deviations from tangential geostrophy},
	volume = {109},
	year = {2004},
	Bdsk-Url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2004JB003012},
	Bdsk-Url-2 = {https://doi.org/10.1029/2004JB003012}}

@article{LeMouel1985,
	abstract = {Motions at the top of the core which generate the observed Secular Variation (S.V.) field are computed. To reduce the well known ambiguity of the solution, two constraints are added: the flow is a large scale one and is geostrophic. The computed flow then has a very simple geometry; its polo{\"\i}dal part is roughly axisymmetrical with respect to an equatorial diameter. This geometry is almost unchanged from 1970 to 1980 while the intensity of the velocity is nearly doubled.},
	author = {Le Mou{\"e}l, J.-L. and Gire, C. and Madden, T.},
	date-added = {2019-05-17 13:38:56 +0200},
	date-modified = {2019-09-27 23:20:50 +0200},
	doi = {https://doi.org/10.1016/0031-9201(85)90140-2},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	note = {Special Issue Irregularities in the Secular Variation and Geodynamic Implications},
	number = {4},
	pages = {270 - 287},
	title = {Motions at core surface in the geostrophic approximation},
	volume = {39},
	year = {1985},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0031920185901402},
	Bdsk-Url-2 = {https://doi.org/10.1016/0031-9201(85)90140-2}}

@article{Aubert2019,
	abstract = {Geomagnetic jerks are abrupt changes in the second time derivative---the secular acceleration---of Earth's magnetic field that punctuate ground observatory records. As their dynamical origin has not yet been established, they represent a major obstacle to the prediction of geomagnetic field behaviour for years to decades ahead. Recent jerks have been linked to short-lived, temporally alternating and equatorially localized pulses of secular acceleration observed in satellite data, associated with rapidly alternating flows at Earth's core surface. Here we show that these signatures can be reproduced in numerical simulations of the geodynamo that realistically account for the interaction between slow core convection and rapid hydromagnetic waves. In these simulations, jerks are caused by the arrival of localized Alfv{\'e}n wave packets radiated from sudden buoyancy releases inside the core. As they reach the core surface, the waves focus their energy towards the equatorial plane and along lines of strong magnetic flux, creating sharp interannual changes in core flow and producing geomagnetic jerks through the induced variations in magnetic field acceleration. The ability to numerically reproduce jerks offers a new way to probe the physical properties of Earth's deep interior.},
	author = {Aubert, Julien and Finlay, Christopher C.},
	da = {2019/05/01},
	date-added = {2019-05-17 11:22:31 +0200},
	date-modified = {2019-05-17 14:09:06 +0200},
	doi = {10.1038/s41561-019-0355-1},
	id = {Aubert2019},
	isbn = {1752-0908},
	journal = {Nature Geosci.},
	number = {5},
	pages = {393--398},
	title = {{Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth's core surface}},
	ty = {JOUR},
	volume = {12},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1038/s41561-019-0355-1}}

@article{Marti2014,
	author = {Marti, P. and Schaeffer, N. and Hollerbach, R. and C{\'e}bron, D. and Nore, C. and Luddens, F. and Guermond, J.-L. and Aubert, J. and Takehiro, S. and Sasaki, Y. and Hayashi, Y.-Y. and Simitev, R. and Busse, F. and Vantieghem, S. and Jackson, A.},
	date-added = {2019-01-28 16:09:36 +0100},
	date-modified = {2019-01-28 16:09:36 +0100},
	doi = {10.1093/gji/ggt518},
	journal = {Geophys. J. Int.},
	number = {1},
	pages = {119-134},
	title = {Full sphere hydrodynamic and dynamo benchmarks},
	volume = {197},
	year = {2014},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggt518},
	Bdsk-Url-2 = {https://dx.doi.org/10.1093/gji/ggt518}}

@article{Schaeffer2005,
	author = {Schaeffer, N. and Cardin, P.},
	date-added = {2019-01-09 15:15:29 +0100},
	date-modified = {2019-01-09 15:15:47 +0100},
	doi = {10.5194/npg-12-947-2005},
	journal = {Nonlin. Processes Geophys.},
	number = {6},
	pages = {947--953},
	title = {Rossby-wave turbulence in a rapidly rotating sphere},
	volume = {12},
	year = {2005},
	Bdsk-Url-1 = {https://www.nonlin-processes-geophys.net/12/947/2005/},
	Bdsk-Url-2 = {https://doi.org/10.5194/npg-12-947-2005}}

@article{Guervilly2019,
	author = {Guervilly, C. and Cardin, P. and Schaeffer, N.},
	date-added = {2018-12-12 17:54:38 +0100},
	date-modified = {2018-12-12 17:57:00 +0100},
	note = {arxiv preprint 1810.09553 available at https://arxiv.org/abs/1810.09553},
	title = {Convective Lengthscale in Planetary Cores},
	year = {2019}}

@incollection{Tobias2012,
	author = {Tobias, S.M. and Cattaneo, F. and Boldyrev, S.},
	booktitle = {Ten Chapters in Turbulence},
	date-added = {2018-12-12 11:28:37 +0100},
	date-modified = {2018-12-13 16:44:56 +0100},
	doi = {10.1017/CBO9781139032810.010},
	editor = {Davidson, Peter A. and Kaneda, Yukio and Sreenivasan, Katepalli R.},
	pages = {351--404},
	place = {Cambridge},
	publisher = {Cambridge University Press},
	title = {{MHD} Dynamos and Turbulence},
	year = {2012},
	Bdsk-Url-1 = {https://doi.org/10.1017/CBO9781139032810.010}}

@article{Calkins2018,
	abstract = {The asymptotic theory of rapidly rotating, convection-driven dynamos in a plane layer is discussed. A key characteristic of these quasi-geostrophic dynamos is that the Lorentz force is comparable in magnitude to the ageostrophic component of the Coriolis force, rather than the leading order component that yields geostrophy. This characteristic is consistent with both observations of planetary dynamos and numerical dynamo investigations, where the traditional Elssasser number, ΛT=O(1). Thus, while numerical dynamo simulations currently cannot access the strongly turbulent flows that are thought to be characteristic of planetary interiors, it is argued that they are in the appropriate geostrophically balanced regime provided that inertial and viscous forces are both small relative to the leading order Coriolis force. Four distinct quasi-geostrophic dynamo regimes are discussed, with each regime characterized by a unique magnetic to kinetic energy density ratio and differing dynamics. The axial torque due to the Lorentz force is shown to be asymptotically small for such quasi-geostrophic dynamos, suggesting that `Taylor's constraint' represents an ambiguous measure of the primary force balance in a rapidly rotating dynamo.},
	author = {Michael A. Calkins},
	date-added = {2018-12-12 10:44:03 +0100},
	date-modified = {2018-12-12 10:44:36 +0100},
	doi = {https://doi.org/10.1016/j.pepi.2017.05.001},
	issn = {0031-9201},
	journal = {Phys. Earth. Planet. Int.},
	pages = {182 - 189},
	title = {Quasi-geostrophic dynamo theory},
	volume = {276},
	year = {2018},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S003192011630317X},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2017.05.001}}

@article{Aurnou2017,
	author = {J. M. Aurnou and E. M. King},
	date-added = {2018-12-11 10:37:03 +0100},
	date-modified = {2018-12-11 10:37:18 +0100},
	doi = {10.1098/rspa.2016.0731},
	journal = {Proc. Roy. Soc. A},
	number = {2199},
	pages = {20160731},
	title = {The cross-over to magnetostrophic convection in planetary dynamo systems},
	volume = {473},
	year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1098/rspa.2016.0731}}

@article{Sheyko2018,
	abstract = {The mechanism by which the Earth's magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Here we present results of a suite of self-consistent spherical shell computations with ultra-low viscosities that replicate this mechanism, but using diffusivities of momentum and magnetic field that are notably dissimilar from one another. This leads to significant scale separation between magnetic and velocity fields, the latter being dominated by small scales. We show a zeroth order balance between the azimuthally-averaged parts of the Coriolis and Lorentz forces at large scales, which occurs when the diffusivities of magnetic field and momentum differ so much, as in our model. Outside boundary layers, viscous forces have a magnitude that is about one thousandth of the Lorentz force. In this dynamo dissipation is almost exclusively Ohmic, as in the Earth, with convection inside the so-called tangent cylinder playing a crucial role; it is also in the ``strong field''regime, with significantly more magnetic energy than kinetic energy (as in the Earth). We finally show a robust empirical scaling law between magnetic dissipation and magnetic energy.},
	author = {Sheyko, Andrey and Finlay, Christopher and Favre, Jean and Jackson, Andrew},
	date-added = {2018-11-28 15:57:10 +0100},
	date-modified = {2018-11-28 15:57:55 +0100},
	doi = {10.1038/s41598-018-30864-1},
	journal = {Sci. Rep.},
	number = {1},
	pages = {12566},
	title = {Scale separated low viscosity dynamos and dissipation within the Earth's core},
	volume = {8},
	year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1038/s41598-018-30864-1}}

@article{Aubert2018,
	author = {Aubert, Julien},
	date-added = {2018-11-28 15:42:05 +0100},
	date-modified = {2018-11-28 15:42:05 +0100},
	doi = {10.1093/gji/ggy161},
	journal = {Geophys. J. Int.},
	number = {1},
	pages = {531-547},
	title = {Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo},
	volume = {214},
	year = {2018},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggy161}}

@incollection{Jault2015treatise,
	abstract = {Abstract This chapter focuses on time-dependent fluid motions in the core interior, which can be constrained by observations of Earth's magnetic field, on timescales that are short compared to the magnetic diffusion time. This dynamics is strongly influenced by Earth's rapid rotation, which rigidifies the motions in the direction parallel to the Earth's rotation axis. This property accounts for the significance of the core--mantle topography. In addition, the stiffening of the fluid in the direction parallel to the rotation axis gives rise to a magnetic diffusion layer attached to the core--mantle boundary, which would otherwise be dispersed by Alfv{\'e}n waves. This chapter complements the descriptions of large-scale flow in the core, of turbulence in the core, and of core--mantle interactions, which can all be found in this volume. },
	address = {Oxford},
	author = {D. Jault and C.C. Finlay},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2018-03-27 11:38:52 +0000},
	date-modified = {2018-03-27 11:39:11 +0000},
	doi = {https://doi.org/10.1016/B978-0-444-53802-4.00150-0},
	edition = {Second Edition},
	editor = {Schubert, Gerald},
	keywords = {Torsional waves},
	pages = {225 - 244},
	publisher = {Elsevier},
	title = {8.09 - Waves in the Core and Mechanical Core--Mantle Interactions},
	year = {2015},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/B9780444538024001500},
	Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-444-53802-4.00150-0}}

@article{Soloviev2017,
	author = {Anatoly Soloviev and Arnaud Chulliat and Shamil Bogoutdinov},
	date-added = {2018-03-23 14:27:11 +0000},
	date-modified = {2018-03-23 14:27:35 +0000},
	doi = {https://doi.org/10.1016/j.pepi.2017.07.005},
	issn = {0031-9201},
	journal = {Phys. Earth. Planet. Int.},
	keywords = {Geomagnetic secular acceleration, Core magnetic field, Geomagnetic jerks, Magnetic observatories, Pattern recognition, Time series smoothing},
	pages = {128 - 142},
	title = {Detection of secular acceleration pulses from magnetic observatory data},
	volume = {270},
	year = {2017},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920117301292},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2017.07.005}}

@article{Torta2015,
	abstract = {Abstract The production of quasi‐definitive data at Ebre observatory has enabled us to detect a new geomagnetic jerk in early 2014. This has been confirmed by analyzing data at several observatories in the European‐African and Western Pacific‐Australian sectors in the classical fashion of looking for the characteristic V shape of the geomagnetic secular variation trend. A global model produced with the latest available satellite and observatory data supports these findings, giving a global perspective on both the jerk and a related secular acceleration pulse at the core‐mantle boundary. We conclude that the jerk was most visible in the Atlantic and European sectors.},
	author = {J. Miquel Torta and F. Javier Pav{\'o}n-Carrasco and Santiago Marsal and Christopher C. Finlay},
	date-added = {2018-03-23 14:21:31 +0000},
	date-modified = {2018-03-23 14:24:40 +0000},
	doi = {10.1002/2015GL065501},
	journal = {Geophysical Research Letters},
	keywords = {geomagnetic jerk, acceleration pulses, quasi‐definitive data, main field modeling, core‐mantle boundary},
	number = {19},
	pages = {7933-7940},
	title = {Evidence for a new geomagnetic jerk in 2014},
	volume = {42},
	year = {2015},
	Bdsk-Url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2015GL065501},
	Bdsk-Url-2 = {https://dx.doi.org/10.1002/2015GL065501}}

@article{Pais2015,
	author = {Pais, M. A. and Morozova, A. L. and Schaeffer, N.},
	date-added = {2018-03-21 21:25:34 +0000},
	date-modified = {2018-03-21 21:26:19 +0000},
	doi = {10.1093/gji/ggu403},
	journal = {Geophys. J. Int.},
	number = {1},
	pages = {402-420},
	title = {Variability modes in core flows inverted from geomagnetic field models},
	volume = {200},
	year = {2015},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggu403},
	Bdsk-Url-2 = {https://dx.doi.org/10.1093/gji/ggu403}}

@article{Gillet2011,
	author = {Gillet, Nicolas and Schaeffer, Nathanael and Jault, Dominique},
	date-added = {2018-03-21 13:34:26 +0000},
	date-modified = {2018-03-21 13:34:26 +0000},
	doi = {{10.1016/j.pepi.2011.01.005}},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	month = {{AUG}},
	number = {{3-4, SI}},
	pages = {{380-390}},
	researcherid-numbers = {{Schaeffer, Nathanael/F-4162-2012}},
	title = {{Rationale and geophysical evidence for quasi-geostrophic rapid dynamics within the Earth's outer core}},
	unique-id = {{ISI:000296207900026}},
	volume = {{187}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2011.01.005%7D}}

@article{Teed2014,
	author = {Teed, R. J. and Jones, C. A. and Tobias, S. M.},
	date-added = {2018-01-31 08:56:44 +0000},
	date-modified = {2018-01-31 09:05:48 +0000},
	doi = {10.1093/gji/ggt432},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {724-735},
	title = {The dynamics and excitation of torsional waves in geodynamo simulations},
	volume = {196},
	year = {2014},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggt432},
	Bdsk-Url-2 = {https://dx.doi.org/10.1093/gji/ggt432}}

@article{Gillet2017,
	author = {Gillet, N. and Jault, D. and Canet, E.},
	date-added = {2018-01-19 12:30:05 +0000},
	date-modified = {2018-01-19 12:30:25 +0000},
	doi = {10.1093/gji/ggx237},
	journal = {Geophys. J. Int.},
	number = {3},
	pages = {1503-1516},
	title = {Excitation of travelling torsional normal modes in an Earth's core model},
	volume = {210},
	year = {2017},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggx237},
	Bdsk-Url-2 = {https://dx.doi.org/10.1093/gji/ggx237}}

@article{Livermore2017,
	author = {Livermore, Philip W. and Hollerbach, Rainer and Finlay, Christopher C.},
	date-added = {2018-01-11 15:25:32 +0000},
	date-modified = {2018-01-11 15:25:55 +0000},
	doi = {{10.1038/NGEO2859}},
	eissn = {{1752-0908}},
	issn = {{1752-0894}},
	journal = {Nature Geosci.},
	month = {{JAN}},
	number = {{1}},
	orcid-numbers = {{Finlay, Christopher C./0000-0002-4592-2290 Livermore, Philip/0000-0001-7591-6716}},
	pages = {{62-68}},
	title = {{An accelerating high-latitude jet in Earth's core}},
	unique-id = {{ISI:000394117300016}},
	volume = {{10}},
	year = {2017},
	Bdsk-Url-1 = {https://dx.doi.org/10.1038/NGEO2859%7D}}

@article{Chulliat2014,
	author = {Chulliat, A. and Maus, S.},
	date-added = {2017-12-20 14:51:34 +0000},
	date-modified = {2017-12-20 14:52:03 +0000},
	doi = {{10.1002/2013JB010604}},
	eissn = {{2169-9356}},
	issn = {{2169-9313}},
	journal = {J. Geophys. Res.},
	month = {{MAR}},
	number = {{3}},
	orcid-numbers = {{Chulliat, Arnaud/0000-0001-7414-9631 Maus, Stefan/0000-0002-9604-3878}},
	pages = {{1531-1543}},
	researcherid-numbers = {{Chulliat, Arnaud/A-5747-2011 }},
	title = {Geomagnetic secular acceleration, jerks, and a localized standing wave at the core surface from 2000 to 2010},
	unique-id = {{ISI:000336844700001}},
	volume = {{119}},
	year = {2014},
	Bdsk-Url-1 = {https://dx.doi.org/10.1002/2013JB010604%7D}}

@article{Lesur2018,
	author = {Vincent Lesur and Ingo Wardinski and Julien Baerenzung and Matthias Holschneider},
	date-added = {2017-12-20 13:43:37 +0000},
	date-modified = {2020-11-30 11:48:32 +0100},
	doi = {https://doi.org/10.1016/j.pepi.2017.05.017},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Geomagnetism, Core field, Secular variation rate of change, Geomagnetic jerks, Correlation based modelling},
	pages = {145-158},
	title = {On the frequency spectra of the core magnetic field Gauss coefficients},
	volume = {276},
	year = {2018},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920116303168},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2017.05.017}}

@article{Hori2017,
	author = {K. Hori and R.J. Teed and C.A. Jones},
	date-added = {2017-12-18 14:45:08 +0000},
	date-modified = {2017-12-18 14:45:24 +0000},
	doi = {https://doi.org/10.1016/j.pepi.2017.07.008},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Waves, Dynamos, Core convection, Toroidal magnetic field, Geomagnetic secular variation},
	title = {The dynamics of magnetic Rossby waves in spherical dynamo simulations: A signature of strong-field dynamos?},
	year = {2017},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920117300730},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.pepi.2017.07.008}}

@article{Bouligand2016,
	author = {Bouligand, C. and Gillet, N. and Jault, D. and Schaeffer, N. and Fournier, A. and Aubert, J.},
	date-added = {2017-12-12 11:00:32 +0000},
	date-modified = {2017-12-12 11:00:56 +0000},
	doi = {10.1093/gji/ggw326},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {1142-1157},
	title = {Frequency spectrum of the geomagnetic field harmonic coefficients from dynamo simulations},
	volume = {207},
	year = {2016},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggw326},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggw326}}

@article{Hulot1994,
	author = {Hulot, G. and Le Mou{\"e}l, J.-L.},
	date-added = {2017-12-11 14:23:08 +0000},
	date-modified = {2017-12-11 14:23:08 +0000},
	journal = {Phys. Earth Planet. Int.},
	pages = {167-183},
	title = {A statistical approach to the {E}arth's main magnetic field},
	volume = {82},
	year = {1994}}

@article{Wardinski2012,
	author = {Wardinski, Ingo and Lesur, Vincent},
	date-added = {2017-12-06 13:52:35 +0000},
	date-modified = {2017-12-06 13:52:46 +0000},
	doi = {{10.1111/j.1365-246X.2012.05384.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUN}},
	number = {{3}},
	orcid-numbers = {{Lesur, Vincent/0000-0003-2568-320X}},
	pages = {{1409-1429}},
	researcherid-numbers = {{Lesur, Vincent/H-1031-2012}},
	title = {{An extended version of the C3FM geomagnetic field model: application of a continuous frozen-flux constraint}},
	unique-id = {{ISI:000303857000015}},
	volume = {{189}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2012.05384.x%7D}}

@article{Wardinski2006,
	abstract = {{{[}1] This study presents an investigation and description of the
   secular variation of the Earth's magnetic field between 1980 and 2000. A
   time-dependent model, (CFM)-F-3 (Continuous Covariant Constrained
   endpoints Field Model), of the main field and its secular variation
   between 1980 and 2000 is developed, with Gauss coefficients expanded in
   time on a basis of cubic B splines. This model is constrained to fit
   field models from high-quality vector measurements of Magsat in 1980 and
   Orsted in 2000 and to fit both magnetic observatory and repeat station
   secular variation estimates for the period in between. These secular
   variation estimates (first time derivatives) are derived from
   observatories monthly or annual means and repeat station data in order
   to reduce the contributions of crustal noise, annual, and semiannual
   variation. On average, the model input consists secular variation
   estimates of the X, Y, and Z components at 130 locations per month.
   Treatment of covariance between the different components allows a higher
   temporal sensitivity of the model, due to the exclusion of some external
   field variation. The model is computed up to degree and order 15. The
   model is a useful extension of the hitherto existing time-dependent
   description of the secular variation, GUFM which describes the secular
   variation until 1990. It reveals a short-term secular variation on
   subdecadal timescale and has a higher spatial resolution, than
   previously resolved. The model is also valuable to test the frozen flux
   hypothesis and to link features of the radial field at the core-mantle
   boundary to the geodynamo.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Wardinski, I (Reprint Author), Geoforschungszentrum Potsdam, Sect 2 3, Telegrafenberg Bldg F428, D-14473 Potsdam, Germany. Geoforschungszentrum Potsdam, Sect 2 3, D-14473 Potsdam, Germany. Univ Liverpool, Dept Earth \& Ocean Sci, Liverpool L69 3GP, Merseyside, England.}},
	article-number = {{B12101}},
	author = {Wardinski, I. and Holme, R.},
	author-email = {{ingo@gfz-potsdam.de}},
	da = {{2017-12-06}},
	date-added = {2017-12-06 13:52:02 +0000},
	date-modified = {2017-12-06 13:52:16 +0000},
	doc-delivery-number = {{115TK}},
	doi = {{10.1029/2006JB004401}},
	issn = {{0148-0227}},
	journal = {{J. Geophys. Res.}},
	journal-iso = {{J. Geophys. Res.-Solid Earth}},
	keywords-plus = {{CORE-MANTLE BOUNDARY; GEOMAGNETIC-FIELD; JERK}},
	language = {{English}},
	month = {{DEC 6}},
	number = {{B12}},
	number-of-cited-references = {{28}},
	oa = {{No}},
	publisher = {{AMER GEOPHYSICAL UNION}},
	research-areas = {{Geochemistry \& Geophysics}},
	times-cited = {{30}},
	title = {{A time-dependent model of the Earth's magnetic field and its secular variation for the period 1980-2000}},
	type = {{Article}},
	unique-id = {{ISI:000242756500001}},
	usage-count-last-180-days = {{0}},
	usage-count-since-2013 = {{4}},
	volume = {{111}},
	web-of-science-categories = {{Geochemistry \& Geophysics}},
	year = {{2006}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2006JB004401%7D}}

@article{Chulliat2010b,
	article-number = {{B07101}},
	author = {Chulliat, A. and Hulot, G. and Newitt, L. R.},
	date-added = {2017-12-06 13:37:32 +0000},
	date-modified = {2017-12-06 13:37:47 +0000},
	doi = {{10.1029/2009JB007143}},
	issn = {{0148-0227}},
	journal = {{J. Geophys. Res.}},
	month = {{JUL 10}},
	orcid-numbers = {{Chulliat, Arnaud/0000-0001-7414-9631 }},
	researcherid-numbers = {{Chulliat, Arnaud/A-5747-2011 Hulot, Gauthier/A-5627-2011}},
	title = {{Magnetic flux expulsion from the core as a possible cause of the unusually large acceleration of the north magnetic pole during the 1990s}},
	unique-id = {{ISI:000279826000003}},
	volume = {{115}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2009JB007143%7D}}

@incollection{Holme2015,
	abstract = {Abstract We discuss the observational constraint of large-scale flow in the core. The time variation of the internal magnetic field has been attributed to internal motions in the Earth's fluid core, associated with the geodynamo. From initially simplistic models of magnetic westward drift, more detailed time-dependent models of the field have motivated the calculation of maps of core-surface flow. Advection is assumed to dominate over diffusion (the `Frozen-flux' approximation), suggesting that the magnetic field provides a passive tracer for core flow. Only one equation is available to constrain two components of flow along the core surface; this leads to an unavoidable nonuniqueness in flow determination. Dynamic assumptions have been adopted to provide additional constraints, but the flows vary in morphology depending on which assumption is used. New assumptions are under development, including improved treatments of magnetic diffusion, which may help us to better understand the nature of the flow, or at least the shortcomings in the models we produce. Modern geomagnetic satellite data allow the creation of models of the geomagnetic secular variation with enhanced detail, but as yet, such models have opened up greater modeling problems rather than increased insight as to the flow. A primary difficulty is the shielding of the core field at spherical harmonic degree above 13 by the magnetic field from the Earth's lithosphere. Despite these problems, we remain convinced that the flow models are of some validity from predictions of variations in core-angular momentum that they allow and the striking correlation of such predictions with observed variations in length of day. The theoretical framework of this comparison, the theory of torsional oscillations, opens up the possibility of probing processes within the Earth's core, particularly the strength of the magnetic field, and may help to explain rapid features of the Earth's secular variation, geomagnetic jerks. Detailed flow structures in the core have also been probed, in particular regions at the north and south poles that suggest the top of vortex motions associated with the influence of the inner core on the dynamics of the outer core. Aside from this, it is difficult to provide more than very general observational constrains on core dynamics; however, data assimilation (the combination of observational data with dynamic models) is starting to yield new insights. },
	address = {Oxford},
	author = {R. Holme},
	booktitle = {{Treatise on Geophysics (Second Edition)}},
	date-added = {2017-12-06 11:30:25 +0000},
	date-modified = {2017-12-06 11:31:01 +0000},
	doi = {https://doi.org/10.1016/B978-0-444-53802-4.00138-X},
	editor = {Schubert, Gerald},
	isbn = {978-0-444-53803-1},
	keywords = {Westward drift},
	pages = {91 - 113},
	publisher = {Elsevier},
	title = {Large-Scale Flow in the Core},
	url = {https://www.sciencedirect.com/science/article/pii/B978044453802400138X},
	year = {2015},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/B978044453802400138X},
	Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-444-53802-4.00138-X}}

@article{Schaeffer2017,
	author = {Schaeffer, N. and Jault, D. and Nataf, H.-C. and Fournier, A.},
	date-added = {2017-09-12 13:00:14 +0000},
	date-modified = {2017-09-12 13:25:01 +0000},
	doi = {10.1093/gji/ggx265},
	journal = {Geophys. J. Int.},
	number = {1},
	pages = {1-29},
	title = {Turbulent geodynamo simulations: a leap towards {E}arth's core},
	volume = {211},
	year = {2017},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggx265},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggx265}}

@article{Olsen2014,
	author = {Olsen, Nils and L{\"u}hr, Hermann and Finlay, Christopher C. and Sabaka, Terence J. and Michaelis, Ingo and Rauberg, Jan and T{\o}ffner-Clausen, Lars},
	date-added = {2017-05-04 11:36:37 +0000},
	date-modified = {2017-05-04 11:37:44 +0000},
	doi = {10.1093/gji/ggu033},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {815},
	title = {{The CHAOS-4 geomagnetic field model}},
	volume = {197},
	year = {2014},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1093/gji/ggu033},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggu033}}

@article{Braginsky1984,
	author = {S. I. Braginsky},
	date-added = {2017-03-28 13:18:32 +0000},
	date-modified = {2017-03-28 13:18:50 +0000},
	doi = {10.1080/03091928408210077},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {1-2},
	pages = {1-78},
	title = {Short-period geomagnetic secular variation},
	volume = {30},
	year = {1984},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091928408210077}}

@article{Mound2015,
	abstract = {Abstract Bulk translation of the Earth's inner core has been proposed as an explanation of observed quasi-hemispheric seismic structure. An important consequence of inner core translation would be the generation of a spherical harmonic degree one heat flow anomaly at the inner core boundary (ICB) that would provide an inhomogeneous forcing for outer core convection. We use geodynamo simulations to investigate the geomagnetic signature of such heterogeneity. Strong hemispheric heterogeneity at the \{ICB\} is found to produce a hemispheric signature in both the morphology of the magnetic field and its secular variation; in particular, we note the formation of high-intensity flux patches at high-latitudes and American longitudes in our model with strong \{ICB\} heterogeneity. In our simulations, this model provides the best match to the Earth's field over the past 400 years according to previously proposed measures of field structure. However, these criteria do not include the hemispheric balance of the field. We propose new criteria to measure this balance and find that our model with strong \{ICB\} heterogeneity produces the poorest match to the hemispheric balance of the historical geomagnetic field. Resolution of the hemispheric balance of the magnetic field throughout the Holocene would provide a strong test of any proposal of rapid inner core translation. },
	author = {Jon Mound and Chris Davies and Luis Silva},
	date-added = {2017-03-08 09:31:48 +0000},
	date-modified = {2017-03-08 09:32:04 +0000},
	doi = {http://dx.doi.org/10.1016/j.epsl.2015.05.028},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {inner core translation},
	pages = {148 - 157},
	title = {Inner core translation and the hemispheric balance of the geomagnetic field},
	volume = {424},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X1500326X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.epsl.2015.05.028}}

@article{Sheyko2016,
	author = {Sheyko, Andrey and Finlay, Christopher C. and Jackson, Andrew},
	date = {2016/11/24/print},
	date-added = {2017-03-08 09:22:05 +0000},
	date-modified = {2017-03-08 09:22:16 +0000},
	day = {24},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {10.1038/nature19842; http://www.nature.com/nature/journal/v539/n7630/abs/nature19842.html#supplementary-information},
	m3 = {Letter},
	month = {11},
	number = {7630},
	pages = {551--554},
	publisher = {Macmillan Publishers Limited, part of Springer Nature. All rights reserved.},
	title = {Magnetic reversals from planetary dynamo waves},
	ty = {JOUR},
	volume = {539},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature19842}}

@article{Schaeffer2016,
	author = {Nathana{\"e}l Schaeffer and Dominique Jault},
	date-added = {2017-03-06 11:34:48 +0000},
	date-modified = {2017-03-06 11:35:16 +0000},
	doi = {10.1002/2016gl068301},
	journal = {Geophys. Res. Lett.},
	month = {may},
	number = {10},
	pages = {4922--4928},
	publisher = {Wiley-Blackwell},
	title = {Electrical conductivity of the lowermost mantle explains absorption of core torsional waves at the equator},
	volume = {43},
	year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1002%2F2016gl068301},
	Bdsk-Url-2 = {http://dx.doi.org/10.1002/2016gl068301}}

@article{Wardinski2008,
	abstract = {In this paper we examine the core surface flow obtained by an inversion of a continuous model of the geomagnetic field and its temporal variation using the diffusion-less induction equation. The continuous \{CHAOS\} model is derived from satellite data up to spherical harmonic degree 14 and covers the period 1999 to 2006. The \{CHAOS\} secular variation, when downward continued to the core surface, shows stripe-like features, which can be attributed to spherical harmonic degree 12 and higher. These contributions are removed by applying a tapering method, and the resulting tapered model is then inverted for the core surface flow. Satellite-based field models have a high spatial resolution; however, their temporal resolution is limited. In order to enhance the temporal resolution of the flow, we additionally constrain the flow to fit the secular variation from ground-based observatory data. A range of solutions, subject to different constraints, are computed, two flow hypotheses being considered: purely toroidal flow and tangentially geostrophic flow. We show that both flow types provide similar results; however, the purely toroidal flow provides a better fit to the secular variation in the equatorial region than the tangentially geostrophic flow. We then analyze the residuals between observed secular variation and its predictions from the flow. We note larger residuals for the tangentially geostrophic flow, where strong radial secular variation and a weak radial field are observed. Although diffusive effects cannot be ruled out as a potential source of the mismatch, we attribute the larger residuals to be caused by a flawed estimation of the poloidal flow. We also seek to relate temporal changes in the fluid flow to the geomagnetic jerk which occurred at the beginning of 2003. It is found that this geomagnetic jerk coincides with variations in the zonal flow components of both flow types, suggesting a possible link to torsional oscillations. However, we argue that other flow components are important to obtain a detailed fit of the observed secular variation. Finally, we compare observed changes in the length-of-day and the predictions from the flow solutions. },
	author = {I. Wardinski and R. Holme and S. Asari and M. Mandea},
	date-added = {2017-03-02 14:30:35 +0000},
	date-modified = {2017-03-02 14:30:52 +0000},
	doi = {http://dx.doi.org/10.1016/j.epsl.2007.12.008},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {geomagnetic jerk},
	number = {3--4},
	pages = {468 - 481},
	title = {The 2003 geomagnetic jerk and its relation to the core surface flows},
	volume = {267},
	year = {2008},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X07007960},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.epsl.2007.12.008}}

@article{Pinheiro2008,
	author = {Pinheiro, K. and Jackson, A.},
	date-added = {2017-03-01 14:50:14 +0000},
	date-modified = {2017-03-06 16:58:08 +0000},
	doi = {10.1111/j.1365-246X.2008.03762.x},
	journal = {Geophys. J. Int.},
	number = {3},
	pages = {781},
	title = {Can a 1-{D} mantle electrical conductivity model generate magnetic jerk differential time delays?},
	volume = {173},
	year = {2008},
	Bdsk-Url-1 = {+%20http://dx.doi.org/10.1111/j.1365-246X.2008.03762.x},
	Bdsk-Url-2 = {http://dx.doi.org/10.1111/j.1365-246X.2008.03762.x}}

@article{Cox2016,
	abstract = {Abstract Torsional Alfv{\'e}n waves involve the interaction of zonal fluid flow and the ambient magnetic field in the core. Consequently, they perturb the background magnetic field and induce a secondary magnetic field. Using a steady background magnetic field from observationally constrained field models and azimuthal velocities from torsional wave forward models, we solve an induction equation for the wave-induced secular variation (SV). We construct time series and maps of wave-induced \{SV\} and investigate how previously identified propagation characteristics manifest in the magnetic signals, and whether our modelled travelling torsional waves are capable of producing signals that resemble jerks in terms of amplitude and timescale. Fast torsional waves with amplitudes and timescales consistent with a recent study of the 6 yr Δ \{LOD\} signal induce very rapid, small (maximum ∼ 2 nT/yr at Earth's surface) \{SV\} signals that would likely be difficult to be resolve in observations of Earth's SV. Slow torsional waves with amplitudes and timescales consistent with other studies produce larger \{SV\} signals that reach amplitudes of ∼ 20 nT/yr at Earth's surface. We applied a two-part linear regression jerk detection method to the \{SV\} induced by slow torsional waves, using the same parameters as used on real SV, which identified several synthetic jerk events. As the local magnetic field morphology dictates which regions are sensitive to zonal core flow, and not all regions are sensitive at the same time, the modelled waves generally produce synthetic jerks that are observed on regional scales and occur in a single \{SV\} component. However, high wave amplitudes during reflection from the stress-free \{CMB\} induce large-scale \{SV\} signals in all components, which results in a global contemporaneous jerk event such as that observed in 1969. In general, the identified events are periodic due to waves passing beneath locations at fixed intervals and the \{SV\} signals are smoothly varying. These smooth signals are more consistent with the geomagnetic jerks envisaged by Demetrescu and Dobrica than the sharp `V' shapes that are typically associated with geomagnetic jerks. },
	author = {G.A. Cox and P.W. Livermore and J.E. Mound},
	date-added = {2017-03-01 14:48:37 +0000},
	date-modified = {2017-03-01 15:00:06 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2016.03.012},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Secular variation},
	pages = {50 - 65},
	title = {The observational signature of modelled torsional waves and comparison to geomagnetic jerks},
	volume = {255},
	year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920116300127},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2016.03.012}}

@article{Silva2012,
	abstract = {At observatory locations, the Earth's magnetic field displays an almost constant secular acceleration, except at times of geomagnetic jerks when this quantity suddenly changes its value. The 2003 geomagnetic jerk was the first to have been recorded globally and uniformly over the Earth, and is well captured by time-varying spherical harmonic models of the geomagnetic field, based on satellite data. We jointly derive instantaneous estimates of the core surface flow and acceleration accounting for the field secular variation and acceleration given by such models. We consider epochs just before and after the 2003 event and show that no steady flow, no matter how general, can simultaneously account for the observed secular variation and acceleration at either epoch. Assuming the flow to be tangentially geostrophic, we next show that even purely toroidal zonal flow accelerations cannot account for the observed secular acceleration and conclude that more general tangentially geostrophic flow accelerations are required by the data. These flow accelerations, however, may well be equatorially symmetric, as predicted by theoretical considerations. Investigating the flow acceleration change throughout the 2003 event shows that these also may be equatorially symmetric, but definitely not purely toroidal zonal. This unambiguously confirms earlier suggestions that the 2003 geomagnetic jerk was a more complex phenomena than a simple consequence of torsional oscillations. },
	author = {Lu{\'\i}s Silva and Gauthier Hulot},
	date-added = {2017-03-01 14:47:25 +0000},
	date-modified = {2017-03-01 14:59:49 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2012.03.002},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Geomagnetic jerks},
	pages = {28 - 50},
	title = {Investigating the 2003 geomagnetic jerk by simultaneous inversion of the secular variation and acceleration for both the core flow and its acceleration},
	volume = {198--199},
	year = {2012},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920112000489},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2012.03.002}}

@article{Bloxham2002,
	annote = {10.1038/nature01134},
	author = {Bloxham, Jeremy and Zatman, Stephen and Dumberry, Mathieu},
	date = {2002/11/07/print},
	date-added = {2017-03-01 14:45:18 +0000},
	date-modified = {2017-03-01 14:59:26 +0000},
	day = {07},
	isbn = {0028-0836},
	journal = {Nature},
	m3 = {10.1038/nature01134},
	month = {11},
	number = {6911},
	pages = {65--68},
	title = {The origin of geomagnetic jerks},
	ty = {JOUR},
	volume = {420},
	year = {2002},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature01134}}

@inproceedings{Malin1983,
	adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	adsurl = {http://adsabs.harvard.edu/abs/1983ebro.conf..239M},
	author = {{Malin}, S.~R.~C. and {Hodder}, B.~M. and {Barraclough}, D.~R.},
	booktitle = {Scientific Contributions in Commemoration of Ebro Observatory's 75th Anniversary},
	date-added = {2017-03-01 14:44:07 +0000},
	date-modified = {2017-03-01 14:44:12 +0000},
	editor = {{Card{\'u}s}, J.~O.},
	keywords = {Acceleration (Physics), Geomagnetism, Secular Variations, Spherical Harmonics, Average, Declination, Magnetic Dipoles, Magnetic Flux},
	title = {{Geomagnetic secular variation: A jerk in 1970}},
	year = 1983}

@article{Courtillot1984,
	annote = {10.1038/311709a0},
	author = {Courtillot, V. and Le Mou\"el, J.-L.},
	date = {1984/10/25/print},
	date-added = {2017-02-28 14:10:44 +0000},
	date-modified = {2017-02-28 14:15:11 +0000},
	day = {25},
	journal = {Nature},
	m3 = {10.1038/311709a0},
	month = {10},
	number = {5988},
	pages = {709--716},
	title = {Geomagnetic secular variation impulses},
	ty = {JOUR},
	volume = {311},
	year = {1984},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/311709a0}}

@article{Gillet2015b,
	abstract = {We present the geomagnetic field model COV-OBS.x1, covering 1840 to 2020, from which have been derived candidate models for the IGRF-12. Towards the most recent epochs, it is primarily constrained by first differences of observatory annual means and measurements from the Oersted, Champ, and Swarm satellite missions. Stochastic information derived from the temporal spectra of geomagnetic series is used to construct the a priori model covariance matrix that complements the constraint brought by the data. This approach makes it possible the use of a posteriori model errors, for instance, to measure the `observations' uncertainties in data assimilation schemes for the study of the outer core dynamics.},
	author = {Gillet, Nicolas and Barrois, Olivier and Finlay, Christopher C.},
	date-added = {2017-02-28 13:37:49 +0000},
	date-modified = {2017-03-01 15:00:31 +0000},
	doi = {10.1186/s40623-015-0225-z},
	issn = {1880-5981},
	journal = {Earth, Planets and Space},
	number = {1},
	pages = {71},
	title = {{Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12}},
	volume = {67},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1186/s40623-015-0225-z}}

@article{Bardsley2016,
	abstract = {We consider a rapidly rotating, Boussinesq fluid stirred by buoyant anomalies. In such a system it is known that, in the absence of a magnetic field, inertial waves whose wave vectors lie normal to the rotation axis play a key role in establishing quasi-geostrophic motion. In particular, buoyant anomalies radiate low-frequency inertial wave packets which disperse along the rotation axis, leading to axially elongated columnar vortices. Here we focus on the influence of an ambient magnetic field on this process, motivated by the dynamics of planetary cores. We find that, once again, the waves responsible for establishing quasi-geostrophic structures have wave vectors normal to the rotation axis; however, these are not conventional inertial waves, but rather hybrid `inertial--Alfv{\'e}n waves'. Their frequency equals that of an Alfv{\'e}n wave but their axial group velocity is half that of the equivalent inertial wave. They have maximal kinetic, magnetic and cross-helicity, carry magneti},
	address = {Cambridge, UK},
	author = {O. P. Bardsley and P. A. Davidson},
	date-added = {2017-02-22 21:26:50 +0000},
	date-modified = {2017-02-22 21:27:41 +0000},
	day = {25},
	doi = {10.1017/jfm.2016.577},
	journal = {J. Fluid. Mech.},
	month = {10},
	publisher = {Cambridge University Press},
	title = {{Inertial--Alfv{\'e}n waves as columnar helices in planetary cores}},
	volume = {805},
	year = {2016},
	Bdsk-Url-1 = {https://www.cambridge.org/core/article/div-class-title-inertial-alfven-waves-as-columnar-helices-in-planetary-cores-div/9A74142083C33DDB8F8A918D5A297195},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2016.577}}

@article{Holme2005,
	author = {Holme, R and de Viron, O},
	date-added = {2017-01-27 13:37:13 +0000},
	date-modified = {2017-01-27 13:37:23 +0000},
	doi = {{10.1111/j.1365-246X.2004.02510.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{FEB}},
	number = {{2}},
	orcid-numbers = {{de Viron, Olivier/0000-0003-3112-9686}},
	pages = {{435-439}},
	researcherid-numbers = {{de Viron, Olivier/N-6647-2014}},
	title = {{Geomagnetic jerks and a high-resolution length-of-day profile for core studies}},
	unique-id = {{ISI:000227134300002}},
	volume = {{160}},
	year = {{2005}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2004.02510.x%7D}}

@article{Chulliat2010,
	article-number = {{L07301}},
	author = {Chulliat, A. and Thebault, E. and Hulot, G.},
	date-added = {2017-01-27 13:33:50 +0000},
	date-modified = {2017-01-27 13:34:06 +0000},
	doi = {{10.1029/2009GL042019}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	month = {{APR 1}},
	orcid-numbers = {{Chulliat, Arnaud/0000-0001-7414-9631 }},
	researcherid-numbers = {{Hulot, Gauthier/A-5627-2011 Chulliat, Arnaud/A-5747-2011 Thebault, Erwan/A-5670-2011}},
	title = {{Core field acceleration pulse as a common cause of the 2003 and 2007 geomagnetic jerks}},
	unique-id = {{ISI:000276314500001}},
	volume = {{37}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2009GL042019%7D}}

@article{Chulliat2015,
	author = {Chulliat, Arnaud and Alken, Patrick and Maus, Stefan},
	date-added = {2017-01-27 13:33:10 +0000},
	date-modified = {2017-01-27 13:33:29 +0000},
	doi = {{10.1002/2015GL064067}},
	eissn = {{1944-8007}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	month = {{MAY 16}},
	number = {{9}},
	orcid-numbers = {{Chulliat, Arnaud/0000-0001-7414-9631}},
	pages = {{3321-3329}},
	researcherid-numbers = {{Chulliat, Arnaud/A-5747-2011}},
	title = {{Fast equatorial waves propagating at the top of the Earth's core}},
	unique-id = {{ISI:000355878300033}},
	volume = {{42}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/2015GL064067%7D}}

@article{Mandea2010,
	abstract = {The secular variation of the core field is generally characterized by smooth variations, sometimes interrupted by abrupt changes, named geomagnetic jerks. The origin of these events, observed and investigated for over three decades, is still not fully understood. Many fundamental features of geomagnetic jerks have been the subject of debate, including their origin internal or external to the Earth, their occurrence dates, their duration and their global or regional character. Specific tools have been developed to detect them in geomagnetic field or secular variation time series. Recently, their investigation has been advanced by the availability of a decade of high-quality satellite measurements. Moreover, advances in the modelling of the core field and its variations have brought new perspectives on the fluid motion at the top of the core, and opened new avenues in our search for the origin of geomagnetic jerks. Correlations have been proposed between geomagnetic jerks and some other geophysical observables, indicating the substantial interest in this topic in our scientific community. This paper summarizes the recent advances in our understanding and interpretation of geomagnetic jerks.},
	author = {Mandea, Mioara and Holme, Richard and Pais, Alexandra and Pinheiro, Katia and Jackson, Andrew and Verbanac, Giuliana},
	date-added = {2017-01-27 13:27:56 +0000},
	date-modified = {2017-01-27 13:28:15 +0000},
	doi = {10.1007/s11214-010-9663-x},
	issn = {1572-9672},
	journal = {Space. Sci. Rev.},
	number = {1},
	pages = {147--175},
	title = {{Geomagnetic Jerks: Rapid Core Field Variations and Core Dynamics}},
	volume = {155},
	year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9663-x}}

@article{Brown2013,
	abstract = {Abstract We present a two-step method for the removal of external field signals and the identification of geomagnetic jerks in magnetic observatory monthly mean data, providing quantitative uncertainty estimates on jerk occurrence times and amplitudes with minimal a priori information. We apply the method to the complete time series of X-, Y- and Z-components at up to 103 observatory locations in the period of 1957--2008. We find features fitting the definition of jerks in individual components to be frequent and not globally contemporaneous. Identified regional jerks have no consistent occurrence pattern and the most widespread in any given year is identified at &lt; 30% of observatories worldwide. Whilst we identify jerks throughout the period of study, relative peaks in the global number of jerk occurrences are found in 1968--71, 1973--74, 1977--79, 1983--85, 1989--93, 1995--98 and 2002--03 with the suggestion of further poorly sampled events in the early 1960s and late 2000s. The mean uncertainties on individual jerk occurrence times and amplitudes are found to be $\pm$ 0.3 yrs and $\pm$ 2.1 nT/yr2, respectively, for all field components. Jerk amplitudes suggest possible periodic trends across Europe and North America, which may be related to the 6-yr periods detected independently in the secular variation and length-of-day. },
	author = {W.J. Brown and J.E. Mound and P.W. Livermore},
	date-added = {2017-01-27 13:24:45 +0000},
	date-modified = {2017-01-27 13:26:44 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2013.06.001},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {External field},
	pages = {62 - 76},
	title = {Jerks abound: An analysis of geomagnetic observatory data from 1957 to 2008},
	volume = {223},
	year = {2013},
	Bdsk-Url-1 = {//www.sciencedirect.com/science/article/pii/S0031920113000708},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2013.06.001}}

@article{Courtillot1978,
	author = {Courtillot, V and Ducruix, J and Le Mou\"el, J.-L.},
	date-added = {2017-01-27 13:21:26 +0000},
	date-modified = {2017-01-27 13:22:55 +0000},
	journal = {C.R. Acad. Sci. Paris. D},
	number = {{12}},
	pages = {{1095-1098}},
	researcherid-numbers = {{Courtillot, Vincent/C-8007-2011}},
	title = {Sur une acc{\'e}l{\'e}ration r{\'e}cente de la variation s{\'e}culaire du champ magn{\'e}tique terrestre},
	unique-id = {{ISI:A1978GD86400005}},
	volume = {{287}},
	year = {{1978}}}

@article{Aubert2017,
	abstract = {Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the lar},
	address = {Cambridge, UK},
	author = {Julien Aubert and Thomas Gastine and Alexandre Fournier},
	date-added = {2017-01-25 15:40:27 +0000},
	date-modified = {2017-01-25 15:41:04 +0000},
	day = {25},
	doi = {10.1017/jfm.2016.789},
	journal = {J. Fluid. Mech.},
	month = {002},
	pages = {558-593},
	publisher = {Cambridge University Press},
	title = {Spherical convective dynamos in the rapidly rotating asymptotic regime},
	volume = {813},
	year = {2017},
	Bdsk-Url-1 = {https://www.cambridge.org/core/article/div-class-title-spherical-convective-dynamos-in-the-rapidly-rotating-asymptotic-regime-div/BCCBB1A4BF5C4362C5221309F52CEA10},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2016.789}}

@article{Finlay2016b,
	abstract = {We use more than 2 years of magnetic data from the Swarm mission, and monthly means from 160 ground observatories as available in March 2016, to update the CHAOS time-dependent geomagnetic field model. The new model, CHAOS-6, provides information on time variations of the core-generated part of the Earth's magnetic field between 1999.0 and 2016.5. We present details of the secular variation (SV) and secular acceleration (SA) from CHAOS-6 at Earth's surface and downward continued to the core surface. At Earth's surface, we find evidence for positive acceleration of the field intensity in 2015 over a broad area around longitude 90$\,^{\circ}$E that is also seen at ground observatories such as Novosibirsk. At the core surface, we are able to map the SV up to at least degree 16. The radial field SA at the core surface in 2015 is found to be largest at low latitudes under the India--South-East Asia region, under the region of northern South America, and at high northern latitudes under Alaska and Siberia. Surprisingly, there is also evidence for significant SA in the central Pacific region, for example near Hawaii where radial field SA is observed on either side of a jerk in 2014. On the other hand, little SV or SA has occurred over the past 17 years in the southern polar region. Inverting for a quasi-geostrophic core flow that accounts for this SV, we obtain a prominent planetary-scale, anti-cyclonic, gyre centred on the Atlantic hemisphere. We also find oscillations of non-axisymmetric, azimuthal, jets at low latitudes, for example close to 40$\,^{\circ}$W, that may be responsible for localized SA oscillations. In addition to scalar data from {\O}rsted, CHAMP, SAC-C and Swarm, and vector data from {\O}rsted, CHAMP and Swarm, CHAOS-6 benefits from the inclusion of along-track differences of scalar and vector field data from both CHAMP and the three Swarm satellites, as well as east--west differences between the lower pair of Swarm satellites, Alpha and Charlie. Moreover, ground observatory SV estimates are fit to a Huber-weighted rms level of 3.1 nT/year for the eastward components and 3.8 and 3.7 nT/year for the vertical and southward components. We also present an update of the CHAOS high-degree lithospheric field, making use of along-track differences of CHAMP scalar and vector field data to produce a new static field model that agrees well with the MF7 field model out to degree 110.},
	author = {Finlay, C. C. and Olsen, Nils and Kotsiaros, Stavros and Gillet, Nicolas and T{\o}ffner-Clausen, Lars},
	da = {2016//},
	date-added = {2017-01-24 11:16:52 +0000},
	date-modified = {2017-12-14 10:06:41 +0000},
	doi = {10.1186/s40623-016-0486-1},
	id = {Finlay2016},
	isbn = {1880-5981},
	journal = {{Earth, Planets and Space}},
	number = {1},
	pages = {112},
	title = {{Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model}},
	ty = {JOUR},
	volume = {68},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1186/s40623-016-0486-1}}

@article{Yadav2016PNAS,
	abstract = {Earth sustains its magnetic field by a dynamo process driven by convection in the liquid outer core. Geodynamo simulations have been successful in reproducing many observed properties of the geomagnetic field. However, although theoretical considerations suggest that flow in the core is governed by a balance between Lorentz force, rotational force, and buoyancy (called MAC balance for Magnetic, Archimedean, Coriolis) with only minute roles for viscous and inertial forces, dynamo simulations must use viscosity values that are many orders of magnitude larger than in the core, due to computational constraints. In typical geodynamo models, viscous and inertial forces are not much smaller than the Coriolis force, and the Lorentz force plays a subdominant role; this has led to conclusions that these simulations are viscously controlled and do not represent the physics of the geodynamo. Here we show, by a direct analysis of the relevant forces, that a MAC balance can be achieved when the viscosity is reduced to values close to the current practical limit. Lorentz force, buoyancy, and the uncompensated (by pressure) part of the Coriolis force are of very similar strength, whereas viscous and inertial forces are smaller by a factor of at least 20 in the bulk of the fluid volume. Compared with nonmagnetic convection at otherwise identical parameters, the dynamo flow is of larger scale and is less invariant parallel to the rotation axis (less geostrophic), and convection transports twice as much heat, all of which is expected when the Lorentz force strongly influences the convection properties.},
	author = {Yadav, R. K. and Gastine, T. and Christensen, U. R. and Wolk, S. J. and Poppenhaeger, K.},
	date-added = {2016-11-14 14:02:54 +0000},
	date-modified = {2017-03-08 09:23:19 +0000},
	doi = {10.1073/pnas.1608998113},
	journal = {PNAS},
	number = {43},
	pages = {12065-12070},
	title = {Approaching a realistic force balance in geodynamo simulations},
	volume = {113},
	year = {2016},
	Bdsk-Url-1 = {http://www.pnas.org/content/113/43/12065.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1073/pnas.1608998113}}

@article{Oruba2016,
	abstract = { In dynamo power-based scaling laws, the power P injected by buoyancy forces is measured by a so-called flux-based Rayleigh number, denoted as RaQ⋆ (see Christensen and Aubert, Geophys. J. Int. 2006, vol. 166, pp. 97--114). Whereas it is widely accepted that this parameter is measured (as opposite to controlled) in dynamos driven by differential heating, the literature is much less clear concerning its nature in the case of imposed heat flux. We clarify this issue by highlighting that in that case, the RaQ⋆ parameter becomes controlled only in the limit of large Nusselt numbers (Nu≫1). We then address the issue of the robustness of the original relation between P and RaQ⋆ with the geometry and the thermal boundary conditions. We show that in the cartesian geometry, as in the spherical geometry with a central mass distribution, this relation is purely linear, in both differential and fixed-flux heating. However, we show that in the geometry commonly studied by geophysicists (spherical with uniform mass distribution), its validity places an upper-bound on the strength of the driving which can be envisaged in a fixed Ekman number simulation. An increase of the Rayleigh number indeed yields deviations (in terms of absolute correction) from the linear relation between P and RaQ⋆. We conclude that in such configurations, the parameter range for which P is controlled is limited. },
	author = {Oruba, L.},
	date-added = {2016-09-06 08:51:31 +0000},
	date-modified = {2016-11-14 13:51:15 +0000},
	doi = {10.1080/03091929.2016.1217523},
	eprint = {http://dx.doi.org/10.1080/03091929.2016.1217523},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	title = {On the role of thermal boundary conditions in dynamo scaling laws},
	url = {http://dx.doi.org/10.1080/03091929.2016.1217523},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091929.2016.1217523}}

@article{Davidson2015,
	abstract = {In most numerical simulations of the Earth's core the dynamo resides outside the tangent cylinder and may be crudely classified as being of the α2 type. In this region the flow comprises a sea of thin columnar vortices aligned with the rotation axis, taking the form of alternating cyclones and anticyclones. The dynamo is thought to be driven by these columnar vortices within which the flow is observed to be highly helical, helicity being a crucial ingredient of planetary dynamos. As noted in Davidson, one of the mysteries of this dynamo cartoon is the origin of the helicity, which is observed to be positive in the south and negative in the north. While Ekman pumping at the mantle can induce helicity in some of the overly viscous numerical simulations, it is extremely unlikely to be a significant source within planets. In this paper we return to the suggestion of Davidson that the helicity observed in the less viscous simulations owes its existence to helical wave packets, launched in and around the equatorial plane where the buoyancy flux is observed to be strong. Here we show that such wave packets act as a potent source of planetary helicity, constituting a simple, robust mechanism that yields the correct sign for h north and south of the equator. Since such a mechanism does not rely on the presence of a mantle, it can operate within both the Earth and the gas giants. Moreover, our numerical simulations show that helical wave packets dispersing from the equator produce a random sea of thin, columnar cyclone/anticyclone pairs, very like those observed in the more strongly forced dynamo simulations. We examine the local dynamics of helical wave packets dispersing from the equatorial regions, as well as the overall nature of an α2-dynamo driven by such wave packets. Our local analysis predicts the mean emf induced by helical waves, an analysis that rests on a number of simple approximations which are consistent with our numerical experiments, while our global analysis yields exact integral relationships between the mean emf induced by the wave packets and the large-scale dipole and azimuthal field. Combining these local and integral equations yields a kinematic model for an α2-dynamo driven by helical waves. Order-of-magnitude estimates based on these equations suggest that such a dynamo is indeed feasible.},
	author = {Davidson, P.A. and Ranjan, A.},
	date-added = {2016-09-02 15:18:43 +0000},
	date-modified = {2016-09-02 15:19:08 +0000},
	doi = {10.1093/gji/ggv232},
	eprint = {http://gji.oxfordjournals.org/content/202/3/1646.full.pdf+html},
	journal = {Geophys. J. Int.},
	number = {3},
	pages = {1646-1662},
	title = {Planetary dynamos driven by helical waves -- II},
	url = {http://gji.oxfordjournals.org/content/202/3/1646.abstract},
	volume = {202},
	year = {2015},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/202/3/1646.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggv232}}

@article{Wu2015,
	author = {Wu, C. and Roberts, P. H.},
	date-added = {2016-06-14 08:58:59 +0000},
	date-modified = {2016-11-14 14:00:35 +0000},
	doi = {10.1080/03091929.2014.988711},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {1},
	pages = {84-110},
	title = {On magnetostrophic mean-field solutions of the geodynamo equations},
	volume = {109},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091929.2014.988711}}

@article{Christensen2009,
	annote = {10.1038/nature07626},
	author = {Christensen, U. R. and Holzwarth, V. and Reiners, A.},
	date = {2009/01/08/print},
	date-added = {2016-06-13 10:31:59 +0000},
	date-modified = {2016-11-14 13:43:06 +0000},
	day = {08},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {http://www.nature.com/nature/journal/v457/n7226/suppinfo/nature07626_S1.html},
	m3 = {10.1038/nature07626},
	month = {01},
	number = {7226},
	pages = {167--169},
	publisher = {Macmillan Publishers Limited. All rights reserved},
	title = {Energy flux determines magnetic field strength of planets and stars},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/nature07626},
	volume = {457},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature07626}}

@article{Ohta2016,
	author = {Ohta, K. and Kuwayama, Y. and Hirose, K. and Shimizu, K. and Ohishi, Y.},
	date = {2016/06/02/print},
	date-added = {2016-06-08 12:34:30 +0000},
	date-modified = {2016-11-14 13:50:55 +0000},
	day = {02},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {10.1038/nature17957},
	m3 = {Letter},
	month = {06},
	number = {7605},
	pages = {95--98},
	publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	title = {{Experimental determination of the electrical resistivity of iron at Earth's core conditions}},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/nature17957},
	volume = {534},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature17957}}

@article{Konopkova2016,
	author = {Kon{\^o}pkov{\'a}, Z. and McWilliams, R. S. and G{\'o}mez-P{\'e}rez, N. and Goncharov, A. F.},
	date = {2016/06/02/print},
	date-added = {2016-06-08 12:34:17 +0000},
	date-modified = {2016-11-14 13:49:16 +0000},
	day = {02},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {10.1038/nature18009},
	m3 = {Letter},
	month = {06},
	number = {7605},
	pages = {99--101},
	publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	title = {Direct measurement of thermal conductivity in solid iron at planetary core conditions},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/nature18009},
	volume = {534},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature18009}}

@article{Simitev2009,
	abstract = {{Bistability and hysteresis of magnetohydrodynamic dipolar dynamos
   generated by turbulent convection in rotating spherical fluid shells is
   demonstrated. Hysteresis appears as a transition between two distinct
   regimes of dipolar dynamos with rather different properties including a
   pronounced difference in the amplitude of the axisymmetric poloidal
   field component and in the form of the differential rotation. The
   bistability occurs from the onset of dynamo action up to about 9 times
   the critical value of the Rayleigh number for onset of convection and
   over a wide range of values of the ordinary and the magnetic Prandtl
   numbers including the value unity. Copyright (C) EPLA, 2009}},
	address = {{17, AVE DU HOGGAR, PA COURTABOEUF, BP 112, F-91944 LES ULIS CEDEX A, FRANCE}},
	affiliation = {{Simitev, RD (Reprint Author), Univ Glasgow, Dept Math, Univ Gardens, Glasgow G12 8QW, Lanark, Scotland. {[}Simitev, R. D.] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland. {[}Busse, F. H.] Univ Bayreuth, Inst Phys, D-95440 Bayreuth, Germany.}},
	article-number = {{19001}},
	author = {Simitev, R. D. and Busse, F. H.},
	author-email = {{r.simitev@maths.gla.ac.uk}},
	date-added = {2016-06-07 09:00:08 +0000},
	date-modified = {2016-06-07 09:00:08 +0000},
	doc-delivery-number = {{411ZH}},
	doi = {{10.1209/0295-5075/85/19001}},
	funding-acknowledgement = {{Royal Society {[}CG0868174]}},
	funding-text = {{The research reported in this paper has been performed in parts by the authors during their stay at the KAVLI Institute of Theoretical Physics, CA, in 2008. RDS has also been supported by the Royal Society Grant CG0868174.}},
	issn = {{0295-5075}},
	journal = {{EPL}},
	journal-iso = {{EPL}},
	keywords-plus = {{DRIVEN DYNAMOS; FLUID SHELLS; GEOMAGNETIC-FIELD; SIMULATION; GEODYNAMO; PARAMETER}},
	language = {{English}},
	month = {{JAN}},
	number = {{1}},
	number-of-cited-references = {{23}},
	publisher = {{EDP SCIENCES S A}},
	subject-category = {{Physics, Multidisciplinary}},
	times-cited = {{0}},
	title = {{Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells}},
	type = {{Article}},
	unique-id = {{ISI:000263692500042}},
	volume = {{85}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1209/0295-5075/85/19001%7D}}

@article{King2015,
	abstract = {The magnetic fields of Earth and other planets are generated by turbulent convection in the vast oceans of liquid metal within them. Although direct observation is not possible, this liquid metal circulation is thought to be dominated by the controlling influences of planetary rotation and magnetic fields through the Coriolis and Lorentz forces. Theory famously predicts that planetary dynamo systems naturally settle into the so-called magnetostrophic state, where the Coriolis and Lorentz forces partially cancel, and convection is optimally efficient. Although this magnetostrophic theory correctly predicts the strength of Earth's magnetic field, no laboratory experiments have reached the magnetostrophic regime in turbulent liquid metal convection. Furthermore, computational dynamo simulations have as yet failed to produce a magnetostrophic dynamo, which has led some to question the existence of the magnetostrophic state. Here, we present results from the first, to our knowledge, turbulent, magnetostrophic convection experiments using the liquid metal gallium. We find that turbulent convection in the magnetostrophic regime is, in fact, maximally efficient. The experimental results clarify these previously disparate results, suggesting that the dynamically optimal magnetostrophic state is the natural expression of turbulent planetary dynamo systems.},
	author = {King, E. M. and Aurnou, J. M.},
	date-added = {2016-06-07 08:35:34 +0000},
	date-modified = {2016-11-14 13:47:56 +0000},
	doi = {10.1073/pnas.1417741112},
	eprint = {http://www.pnas.org/content/112/4/990.full.pdf},
	journal = {PNAS},
	number = {4},
	pages = {990-994},
	title = {Magnetostrophic balance as the optimal state for turbulent magnetoconvection},
	url = {http://www.pnas.org/content/112/4/990.abstract},
	volume = {112},
	year = {2015},
	Bdsk-Url-1 = {http://www.pnas.org/content/112/4/990.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1073/pnas.1417741112}}

@article{Hughes2016,
	author = {Hughes, D. W. and Cattaneo, F.},
	date-added = {2016-06-07 08:35:15 +0000},
	date-modified = {2016-11-14 13:47:06 +0000},
	doi = {10.1103/PhysRevE.93.061101},
	issue = {6},
	journal = {Phys. Rev. E},
	month = {Jun},
	numpages = {5},
	pages = {061101},
	publisher = {American Physical Society},
	title = {Strong-field dynamo action in rapidly rotating convection with no inertia},
	url = {http://link.aps.org/doi/10.1103/PhysRevE.93.061101},
	volume = {93},
	year = {2016},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.93.061101},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.93.061101}}

@article{Braginsky1967,
	author = {Braginsky, S. I.},
	date-added = {2016-06-04 09:54:09 +0000},
	date-modified = {2016-11-14 13:38:22 +0000},
	journal = {Geomag. Aeron.},
	pages = {1050-1060},
	title = {Magnetic waves in the {E}arth's core},
	volume = {7},
	year = {1967}}

@article{Grote2000,
	author = {Grote, E. and Busse, F. H. and Tilgner, A.},
	date-added = {2016-06-01 13:06:19 +0000},
	date-modified = {2016-06-01 13:06:35 +0000},
	journal = {Geophysical research letters},
	number = {13},
	pages = {2001--2004},
	publisher = {Wiley Online Library},
	title = {Effects of hyperdiffusivities on dynamo simulations},
	volume = {27},
	year = {2000}}

@article{Nelson2013,
	abstract = {Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global three-dimensional magnetohydrodynamic simulations with the anelastic spherical harmonic code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3 Ω ☉ ), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.},
	author = {Nicholas J. Nelson and Benjamin P. Brown and Allan Sacha Brun and Mark S. Miesch and Juri Toomre},
	date-added = {2016-05-31 11:41:44 +0000},
	date-modified = {2016-05-31 11:42:14 +0000},
	journal = {The Astrophysical Journal},
	number = {2},
	pages = {73},
	title = {Magnetic Wreaths and Cycles in Convective Dynamos},
	url = {http://stacks.iop.org/0004-637X/762/i=2/a=73},
	volume = {762},
	year = {2013},
	Bdsk-Url-1 = {http://stacks.iop.org/0004-637X/762/i=2/a=73}}

@article{Baerenzung2010,
	author = {Baerenzung, J. and Mininni, P. D. and Pouquet, A. and Politano, H. and Ponty, Y.},
	date-added = {2016-05-31 11:40:29 +0000},
	date-modified = {2016-05-31 11:40:37 +0000},
	doi = {http://dx.doi.org/10.1063/1.3292008},
	eid = 025104,
	journal = {Physics of Fluids},
	number = {2},
	title = {Spectral modeling of rotating turbulent flows},
	url = {http://scitation.aip.org/content/aip/journal/pof2/22/2/10.1063/1.3292008},
	volume = {22},
	year = {2010},
	Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/pof2/22/2/10.1063/1.3292008},
	Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.3292008}}

@article{Baerenzung2008,
	author = {Baerenzung, J. and Politano, H. and Ponty, Y. and Pouquet, A.},
	date-added = {2016-05-31 11:39:10 +0000},
	date-modified = {2016-05-31 11:39:17 +0000},
	doi = {10.1103/PhysRevE.78.026310},
	issue = {2},
	journal = {Phys. Rev. E},
	month = {Aug},
	numpages = {11},
	pages = {026310},
	publisher = {American Physical Society},
	title = {Spectral modeling of magnetohydrodynamic turbulent flows},
	url = {http://link.aps.org/doi/10.1103/PhysRevE.78.026310},
	volume = {78},
	year = {2008},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.78.026310},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.78.026310}}

@article{Gastine2014,
	abstract = {Abstract The surface winds of Jupiter and Saturn are primarily zonal. Each planet exhibits strong prograde equatorial flow flanked by multiple alternating zonal winds at higher latitudes. The depth to which these flows penetrate has long been debated and is still an unsolved problem. Previous rotating convection models that obtained multiple high latitude zonal jets comparable to those on the giant planets assumed an incompressible (Boussinesq) fluid, which is unrealistic for gas giant planets. Later models of compressible rotating convection obtained only few high latitude jets which were not amenable to scaling analysis. Here we present 3-D numerical simulations of compressible convection in rapidly-rotating spherical shells. To explore the formation and scaling of high-latitude zonal jets, we consider models with a strong radial density variation and a range of Ekman numbers, while maintaining a zonal flow Rossby number characteristic of Saturn. All of our simulations show a strong prograde equatorial jet outside the tangent cylinder. At low Ekman numbers several alternating jets form in each hemisphere inside the tangent cylinder. To analyze jet scaling of our numerical models and of Jupiter and Saturn, we extend Rhines scaling based on a topographic β -parameter, which was previously applied to an incompressible fluid in a spherical shell, to compressible fluids. The jet-widths predicted by this modified Rhines length are found to be in relatively good agreement with our numerical model results and with cloud tracking observations of Jupiter and Saturn. },
	author = {T. Gastine and M. Heimpel and J. Wicht},
	date-added = {2016-05-31 11:38:03 +0000},
	date-modified = {2016-05-31 11:38:26 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2014.03.011},
	issn = {0031-9201},
	journal = {Physics of the Earth and Planetary Interiors},
	keywords = {Saturn interior},
	pages = {36 - 50},
	title = {Zonal flow scaling in rapidly-rotating compressible convection},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920114001009},
	volume = {232},
	year = {2014},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920114001009},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2014.03.011}}

@article{Zhang1997,
	author = {Zhang, K. and Jones, C. A.},
	date-added = {2016-05-31 11:36:23 +0000},
	date-modified = {2016-05-31 11:36:40 +0000},
	journal = {Geophysical research letters},
	number = {22},
	pages = {2869-2872},
	publisher = {Wiley Online Library},
	title = {The effect of hyperviscosity on geodynamo models},
	volume = {24},
	year = {1997}}

@article{Matsui2013,
	author = {Matsui, H. and Buffett, B. A.},
	date-added = {2016-05-31 11:31:06 +0000},
	date-modified = {2016-11-14 13:50:00 +0000},
	doi = {{10.1016/j.pepi.2013.08.004}},
	eissn = {{1872-7395}},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	month = {{OCT}},
	note = {{13th Biennial Symposium of Study of the Earth's Deep Interior (SEDI), Leeds, England, JUL 01-06, 2012}},
	number = {{SI}},
	organization = {{Royal Astron Soc; British Geophys Assoc; Mineral Soc; World Univ Network; US Natl Sci Fdn; French CNRS INSU}},
	pages = {{77-85}},
	title = {{Characterization of subgrid-scale terms in a numerical geodynamo simulation}},
	unique-id = {{ISI:000326136900009}},
	volume = {{223}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2013.08.004%7D}}

@article{Braginsky1993,
	author = {Braginsky, S. I.},
	date-added = {2016-05-30 15:13:41 +0000},
	date-modified = {2016-06-06 12:48:36 +0000},
	issn = {{0022-1392}},
	journal = {J. Geomag. Geoelectr.},
	note = {{3rd Symposium of Study of the Earths Deep Interior-Core-Mantle Boundary Region: Structure and Dynamics, Mizusawa, Japan, JUL 06-10, 1992}},
	number = {{11-12}},
	pages = {{1517-1538}},
	title = {{MAC}-oscillations in the hidden ocean of the core},
	volume = {{45}},
	year = {{1993}}}

@article{Petschel2015,
	author = {Petschel,K. and Stellmach,S. and Wilczek,M. and L{\"u}lff,J. and Hansen,U.},
	date-added = {2016-05-30 14:56:13 +0000},
	date-modified = {2016-05-30 14:57:58 +0000},
	doi = {10.1017/jfm.2015.216},
	issn = {1469-7645},
	journal = {J. Fluid. Mech.},
	month = {6},
	numpages = {23},
	pages = {395--417},
	title = {Kinetic energy transport in Rayleigh-B\'enard convection},
	url = {http://journals.cambridge.org/article_S0022112015002165},
	volume = {773},
	year = {2015},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112015002165},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2015.216}}

@article{Christensen2010ISSI,
	abstract = {Scaling laws for planetary dynamos relate the characteristic magnetic field strength, characteristic flow velocity and other properties to primary quantities such as core size, rotation rate, electrical conductivity and heat flux. Many different scaling laws have been proposed, often relying on the assumption of a balance of Coriolis force and Lorentz force in the dynamo. Their theoretical foundation is reviewed. The advent of direct numerical simulations of planetary dynamos and the ability to perform them for a sufficiently wide range of control parameters allows to test the scaling laws. The results support a magnetic field scaling that is not based on a force balance, but on the energy flux available to balance ohmic dissipation. In its simplest form, it predicts a field strength that is independent of rotation rate and electrical conductivity and proportional to the cubic root of the available energy flux. However, rotation rate controls whether the magnetic field is dipolar or multipolar. Scaling laws for velocity, heat transfer and ohmic dissipation are also discussed. The predictions of the energy-based scaling law agree well with the observed field strength of Earth and Jupiter, but for other planets they are more difficult to test or special pleading is required to explain their field strength. The scaling law also explains the very high field strength of rapidly rotating low-mass stars, which supports its rather general validity.},
	author = {Christensen, U. R.},
	date-added = {2016-05-27 20:52:29 +0000},
	date-modified = {2016-05-27 20:52:43 +0000},
	doi = {10.1007/s11214-009-9553-2},
	issn = {1572-9672},
	journal = {Space. Sci. Rev.},
	number = {1},
	pages = {565--590},
	title = {Dynamo Scaling Laws and Applications to the Planets},
	url = {http://dx.doi.org/10.1007/s11214-009-9553-2},
	volume = {152},
	year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-009-9553-2}}

@article{Julien2012,
	adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	adsurl = {http://adsabs.harvard.edu/abs/2012PhRvL.109y4503J},
	author = {{Julien}, K. and {Knobloch}, E. and {Rubio}, A.~M. and {Vasil}, G.~M.},
	date-added = {2016-05-26 13:43:17 +0000},
	date-modified = {2016-05-26 13:43:26 +0000},
	doi = {10.1103/PhysRevLett.109.254503},
	eid = {254503},
	journal = {Phys. Rev. Lett.},
	keywords = {Rotating and swirling flows, Thermal convection, Turbulent flows},
	month = dec,
	number = 25,
	pages = {254503},
	title = {{Heat Transport in Low-Rossby-Number Rayleigh-B{\'e}nard Convection}},
	volume = 109,
	year = 2012,
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.109.254503}}

@article{King2010,
	article-number = {{Q06016}},
	author = {King, E. M. and Soderlund, K. M. and Christensen, U. R. and Wicht, J. and Aurnou, J. M.},
	date-added = {2016-05-26 13:41:45 +0000},
	date-modified = {2016-11-14 13:48:45 +0000},
	doi = {{10.1029/2010GC003053}},
	issn = {{1525-2027}},
	journal = {{Geochem. Geophys. Geosyst.}},
	month = {{JUN 29}},
	researcherid-numbers = {{King, Eric/A-2274-2009}},
	title = {{Convective heat transfer in planetary dynamo models}},
	unique-id = {{ISI:000279494900002}},
	volume = {{11}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2010GC003053%7D}}

@article{Kunnen2010,
	author = {Kunnen, R. P. J. and Geurts, B. J. and Clercx, H. J. H.},
	date-added = {2016-05-26 11:58:01 +0000},
	date-modified = {2016-05-26 11:58:20 +0000},
	doi = {10.1017/S002211200999190X},
	issn = {1469-7645},
	journal = {Journal of Fluid Mechanics},
	month = {1},
	numpages = {32},
	pages = {445--476},
	title = {Experimental and numerical investigation of turbulent convection in a rotating cylinder},
	url = {http://journals.cambridge.org/article_S002211200999190X},
	volume = {642},
	year = {2010},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S002211200999190X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/S002211200999190X}}

@article{Yadav2013,
	abstract = {Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and stellar dynamos. This qualitative agreement fuels the idea that both numerical models and astrophysical objects may operate in the same asymptotic regime of dynamics. This can be tested by exploring the scaling behavior of the models. For convection-driven incompressible spherical shell dynamos with constant material properties, scaling laws had been established previously that relate flow velocity and magnetic field strength to the available power. Here we analyze 273 direct numerical simulations using the anelastic approximation, involving also cases with radius-dependent magnetic, thermal, and viscous diffusivities. These better represent conditions in gas giant planets and low-mass stars compared to Boussinesq models. Our study provides strong support for the hypothesis that both mean velocity and mean magnetic field strength scale as a function of the power generated by buoyancy forces in the same way for a wide range of conditions.},
	author = {Yadav, R. K. and Gastine, T. and Christensen, U. R. and Duarte, L.D.V.},
	date-added = {2016-05-26 09:15:22 +0000},
	date-modified = {2016-11-14 14:04:57 +0000},
	journal = {The Astrophysical Journal},
	number = {1},
	pages = {6},
	title = {Consistent Scaling Laws in Anelastic Spherical Shell Dynamos},
	url = {http://stacks.iop.org/0004-637X/774/i=1/a=6},
	volume = {774},
	year = {2013},
	Bdsk-Url-1 = {http://stacks.iop.org/0004-637X/774/i=1/a=6}}

@article{Gilman1977,
	adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	adsurl = {http://adsabs.harvard.edu/abs/1977GApFD...8...93G},
	author = {Gilman, P. A.},
	date-added = {2016-05-25 14:32:04 +0000},
	date-modified = {2016-05-25 14:32:22 +0000},
	doi = {10.1080/03091927708240373},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	keywords = {CONVECTION, ROTATION, THEORY},
	pages = {93-135},
	title = {{Nonlinear Dynamics of Boussinesq Convection in a Deep Rotating Spherical Shell. I.}},
	volume = 8,
	year = 1977,
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091927708240373}}

@article{Gastine2015,
	author = {Gastine,T. and Wicht,J. and Aurnou,J. M.},
	date-added = {2016-05-25 12:28:06 +0000},
	date-modified = {2016-11-14 13:44:59 +0000},
	doi = {10.1017/jfm.2015.401},
	issn = {1469-7645},
	journal = {Journal of Fluid Mechanics},
	month = {9},
	numpages = {44},
	pages = {721--764},
	title = {Turbulent {R}ayleigh-{B}\'enard convection in spherical shells},
	url = {http://journals.cambridge.org/article_S0022112015004012},
	volume = {778},
	year = {2015},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112015004012},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2015.401}}

@article{Christensen2008NV,
	annote = {10.1038/4541058a},
	author = {Christensen, U. R.},
	date = {2008/08/28/print},
	date-added = {2016-05-25 11:44:46 +0000},
	date-modified = {2016-11-14 13:42:07 +0000},
	day = {28},
	isbn = {0028-0836},
	journal = {Nature},
	m3 = {10.1038/4541058a},
	month = {08},
	number = {7208},
	pages = {1058--1059},
	publisher = {Nature Publishing Group},
	title = {Earth science: A sheet-metal geodynamo},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/4541058a},
	volume = {454},
	year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/4541058a}}

@phdthesis{Sheyko2014,
	author = {Sheyko, Andrey},
	date-added = {2016-05-25 11:41:06 +0000},
	date-modified = {2016-05-25 11:41:45 +0000},
	school = {ETH Z{\"u}rich},
	title = {Numerical investigations of rotating MHD in a spherical shell},
	year = {2014}}

@article{Kageyama2008,
	author = {Kageyama, A. and Miyagoshi, T. and Sato, T.},
	date-added = {2016-05-25 11:40:42 +0000},
	date-modified = {2016-11-14 13:47:31 +0000},
	day = {28},
	doi = {10.1038/nature07227},
	issn = {0028-0836},
	journal = {Nature},
	number = {7208},
	pages = {1106--1109},
	publisher = {Macmillan Publishers Limited. All rights reserved},
	title = {Formation of current coils in geodynamo simulations},
	url = {http://dx.doi.org/10.1038/nature07227},
	volume = {454},
	year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature07227}}

@article{Starchenko2002,
	abstract = {Recent studies of convection-driven dynamos in the outer core of the Earth have improved our understanding of the dynamical regime in fluid planetary cores. We consider the possible dynamical regimes in the cores of the Earth, Jupiter, and Saturn, and hence we estimate the typical velocities and magnetic fields expected in their interiors. These estimates are in reasonable agreement with observations of the large-scale internal fields of those planets. We use the fully self-consistent anelastic \{MHD\} (magnetohydrodynamics) equations which have been developed for the Earth, while the details of similar systems for Jupiter and Saturn are specified here. The known heat and composition fluxes together with magnetic, Archimedean, and Coriolis force balance give us typical velocity, entropy, and composition strengths independent of the rather poorly known transport coefficients. Those turbulent diffusion and magnetic diffusion coefficients are also estimated from mixing length theory and compared with available numerical models and standard kinematic approaches. },
	author = {S.V. Starchenko and C.A. Jones},
	date-added = {2016-05-23 08:17:52 +0000},
	date-modified = {2016-05-23 08:17:56 +0000},
	doi = {http://dx.doi.org/10.1006/icar.2002.6842},
	issn = {0019-1035},
	journal = {Icarus},
	keywords = {Saturn},
	number = {2},
	pages = {426 - 435},
	title = {Typical Velocities and Magnetic Field Strengths in Planetary Interiors},
	url = {http://www.sciencedirect.com/science/article/pii/S0019103502968429},
	volume = {157},
	year = {2002},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0019103502968429},
	Bdsk-Url-2 = {http://dx.doi.org/10.1006/icar.2002.6842}}

@misc{MagIC,
	author = {{Gastine}, T. and {Wicht}, J. and {Barik}, A. and {Putigny}, B. and {Duarte}, L.~D.~V.},
	date-added = {2016-05-22 20:09:37 +0000},
	date-modified = {2016-05-22 20:09:37 +0000},
	doi = {10.5281/zenodo.51723},
	month = may,
	title = {{MagIC v5.4, doi:10.5281/zenodo.51723}},
	url = {http://dx.doi.org/10.5281/zenodo.51723},
	year = 2016,
	Bdsk-Url-1 = {http://dx.doi.org/10.5281/zenodo.51723}}

@article{Calkins2015,
	author = {Calkins, M. A. and Julien, K. and Tobias, S. M. and Aurnou,J. M.},
	date-added = {2016-05-22 15:18:17 +0000},
	date-modified = {2016-11-14 13:40:03 +0000},
	doi = {10.1017/jfm.2015.464},
	issn = {1469-7645},
	journal = {J. Fluid. Mech.},
	month = {10},
	numpages = {24},
	pages = {143--166},
	title = {A multiscale dynamo model driven by quasi-geostrophic convection},
	url = {http://journals.cambridge.org/article_S0022112015004644},
	volume = {780},
	year = {2015},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112015004644},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2015.464}}

@article{Aurnou2015,
	abstract = {Abstract An accurate description of turbulent core convection is necessary in order to build robust models of planetary core processes. Towards this end, we focus here on the physics of rapidly rotating convection. In particular, we present a closely coupled suite of advanced asymptotically-reduced theoretical models, efficient Cartesian direct numerical simulations (DNS) and laboratory experiments. Good convergence is demonstrated between these three approaches, showing that a comprehensive understanding of the dynamics appears to be within reach in our simplified rotating convection system. The goal of this paper is to review these findings, and to discuss their possible implications for planetary cores dynamics. },
	author = {J.M. Aurnou and M.A. Calkins and J.S. Cheng and K. Julien and E.M. King and D. Nieves and K.M. Soderlund and S. Stellmach},
	date-added = {2016-05-22 14:58:54 +0000},
	date-modified = {2016-05-22 14:59:03 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2015.07.001},
	issn = {0031-9201},
	journal = {Phys. Earth. Planet. Int.},
	keywords = {Dynamo theory},
	pages = {52 - 71},
	title = {Rotating convective turbulence in Earth and planetary cores},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920115000977},
	volume = {246},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920115000977},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2015.07.001}}

@incollection{Christensen2015,
	abstract = {Abstract Numerical simulations of the geodynamo that solve the fundamental equations of convection-driven flow and magnetic induction in a rotating spherical shell successfully reproduce many observed features of the geomagnetic field. Most models employ a spectral transform method based on spherical harmonic functions. Numerical dynamos can elucidate the basic mechanism that generates the magnetic field in Earth's core. This chapter also compares in detail the morphology of the magnetic field, its power spectrum and characteristic properties of secular variations in models with that of the Earth's field. Models show that persistent non-axisymmetric features of the geomagnetic field can have their origin in the influence of Earth's mantle on the core. },
	address = {Oxford},
	author = {U.R. Christensen and J. Wicht},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2016-05-20 12:35:47 +0000},
	date-modified = {2016-11-14 13:41:11 +0000},
	doi = {http://dx.doi.org/10.1016/B978-0-444-53802-4.00145-7},
	edition = {Second Edition},
	editor = {Schubert, Gerald},
	isbn = {978-0-444-53803-1},
	keywords = {Spherical harmonics},
	pages = {245 - 277},
	publisher = {Elsevier},
	title = {8.10 - {N}umerical {D}ynamo {S}imulations},
	url = {http://www.sciencedirect.com/science/article/pii/B9780444538024001457},
	year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B9780444538024001457},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/B978-0-444-53802-4.00145-7}}

@article{Yadav2016,
	abstract = {We study rotating thermal convection in spherical shells as prototype for flow in the cores of terrestrial planets, gas planets or in stars. We base our analysis on a set of about 450 direct numerical simulations of the (magneto)hydrodynamic equations under the Boussinesq approximation. The Ekman number ranges from 10−3 to 10−5. The supercriticality of the convection reaches about 1000 in some models. Four sets of simulations are considered: non-magnetic simulations and dynamo simulations with either free-slip or no-slip flow boundary conditions. The non-magnetic setup with free-slip boundaries generates the strongest zonal flows. Both non-magnetic simulations with no-slip flow boundary conditions and self-consistent dynamos with free-slip boundaries have drastically reduced zonal-flows. Suppression of shear leads to a substantial gain in heat-transfer efficiency, increasing by a factor of 3 in some cases. Such efficiency enhancement occurs as long as the convection is significantly influenced by rotation. At higher convective driving the heat-transfer efficiency tends towards that of the classical non-rotating Rayleigh--B{\'e}nard system. Analysis of the latitudinal distribution of heat flow at the outer boundary reveals that the shear is most effective at suppressing heat-transfer in the equatorial regions. Simulations with convection zones of different thickness show that the zonal flows become less energetic in thicker shells, and, therefore, their effect on heat-transfer efficiency decreases. Furthermore, we explore the influence of the magnetic field on the non-zonal flow components of the convection. For this we compare the heat-transfer efficiency of no-slip non-magnetic cases with that of the no-slip dynamo simulations. We find that at E = 10−5 magnetic field significantly affects the convection and a maximum gain of about 30 per cent (as compared to the non-magnetic case) in heat-transfer efficiency is obtained for an Elsasser number of about 3. Our analysis motivates us to speculate that convection in the polar regions in dynamos at E = 10−5 is probably in a `magnetostrophic' regime.},
	author = {Yadav, R.K. and Gastine, T. and Christensen, U.R. and Duarte, L.D.V. and Reiners, A.},
	date-added = {2016-05-20 12:19:34 +0000},
	date-modified = {2016-11-14 14:01:53 +0000},
	doi = {10.1093/gji/ggv506},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {1120-1133},
	title = {Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells},
	url = {http://gji.oxfordjournals.org/content/204/2/1120.abstract},
	volume = {204},
	year = {2016},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/204/2/1120.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggv506}}

@incollection{Roberts1978,
	address = {London},
	author = {Roberts, P.H.},
	booktitle = {Rotating Fluids in Geophysics},
	date-added = {2016-05-20 10:45:54 +0000},
	date-modified = {2016-05-20 12:19:16 +0000},
	editor = {Roberts, P. H. and Soward, A. M.},
	pages = {421-435},
	publisher = {Academic Press},
	title = {Magnetoconvection in a rapidly rotating fluid},
	year = {1978}}

@article{Malkus1975,
	author = {Malkus, W. V. R. and Proctor, M. R. E.},
	date-added = {2016-05-20 10:39:16 +0000},
	date-modified = {2016-05-20 10:39:52 +0000},
	doi = {10.1017/S0022112075000390},
	issn = {1469-7645},
	issue = {03},
	journal = {J. Fluid. Mech.},
	month = {2},
	numpages = {27},
	pages = {417--443},
	title = {The macrodynamics of alpha-effect dynamos in rotating fluids},
	url = {http://journals.cambridge.org/article_S0022112075000390},
	volume = {67},
	year = {1975},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112075000390},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/S0022112075000390}}

@article{Soward1974,
	abstract = {A hydromagnetic dynamo model is considered. A Boussinesq, electrically conducting fluid is confined between two horizontal planes and is heated from below. The system rotates rapidly about the vertical axis with constant angular velocity. It is supposed that instability first sets in as stationary convection characterized by a small horizontal length scale. In preliminary calculations the Lorentz force is neglected so that the magnetic induction equation and the equation of motion are decoupled. The possibility that motions occurring at the onset of instability may sustain magnetic fields is thus reduced to a kinematic dynamo problem. Moreover, the existence of two length scales introduces simplifications which enable the problem to be studied by well-known techniques. The effect of the Lorentz force on the finite amplitude dynamics of the system is investigated also. Since only weak magnetic fields are considered the kinetic energy of the motion is fixed by other considerations and it is only the fine structure of the flow that is influenced by the magnetic field. A set of nonlinear equations, which govern the evolution of the hydromagnetic dynamo, are derived from an asymptotic analysis. The equations are investigated in detail both analytically and numerically. In spite of serious doubts concerning the existence of sufficiently complex stable motions, stable periodic dynamos are shown to exist. An interesting analytic solution of these equations, which may be pertinent to other problems arising from finite-amplitude Benard convection, is presented in the final section.},
	author = {Soward, A. M.},
	date-added = {2016-05-20 10:37:23 +0000},
	date-modified = {2016-05-20 10:37:35 +0000},
	doi = {10.1098/rsta.1974.0003},
	eprint = {http://rsta.royalsocietypublishing.org/content/275/1256/611.full.pdf},
	issn = {0080-4614},
	journal = {Phil. Trans. Roy. Soc. A},
	number = {1256},
	pages = {611--646},
	publisher = {The Royal Society},
	title = {A Convection-Driven Dynamo: I. The Weak Field Case},
	url = {http://rsta.royalsocietypublishing.org/content/275/1256/611},
	volume = {275},
	year = {1974},
	Bdsk-Url-1 = {http://rsta.royalsocietypublishing.org/content/275/1256/611},
	Bdsk-Url-2 = {http://dx.doi.org/10.1098/rsta.1974.0003}}

@article{Hollerbach1996,
	abstract = {I trace the development of geodynamo theory leading from Larmor's original hypothesis (Larmor, 1919, Rep. Br. Assoc. Adv. Sci., A, 159--160) to the present. I consider a number of kinematic results, from Cowling's proof (Cowling, 1934, Mon. Not. R. Astron. Soc., 94: 39--48) that two-dimensional dynamo action is not possible, to the proofs by Backus (1958, Ann. Phys., 4: 372--447) and Herzenberg (1958, Philos. Trans. R. Soc. London, Ser. A, 250: 543--585) that three-dimensional dynamo action is possible. I next turn to various mean-field and convective models in which the fluid flow is no longer kinematically prescribed, but is itself dynamically determined. In these dynamical models, I describe the distinction between weak and strong field regimes that comes about owing to the effect of the field on the pattern of convection in a rapidly rotating system. I consider the dynamics of Taylor's constraint (Taylor, 1963, Proc. R. Soc. London, Ser. A, 274: 274--283), and demonstrate how it makes the analysis of the geophysically appropriate strong field regime particularly difficult. },
	author = {Hollerbach, R.},
	date-added = {2016-05-20 10:28:23 +0000},
	date-modified = {2016-11-14 13:46:46 +0000},
	doi = {http://dx.doi.org/10.1016/S0031-9201(96)03185-8},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	number = {3--4},
	pages = {163 - 185},
	title = {On the theory of the geodynamo},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920196031858},
	volume = {98},
	year = {1996},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920196031858},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0031-9201(96)03185-8}}

@article{Takahashi2012,
	author = {Takahashi,F. and Shimizu,H.},
	date-added = {2016-05-17 17:05:49 +0000},
	date-modified = {2016-05-17 17:06:06 +0000},
	doi = {10.1017/jfm.2012.154},
	issn = {1469-7645},
	journal = {J. Fluid. Mech.},
	month = {6},
	numpages = {23},
	pages = {228--250},
	title = {A detailed analysis of a dynamo mechanism in a rapidly rotating spherical shell},
	url = {http://journals.cambridge.org/article_S0022112012001541},
	volume = {701},
	year = {2012},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112012001541},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2012.154}}

@article{Livermore2016ns,
	author = {Livermore, P. W. and Bailey, L. M. and Hollerbach, R.},
	date-added = {2016-05-17 13:39:09 +0000},
	date-modified = {2017-12-12 15:22:35 +0000},
	journal = {Sci. Rep.},
	pages = {22812},
	title = {A comparison of no-slip, stress-free and inviscid models of rapidly rotating fluid in a spherical shell},
	volume = {6},
	year = {2016}}

@article{Yadav2013FS,
	author = {Yadav, R. K. and Gastine, T. and Christensen, U. R.},
	date-added = {2016-05-17 13:28:29 +0000},
	date-modified = {2016-11-14 14:01:20 +0000},
	doi = {http://dx.doi.org/10.1016/j.icarus.2013.02.030},
	issn = {0019-1035},
	journal = {Icarus},
	keywords = {interior},
	number = {1},
	pages = {185 - 193},
	title = {Scaling laws in spherical shell dynamos with free-slip boundaries},
	url = {http://www.sciencedirect.com/science/article/pii/S0019103513001188},
	volume = {225},
	year = {2013},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0019103513001188},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.icarus.2013.02.030}}

@article{Soderlund2015,
	abstract = {Fluid motions within planetary cores generate magnetic fields through dynamo action. These core processes are driven by thermo-compositional convection subject to the competing influences of rotation, which tends to organize the flow into axial columns, and the Lorentz force, which tends to inhibit the relative movement of the magnetic field and the fluid. It is often argued that these forces are predominant and approximately equal in planetary cores; we test this hypothesis using a suite of numerical geodynamo models to calculate the Lorentz to Coriolis force ratio directly. Our results show that this ratio can be estimated by                                                                                                                                                                       $\Lambda$                                                                          d                                                                          ∗                                                                    ≃                                                                        $\Lambda$                                                                          i                                                                    R                                                                        m                                                                          −                          1                          /                          2                                                                                                      						{\$}{\backslash}Lambda {\_}{\{}d{\}}^{\{}*{\}} {\backslash}simeq {\backslash}Lambda {\_}{\{}i{\}} Rm^{\{}-1/2{\}}{\$}					                 ($\Lambda$				                                      i                 is the traditionally defined Elsasser number for imposed magnetic fields and Rm is the system-scale ratio of magnetic induction to magnetic diffusion). Best estimates of core flow speeds and magnetic field strengths predict the geodynamo to be in magnetostrophic balance where the Lorentz and Coriolis forces are comparable. The Lorentz force may also be significant, i.e., within an order of magnitude of the Coriolis force, in the Jovian interior. In contrast, the Lorentz force is likely to be relatively weak in the cores of Saturn, Uranus, Neptune, Ganymede, and Mercury.},
	author = {Soderlund, K. M. and Sheyko, A. and King, E. M. and Aurnou, J. M.},
	date-added = {2016-05-12 14:34:31 +0000},
	date-modified = {2016-11-14 13:58:17 +0000},
	doi = {10.1186/s40645-015-0054-5},
	issn = {2197-4284},
	journal = {Progress in Earth and Planetary Science},
	number = {1},
	pages = {1--10},
	title = {{The competition between Lorentz and Coriolis forces in planetary dynamos}},
	url = {http://dx.doi.org/10.1186/s40645-015-0054-5},
	volume = {2},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1186/s40645-015-0054-5}}

@article{King2009,
	annote = {10.1038/nature07647},
	author = {King, Eric M. and Stellmach, Stephan and Noir, Jerome and Hansen, Ulrich and Aurnou, Jonathan M.},
	date = {2009/01/15/print},
	date-added = {2016-05-10 16:07:09 +0000},
	date-modified = {2016-05-10 16:07:16 +0000},
	day = {15},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {http://www.nature.com/nature/journal/v457/n7227/suppinfo/nature07647_S1.html},
	m3 = {10.1038/nature07647},
	month = {01},
	number = {7227},
	pages = {301--304},
	publisher = {Macmillan Publishers Limited. All rights reserved},
	title = {Boundary layer control of rotating convection systems},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/nature07647},
	volume = {457},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature07647}}

@article{Gillet2006,
	author = {Gillet, N. and Jones, C. A.},
	date-added = {2016-05-10 16:06:44 +0000},
	date-modified = {2016-05-10 16:07:04 +0000},
	doi = {10.1017/S0022112006009219},
	issn = {1469-7645},
	journal = {J. Fluid. Mech.},
	month = {5},
	numpages = {27},
	pages = {343--369},
	title = {The quasi-geostrophic model for rapidly rotating spherical convection outside the tangent cylinder},
	url = {http://journals.cambridge.org/article_S0022112006009219},
	volume = {554},
	year = {2006},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112006009219},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/S0022112006009219}}

@article{Stellmach2014,
	author = {Stellmach, S. and Lischper, M. and Julien, K. and Vasil, G. and Cheng, J. S. and Ribeiro, A. and King, E. M. and Aurnou, J. M.},
	date-added = {2016-05-10 16:06:32 +0000},
	date-modified = {2016-05-10 16:06:39 +0000},
	doi = {10.1103/PhysRevLett.113.254501},
	issue = {25},
	journal = {Phys. Rev. Lett.},
	month = {Dec},
	numpages = {5},
	pages = {254501},
	publisher = {American Physical Society},
	title = {Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers versus Interior Dynamics},
	url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.254501},
	volume = {113},
	year = {2014},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.113.254501},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.113.254501}}

@article{Aurnou2007,
	author = {J. M. Aurnou},
	date-added = {2016-05-10 16:05:51 +0000},
	date-modified = {2016-05-10 16:06:03 +0000},
	doi = {10.1080/03091920701472568},
	eprint = {http://dx.doi.org/10.1080/03091920701472568},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {5-6},
	pages = {327-345},
	title = {Planetary core dynamics and convective heat transfer scaling},
	url = {http://dx.doi.org/10.1080/03091920701472568},
	volume = {101},
	year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091920701472568}}

@article{Dormy2016,
	author = {Dormy, E.},
	date-added = {2016-05-04 13:47:04 +0000},
	date-modified = {2016-11-14 13:44:10 +0000},
	doi = {10.1017/jfm.2015.747},
	issn = {1469-7645},
	journal = {J. Fluid. Mech.},
	month = {2},
	numpages = {14},
	pages = {500--513},
	title = {Strong-field spherical dynamos},
	url = {http://journals.cambridge.org/article_S0022112015007478},
	volume = {789},
	year = {2016},
	Bdsk-Url-1 = {http://journals.cambridge.org/article_S0022112015007478},
	Bdsk-Url-2 = {http://dx.doi.org/10.1017/jfm.2015.747}}

@article{Cheng2015,
	author = {J.S. Cheng and J.M. Aurnou},
	date-added = {2016-05-04 13:00:50 +0000},
	date-modified = {2016-05-04 13:00:50 +0000},
	doi = {http://dx.doi.org/10.1016/j.epsl.2015.12.004},
	issn = {0012-821X},
	journal = {Earth and Planetary Science Letters},
	keywords = {rotating convection},
	pages = {121 - 129},
	title = {Tests of diffusion-free scaling behaviors in numerical dynamo datasets},
	url = {http://www.sciencedirect.com/science/article/pii/S0012821X15007670},
	volume = {436},
	year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X15007670},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.epsl.2015.12.004}}

@article{King2013,
	author = {King, E. M. and Buffett, B. A.},
	date-added = {2016-05-04 13:00:46 +0000},
	date-modified = {2016-11-14 13:48:14 +0000},
	doi = {{10.1016/j.epsl.2013.04.001}},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Lett.},
	month = {{JUN}},
	pages = {{156-162}},
	title = {{Flow speeds and length scales in geodynamo models: The role of viscosity}},
	unique-id = {{ISI:000321077400016}},
	volume = {{371}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2013.04.001%7D}}

@article{Oruba2014,
	author = {Oruba, L. and Dormy, E.},
	date-added = {2016-05-04 13:00:43 +0000},
	date-modified = {2016-05-04 13:00:43 +0000},
	doi = {{10.1093/gji/ggu159}},
	eissn = {{1365-246X}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{AUG}},
	number = {{2}},
	pages = {{828-847}},
	title = {{Predictive scaling laws for spherical rotating dynamos}},
	unique-id = {{ISI:000339717700012}},
	volume = {{198}},
	year = {{2014}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggu159%7D}}

@article{Stelzer2013,
	abstract = {{Earth's magnetic field is generated by processes in the electrically
   conducting, liquid outer core, subsumed under the term `geodynamo'. In
   the last decades, great effort has been put into the numerical
   simulation of core dynamics following from the magnetohydrodynamic
   equations. However, the numerical simulations are far from Earth's core
   in terms of several control parameters. Different scaling analyses found
   simple scaling laws for quantities like heat transport, flow velocity,
   magnetic field strength and magnetic dissipation time.
   We use an extensive data set of 116 numerical dynamo models compiled by
   Christensen and co-workers to analyse these scalings from a rigorous
   model selection point of view. Our method of choice is leave-one-out
   cross-validation which rates models according to their predictive
   abilities. In contrast to earlier results, we find that diffusive
   processes are not negligible for the flow velocity and magnetic field
   strength in the numerical dynamos. Also the scaling of the magnetic
   dissipation time turns out to be more complex than previously suggested.
   Assuming that the processes relevant in the numerical models are the
   same as in Earth's core, we use this scaling to estimate an Ohmic
   dissipation of 3-8 TW for the core. This appears to be consistent with
   recent high core mantle boundary heat flux scenarios.}},
	author = {Stelzer, Z. and Jackson, A.},
	date-added = {2016-05-04 13:00:41 +0000},
	date-modified = {2016-05-04 13:00:41 +0000},
	doi = {{10.1093/gji/ggt083}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUN}},
	number = {{3}},
	pages = {{1265-1276}},
	title = {{Extracting scaling laws from numerical dynamo models}},
	unique-id = {{ISI:000319482100015}},
	volume = {{193}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggt083%7D}}

@article{Hulot1997,
	author = {Hulot, G and Khokhlov, A and LeMouel, JL},
	date-added = {2016-04-04 15:09:45 +0000},
	date-modified = {2016-04-04 15:09:55 +0000},
	doi = {{10.1111/j.1365-246X.1997.tb01587.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{MAY}},
	number = {{2}},
	pages = {{347-354}},
	researcherid-numbers = {{Hulot, Gauthier/A-5627-2011}},
	title = {{Uniqueness of mainly dipolar magnetic fields recovered from directional data}},
	unique-id = {{ISI:A1997XA22900011}},
	volume = {{129}},
	year = {{1997}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.1997.tb01587.x%7D}}

@article{Jones2011,
	abstract = {Benchmark solutions for fully nonlinear anelastic compressible convection and dynamo action in a rotating spherical shell are proposed. Three benchmarks are specified. The first is a purely hydrodynamic case, which is steady in a uniformly drifting frame. The second is a self-excited saturated dynamo solution, also steady in a drifting frame. The third is again a self-excited dynamo but is unsteady in time, and it has a higher Rayleigh number than the steady dynamo benchmark. Four independent codes have been tested against these benchmarks, and very satisfactory agreement has been found. This provides an accurate reference standard against which new anelastic codes can be tested. },
	author = {C.A. Jones and P. Boronski and A.S. Brun and G.A. Glatzmaier and T. Gastine and M.S. Miesch and J. Wicht},
	date-added = {2016-04-04 15:01:57 +0000},
	date-modified = {2016-04-04 15:02:01 +0000},
	doi = {http://dx.doi.org/10.1016/j.icarus.2011.08.014},
	issn = {0019-1035},
	journal = {Icarus},
	keywords = {Interiors},
	number = {1},
	pages = {120 - 135},
	title = {Anelastic convection-driven dynamo benchmarks},
	url = {http://www.sciencedirect.com/science/article/pii/S0019103511003319},
	volume = {216},
	year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0019103511003319},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.icarus.2011.08.014}}

@article{Jonkers:2003qy,
	author = {Jonkers, A. R. T. and Jackson, A. and Murray, A.},
	date-added = {2016-03-31 20:16:23 +0000},
	date-modified = {2016-03-31 20:27:24 +0000},
	journal = {Rev. Geophysics},
	number = {2},
	pages = {1006},
	title = {Four centuries of geomagnetic secular variation from historical records},
	volume = {41},
	year = {2003}}

@article{Civet:2015oz,
	author = {Civet, F. and Th{\'e}bault, Erwan and Verhoeven, O. and Langlais, B. and Saturnino, D.},
	date-added = {2016-03-29 22:22:13 +0000},
	date-modified = {2016-03-29 22:24:40 +0000},
	journal = {Geophys. Res. Let.},
	pages = {3338-3346},
	title = {Electrical conductivity of the {E}arth's mantle from the first {S}warm magnetic field measurements},
	volume = {42},
	year = {2015}}

@article{Sabaka2015,
	author = {Sabaka, T. J. and Olsen, N. and Tyler, R. H. and Kuvshinov, A.},
	date-added = {2016-03-29 21:38:35 +0000},
	date-modified = {2019-05-17 11:17:04 +0200},
	journal = {Geophys. J. Int.},
	pages = {1596-1626},
	title = {{CM5}, a pre-{\it Swarm} comprehensive geomagnetic field model derived from over 12 yr of {CHAMP}, {\OE}rsted, {SAC-C} and observatory data},
	volume = {200},
	year = {2015}}

@article{Jackson:1996xy,
	author = {Jackson, A.},
	date-added = {2016-03-29 21:25:25 +0000},
	date-modified = {2016-03-29 21:26:34 +0000},
	journal = {Phys. Earth Planet. Int.},
	pages = {283--302},
	title = {Bounding the long-wavelength crustal magnetic field},
	volume = {98},
	year = {1996}}

@article{Paek:2012fu,
	author = {Paek, H. and Huang, H.-P.},
	date-added = {2016-03-29 14:23:52 +0000},
	date-modified = {2016-03-29 14:25:57 +0000},
	journal = {{J. Geophys. Res.}},
	pages = {D20102},
	title = {A comparison of the interannual variability in atmospheric angular momentum and length-of-day using multiple reanalysis data sets},
	volume = {117},
	year = {2012}}

@article{ORourke2016,
	author = {O'Rourke, Joseph G. and Stevenson, David J.},
	date = {2016/01/21/print},
	date-added = {2016-03-30 12:41:23 +0000},
	date-modified = {2016-03-30 12:41:30 +0000},
	day = {21},
	isbn = {0028-0836},
	journal = {Nature},
	l3 = {10.1038/nature16495},
	m3 = {Letter},
	month = {01},
	number = {7586},
	pages = {387--389},
	publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	title = {Powering Earth's dynamo with magnesium precipitation from the core},
	ty = {JOUR},
	url = {http://dx.doi.org/10.1038/nature16495},
	volume = {529},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature16495}}

@article{Aubert2015S,
	author = {Aubert, Julien},
	date-added = {2016-03-29 11:31:12 +0000},
	date-modified = {2016-03-29 11:31:12 +0000},
	doi = {10.1126/science.aac6224},
	eprint = {http://science.sciencemag.org/content/349/6247/475.full.pdf},
	issn = {0036-8075},
	journal = {Science},
	number = {6247},
	pages = {475--476},
	publisher = {American Association for the Advancement of Science},
	title = {Ancient planetary dynamos, take two},
	url = {http://science.sciencemag.org/content/349/6247/475},
	volume = {349},
	year = {2015},
	Bdsk-Url-1 = {http://science.sciencemag.org/content/349/6247/475},
	Bdsk-Url-2 = {http://dx.doi.org/10.1126/science.aac6224}}

@article{Kuang:1993yu,
	author = {Kuang, W. and Bloxham, J.},
	date-added = {2016-03-28 12:17:59 +0000},
	date-modified = {2016-03-28 12:20:33 +0000},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	pages = {161--195},
	title = {On the effect of boundary topography on flow in the {E}arth's core},
	volume = {72},
	year = {1993}}

@incollection{Bizouard:2009om,
	author = {Bizouard, C. and Gambis, D.},
	booktitle = {Geodetic Reference Frames},
	date-added = {2016-03-25 13:57:50 +0000},
	date-modified = {2016-04-04 14:41:18 +0000},
	editor = {Drewes, H.},
	pages = {265--270},
	publisher = {Springer},
	title = {The combined solution {CO4} for {E}arth orientation parameters consistent with {I}nternational {T}errestrial {R}eference {F}rame 2005},
	year = {2009}}

@article{Mitrovica:2015il,
	author = {Mitrovica, J. X. and Hay, C. C. and Morrow, E. and Kopp, R. E. and Dumberry, M. and Stanley, S.},
	date-added = {2016-03-25 13:49:17 +0000},
	date-modified = {2016-03-25 13:52:37 +0000},
	journal = {Science Advances},
	pages = {e1500679},
	title = {Reconciling past changes in {E}arth's rotation with 20th century global sea-level rise: {R}esolving {M}unk's enigma},
	volume = {11},
	year = {2015}}

@article{Chao:2014lr,
	author = {Chao, B. F. and Chung, W. and Shih, Z and Hsieh, Y.},
	date-added = {2016-03-25 13:35:24 +0000},
	date-modified = {2016-03-25 13:37:13 +0000},
	journal = {Terra Nova},
	pages = {260--264},
	title = {Earth's rotation variations: a wavelet analysis},
	volume = {26},
	year = {2014}}

@article{Gillet:2011bs,
	author = {Gillet, N. and Schaeffer, Nathana{\"e}l and Jault, D.},
	date-added = {2016-03-25 13:31:47 +0000},
	date-modified = {2016-03-25 13:33:34 +0000},
	journal = {Phys. Earth. Planet. Int.},
	pages = {380--390},
	title = {Rationale and geophysical evidence for quasi-geostrophic rapid dynamics within the {E}arth's outer core},
	volume = {187},
	year = {2011}}

@article{Gross:2004ek,
	author = {Gross, R. S. and Fukumori, I. and Menemenlis, D. and Gegout, P.},
	date-added = {2016-03-25 13:21:37 +0000},
	date-modified = {2016-03-25 13:24:14 +0000},
	journal = {J. Geophys. Res.},
	pages = {B01406},
	title = {Atmospheric and oceanic excitation of length-of-day variations during 1980-2000},
	volume = {109},
	year = {2004}}

@article{Stephenson:1995qd,
	author = {Stephenson, F. R. and Morrison, L. V.},
	date-added = {2016-03-25 13:09:08 +0000},
	date-modified = {2016-03-25 13:19:47 +0000},
	journal = {Phil. Trans. Roy. Soc. A},
	pages = {165--202},
	title = {Long-term fluctuations in the {E}arth's rotation: 700 {BC} to {AD} 1990},
	volume = {351},
	year = {1995}}

@incollection{Gross:2015yu,
	author = {Gross, R. S.},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2016-03-25 11:14:58 +0000},
	date-modified = {2016-03-25 11:19:06 +0000},
	editor = {Schubert, G.},
	pages = {215--261},
	publisher = {Elsevier},
	title = {Earth rotation variations - {L}ong period},
	volume = {3},
	year = {2015}}

@article{Hori2015,
	author = {Hori, K. and Jones, C. A. and Teed, R. J.},
	date-added = {2016-03-23 13:45:54 +0000},
	date-modified = {2016-03-23 13:46:05 +0000},
	doi = {{10.1002/2015GL064733}},
	eissn = {{1944-8007}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	month = {{AUG 28}},
	number = {{16}},
	pages = {{6622-6629}},
	title = {{Slow magnetic Rossby waves in the Earth's core}},
	unique-id = {{ISI:000363410800012}},
	volume = {{42}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/2015GL064733%7D}}

@article{Teed2015,
	author = {Teed, R. J. and Jones, C. A. and Tobias, S. M.},
	date-added = {2016-03-23 13:45:37 +0000},
	date-modified = {2016-11-14 13:59:32 +0000},
	doi = {{10.1016/j.epsl.2015.02.045}},
	eissn = {{1385-013X}},
	issn = {{0012-821X}},
	journal = {Earth Plan. Sci. Lett.},
	month = {{JUN 1}},
	pages = {{22-31}},
	title = {{The transition to Earth-like torsional oscillations in magnetoconvection simulations}},
	unique-id = {{ISI:000353852500024}},
	volume = {{419}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2015.02.045%7D}}

@article{Davidson2013,
	abstract = {We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed by Christensen and Aubert. The main difference is that, in view of the small value of the Rossby number in planetary cores, we insist that the non-linear inertial term,  ${\boldsymbol u} \cdot \nabla {\boldsymbol u}$, is negligible. This changes the exponents in the power-laws which relate the various properties of the fluid dynamo to the planetary dipole moment and rotation rate. Our scaling laws are consistent with the available numerical evidence.},
	author = {Davidson, P. A.},
	date-added = {2016-03-22 14:57:45 +0000},
	date-modified = {2016-11-14 13:43:53 +0000},
	doi = {10.1093/gji/ggt167},
	journal = {Geophys. J. Int.},
	number = {1},
	pages = {67-74},
	title = {Scaling laws for planetary dynamos},
	volume = {195},
	year = {2013},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/195/1/67.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggt167}}

@article{Matsui2016,
	author = {Hiroaki Matsui and others},
	date-added = {2016-03-22 14:39:28 +0000},
	date-modified = {2019-02-01 10:30:14 +0100},
	journal = {{Geochem. Geophys. Geosyst.}},
	pages = {1586-1607},
	title = {Performance benchmarks for a next generation numerical dynamo model},
	volume = {17},
	year = {2016}}

@article{Thebault2015b,
	abstract = {The magnetic field of the Earth's lithosphere arises from rock magnetization contrasts that were shaped over geological times. The field can be described mathematically in spherical harmonics or with distributions of magnetization. We exploit this dual representation and assume that the lithospheric field is induced by spatially varying susceptibility values within a shell of constant thickness. By introducing a statistical assumption about the power spectrum of the susceptibility, we then derive a statistical expression for the spatial power spectrum of the crustal magnetic field for the spatial scales ranging from 60 to 2500 km. This expression depends on the mean induced magnetization, the thickness of the shell, and a power law exponent for the power spectrum of the susceptibility. We test the relevance of this form with a misfit analysis to the observational NGDC-720 lithospheric magnetic field model power spectrum. This allows us to estimate a mean global apparent induced magnetization value between 0.3 and 0.6 A m−1, a mean magnetic crustal thickness value between 23 and 30 km, and a root mean square for the field value between 190 and 205 nT at 95 per cent. These estimates are in good agreement with independent models of the crustal magnetization and of the seismic crustal thickness. We carry out the same analysis in the continental and oceanic domains separately. We complement the misfit analyses with a Kolmogorov--Smirnov goodness-of-fit test and we conclude that the observed power spectrum can be each time a sample of the statistical one.},
	author = {Th{\'e}bault, E. and Vervelidou, F.},
	date-added = {2016-03-21 13:54:05 +0000},
	date-modified = {2016-03-21 13:54:26 +0000},
	doi = {10.1093/gji/ggu463},
	eprint = {http://gji.oxfordjournals.org/content/201/2/605.full.pdf+html},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {605-620},
	title = {A statistical spatial power spectrum of the Earth's lithospheric magnetic field},
	url = {http://gji.oxfordjournals.org/content/201/2/605.abstract},
	volume = {201},
	year = {2015},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/201/2/605.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggu463}}

@article{Holschneider2016,
	author = {Holschneider, M. and Lesur, V. and Mauerberger, S. and Baerenzung, J.},
	date-added = {2016-03-21 10:43:17 +0000},
	date-modified = {2016-04-01 11:39:59 +0000},
	journal = {J. Geophys. Res.},
	title = {Correlation based modelling and separation of geomagnetic field components},
	year = {in press}}

@article{LeGoff2004,
	abstract = {We have developed a new three-axis vibrating sample magnetometer, which allows continuous high-temperature magnetization measurements of individual cylindrical ∼0.75 cm3 samples up to ∼650 $\,^{\circ}$C and the acquisition of thermoremanent magnetization (TRM) in any direction and field intensity up to 200 μT. We propose a fast (less than 2.5 h) automated experimental procedure adapted from Boyd's [Nature 319 (1986) 208--209] modified version of the Thellier and Thellier [Ann. Geophys. 15 (1959) 285--376] method which provides continuous intensity determinations over a large (typically 300 $\,^{\circ}$C) temperature interval for each sample. This procedure allows one to take into account both the cooling rate dependence of \{TRM\} acquisition and anisotropy of TRM. Several examples of analyses of ancient magnetization demonstrate the quality and reliability of the data and illustrate the promising potential of this new instrument in paleo- and archeomagnetism. },
	author = {Le Goff, M. and Gallet, Y.},
	date-added = {2016-03-17 15:15:39 +0000},
	date-modified = {2016-03-17 15:16:26 +0000},
	doi = {http://dx.doi.org/10.1016/j.epsl.2004.10.025},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Lett.},
	keywords = {anisotropy},
	number = {1--2},
	pages = {31 - 43},
	title = {A new three-axis vibrating sample magnetometer for continuous high-temperature magnetization measurements: applications to paleo- and archeo-intensity determinations},
	url = {http://www.sciencedirect.com/science/article/pii/S0012821X04006326},
	volume = {229},
	year = {2004},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X04006326},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.epsl.2004.10.025}}

@article{Roberts2007,
	author = {Roberts, P. H. and Yu, Z. J. and Russell, C. T.},
	date-added = {2016-03-16 14:25:17 +0000},
	date-modified = {2016-03-16 14:25:17 +0000},
	doi = {{10.1080/03091920601083820}},
	issn = {{0309-1929}},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	month = {{FEB}},
	number = {{1}},
	pages = {{11-35}},
	title = {On the 60-year signal from the core},
	unique-id = {{ISI:000246109700002}},
	volume = {{101}},
	year = {{2007}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091920601083820%7D}}

@article{Cebron2014,
	abstract = {Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star τ-boo, Mars, or the early Moon. By simulating a small local patch of a rotating fluid, Barker & Lithwick have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested in the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results and numerical results obtained in a truly deformed ellipsoid, which confirms the presence of elliptical instability. We then perform magnetohydrodynamic simulations and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating a dipole-dominated large-scale magnetic field in global simulations of a fluid rotating sphere.},
	author = {D. C{\'e}bron and R. Hollerbach},
	date-added = {2016-03-16 14:13:53 +0000},
	date-modified = {2016-03-16 14:13:59 +0000},
	journal = {The Astrophysical Journal Letters},
	number = {1},
	pages = {L25},
	title = {Tidally Driven Dynamos in a Rotating Sphere},
	url = {http://stacks.iop.org/2041-8205/789/i=1/a=L25},
	volume = {789},
	year = {2014},
	Bdsk-Url-1 = {http://stacks.iop.org/2041-8205/789/i=1/a=L25}}

@article{Labbe2015,
	author = {F. Labb{\'e} and D. Jault and N. Gillet},
	date-added = {2016-03-16 14:13:37 +0000},
	date-modified = {2016-03-16 14:13:49 +0000},
	doi = {10.1080/03091929.2015.1094569},
	eprint = {http://dx.doi.org/10.1080/03091929.2015.1094569},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {6},
	pages = {587-610},
	title = {On magnetostrophic inertia-less waves in quasi-geostrophic models of planetary cores},
	url = {http://dx.doi.org/10.1080/03091929.2015.1094569},
	volume = {109},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/03091929.2015.1094569}}

@article{Schaeffer2012,
	abstract = {Alfv{\'e}n waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case, Pm = 1, there is no reflection on an insulating, no-slip boundary, and the incoming wave energy is entirely dissipated in the boundary layer.We investigate the consequences of this remarkable behaviour for the numerical modelling of torsional Alfv{\'e}n waves (also known as torsional oscillations), which represent a special class of Alfv{\'e}n waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm ≪ 1, these waves are reflected at the core equator, but they are entirely absorbed for Pm = 1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm ≥ 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal modes.},
	author = {Schaeffer, Nathana{\"e}l and Jault, Dominique and Cardin, Philippe and Drouard, Marie},
	date-added = {2016-03-16 13:56:12 +0000},
	date-modified = {2016-03-16 13:56:49 +0000},
	doi = {10.1111/j.1365-246X.2012.05611.x},
	eprint = {http://gji.oxfordjournals.org/content/191/2/508.full.pdf+html},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {508-516},
	title = {On the reflection of Alfv{\'e}n waves and its implication for Earth's core modelling},
	url = {http://gji.oxfordjournals.org/content/191/2/508.abstract},
	volume = {191},
	year = {2012},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/191/2/508.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1111/j.1365-246X.2012.05611.x}}

@article{Lesur2015,
	abstract = {Recent first principles calculations of the Earth's outer core thermal and electrical conductivities have raised their values by a factor of three. This has significant implications for geodynamo operation, in particular, forcing the development of a stably stratified layer at the core--mantle boundary (CMB). This study seeks to test the hypothesis of a stably stratified layer in the uppermost core by analysing geomagnetic observations made by the CHAMP satellite. An inversion method is utilized that jointly solves for the time-dependent main field and the core surface flow, where we assume the temporal variability of the main field, its secular variation (SV), to be entirely due to advective motion within the liquid outer core. The results show that a large-scale pure toroidal flow, consistent with a stably stratified layer atop the outer core, is not compatible with the observed magnetic field during the CHAMP era. However, allowing just a small amount of poloidal flow leads to a model fitting the observations satisfactorily. As this poloidal flow component is large scale, within a predominantly toroidal, essentially tangentially geostrophic flow, it is compatible with a stably stratified upper outer core. Further, our assumption of little or no diffusive SV may not hold, and a small amount of SV generated locally by diffusion might lead to a large-scale pure toroidal flow providing an acceptable fit to the data.},
	author = {Lesur, V. and Whaler, K. and Wardinski, I.},
	date-added = {2016-03-16 13:03:11 +0000},
	date-modified = {2017-03-06 16:58:44 +0000},
	doi = {10.1093/gji/ggv031},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {929-946},
	title = {Are geomagnetic data consistent with stably stratified flow at the core--mantle boundary?},
	volume = {201},
	year = {2015},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/201/2/929.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggv031}}

@article{Gillet2015,
	author = {Gillet, N. and Jault, D. and Finlay, C. C.},
	date-added = {2016-03-16 08:58:49 +0000},
	date-modified = {2016-03-16 08:58:49 +0000},
	doi = {10.1002/2014JB011786s},
	journal = {J. Geophys. Res.},
	pages = {3991-4013},
	title = {{Planetary gyre, time-dependent eddies, torsional waves and equatorial jets at the Earth's core surface}},
	volume = {120},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/2014JB011786s}}

@article{Buffett2016,
	abstract = {Earth's liquid core hosts a diverse set of waves with periods ranging from days to thousands of years. One class of waves with periods of several decades is known to arise from an interplay between magnetic, Archimedes and Coriolis forces. These so-called MAC waves are thought to be relevant for interpreting historical fluctuations in the geomagnetic field. In this study, we show that MAC waves provide a good description of time-dependent zonal flow at the top of the core. The same collection of waves also offers a simple explanation for observed fluctuations in the dipole field. Both of these predictions require a stratified layer at the top of the core with a thickness of 130--140 km and a buoyancy frequency comparable to Earth's rotation rate. We extend these predictions to include changes in the length of day (LOD) and find that MAC waves can account for about half of the observed fluctuation at decadal periods. Larger fluctuations are possible when electromagnetic stresses couple MAC waves to flow in the interior of the core. In fact, an idealized model for the coupled motion overestimates the LOD fluctuations, probably reflecting limitations in this idealized model. Our results offer support for stable stratification at the top of the core and suggest a common origin for decadal fluctuations in the geomagnetic field and the LOD.},
	author = {Buffett, Bruce and Knezek, Nicholas and Holme, Richard},
	date-added = {2016-03-16 08:51:29 +0000},
	date-modified = {2016-03-16 13:03:44 +0000},
	doi = {10.1093/gji/ggv552},
	eprint = {http://gji.oxfordjournals.org/content/204/3/1789.full.pdf+html},
	journal = {Geophys. J. Int.},
	number = {3},
	pages = {1789-1800},
	title = {Evidence for {MAC} waves at the top of {E}arth's core and implications for variations in length of day},
	url = {http://gji.oxfordjournals.org/content/204/3/1789.abstract},
	volume = {204},
	year = {2016},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/204/3/1789.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggv552}}

@article{LeMouel1984,
	author = {Le Mou\"el, J.-L.},
	date-added = {2016-03-11 14:00:49 +0000},
	date-modified = {2016-03-11 14:01:40 +0000},
	doi = {{10.1038/311734a0}},
	issn = {{0028-0836}},
	journal = {Nature},
	number = {{5988}},
	pages = {{734-735}},
	title = {OUTER-CORE GEOSTROPHIC FLOW AND SECULAR VARIATION OF EARTHS GEOMAGNETIC-FIELD},
	unique-id = {{ISI:A1984TP85200040}},
	volume = {{311}},
	year = {{1984}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/311734a0%7D}}

@article{Jackson1997,
	abstract = {We present new models of core surface motions for the period 1840--1990. The models are derived under the frozen flux and tangentially geostrophic approximations which neglect, firstly, the contribution of magnetic diffusion to the observed secular variation, and secondly, the contribution of Lorentz forces in the horizontal force balance at the top of the core. The flows are constructed on a temporal basis of B-splines, erected over the 150-year period 1840--1990, and on a spatial basis of toroidal and poloidal vectors in a spectral spherical harmonic expansion. Our parametrisation uses 12348 parameters in total, but the use of the B-spline basis allows us to solve the resulting linear system using less than 10 \{MWords\} of storage. The time-dependent flows are derived so as to be the simplest in a precisely defined spatial and temporal sense which remain compatible with the available data. Of particular interest is the time-dependency of the flows: we expect the flows to be unsteady because changes in the length-of-day on a decade timescale are believed to indicate changes of angular momentum of the core. We show that, despite minimising temporal variations in the flow, such variations are necessary in order for the flows to be able to fit observatory data to an acceptable level; this is seen by comparing the data directly with the observatory time series, and the fit is also quantified globally. Additionally, the root mean square radial secular variation averaged over the earth's surface exhibits two maxima in 1914 and 1978, and the root mean square flow speed averaged over the core surface exhibits two similar peaks at the same times which are a direct consequence of this. We confirm and extend the results of earlier studies showing the probable connection between the surface motions and the changes in the length-of-day. Some `oscillatory' behaviour can be seen, although the time-period studied is too short to be definitely indicative of truly periodic phenomena. },
	author = {Andrew Jackson},
	date-added = {2016-03-11 13:55:04 +0000},
	date-modified = {2016-03-11 13:55:14 +0000},
	doi = {http://dx.doi.org/10.1016/S0031-9201(97)00039-3},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	note = {The Jackfest special issue: A collection of papers to honor Jack Jacobs},
	number = {3--4},
	pages = {293 - 311},
	title = {Time-dependency of tangentially geostrophic core surface motions},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920197000393},
	volume = {103},
	year = {1997},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920197000393},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0031-9201(97)00039-3}}

@article{Sanchez2016,
	author = {Sanchez, S. and Fournier, A. and Aubert, J. and Cosme, E. and Gallet, Y.},
	date-added = {2016-03-11 10:43:38 +0000},
	date-modified = {2016-04-04 14:41:56 +0000},
	journal = {Geophys. J. Int.},
	title = {Modeling the archeomagnetic field under spatial constraints from dynamo simulations: a resolution analysis},
	year = {submitted}}

@article{Hartmann2011,
	author = {Hartmann, Gelvam A. and Genevey, Agnes and Gallet, Yves and Trindade, Ricardo I. F. and Le Goff, Maxime and Najjar, Rosana and Etchevarne, Carlos and Afonso, Marisa C.},
	date-added = {2016-03-11 10:20:46 +0000},
	date-modified = {2016-03-11 10:21:22 +0000},
	doi = {{10.1016/j.epsl.2011.03.030}},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Lett.},
	month = {{JUN 1}},
	number = {{1-2}},
	orcid-numbers = {{Trindade, Ricardo/0000-0001-9848-9550 Hartmann, Gelvam/0000-0001-6078-3893 Genevey, Agnes/0000-0002-7756-9102}},
	pages = {{66-76}},
	researcherid-numbers = {{Trindade, Ricardo/A-8146-2008 Hartmann, Gelvam/K-4856-2012 }},
	title = {{New historical archeointensity data from Brazil: Evidence for a large regional non-dipole field contribution over the past few centuries}},
	unique-id = {{ISI:000291525800007}},
	volume = {{306}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2011.03.030%7D}}

@article{Hartmann2010,
	author = {Hartmann, Gelvam A. and Genevey, Agnes and Gallet, Yves and Trindade, Ricardo I. F. and Etchevarne, Carlos and Le Goff, Maxime and Afonso, Marisa C.},
	date-added = {2016-03-11 10:20:46 +0000},
	date-modified = {2016-03-11 10:21:16 +0000},
	doi = {{10.1016/j.epsl.2010.05.016}},
	issn = {{0012-821X}},
	journal = {Earth Plan. Sci. Lett.},
	month = {{AUG 1}},
	number = {{3-4}},
	orcid-numbers = {{Trindade, Ricardo/0000-0001-9848-9550 Hartmann, Gelvam/0000-0001-6078-3893 Genevey, Agnes/0000-0002-7756-9102}},
	pages = {{340-352}},
	researcherid-numbers = {{Trindade, Ricardo/A-8146-2008 Hartmann, Gelvam/K-4856-2012 }},
	title = {{Archeointensity in Northeast Brazil over the past five centuries}},
	unique-id = {{ISI:000280940300017}},
	volume = {{296}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2010.05.016%7D}}

@inproceedings{Reigber2002,
	abstract = {{The German small satellite CHAMP is on the final track for launch on
   July 15, 2000 into a circular, near-polar and 460 km altitude orbit. The
   satellite carries a number of instruments, partly provided by NASA, CNES
   and USAF, with synergetic use for precise orbit determination, global
   gravity and magnetic field recovery, and GPS atmosphere and ionosphere
   profiling. The mission is projected for a five years' lifetime while the
   orbit slowly decays to below 300 km altitude. The ground segment is run
   by DLR for mission operations and by GFZ for mission/science
   interaction, science data processing, archiving and distribution.
   Ionosphere profiling is a task of DLR. CHAMP's commissioning phase for
   system verification, payload data and software calibration/validation is
   supposed to last nine months, followed by the nominal exploitation
   phase. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights
   reserved.}},
	author = {Reigber, C and Luhr, H and Schwintzer, P},
	booktitle = {New trends in space geodesy},
	date-added = {2016-03-10 15:49:47 +0000},
	date-modified = {2016-03-10 15:50:12 +0000},
	doi = {{10.1016/S0273-1177(02)00276-4}},
	editor = {{Drewes, H and Dow, JM}},
	issn = {{0273-1177}},
	note = {{B2 1-PSD1 Symposium of COSPAR Scientific Commission B held at the 33rd COSPAR Scientific Assembly, WARSAW, POLAND, JUL, 2000}},
	number = {{2}},
	organization = {{Agenzia Spatiale Italiana; CNES; European Space Agcy; Int Union Geodesy \& Geophys; Int Assoc Geodesy}},
	pages = {{129-134}},
	series = {{ADVANCES IN SPACE RESEARCH}},
	title = {{CHAMP mission status}},
	unique-id = {{ISI:000177857000001}},
	volume = {{30}},
	year = {{2002}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0273-1177(02)00276-4%7D}}

@article{Friis2006,
	abstract = {{The Swarm mission was selected as the 5th mission in ESA's Earth
   Explorer Programme in 2004. The mission will provide the best ever
   survey of the geomagnetic field and its temporal evolution that will
   lead to new insights into the Earth system by improving our
   understanding of the Earth's interior and its effect on Geospace, the
   vast region around the Earth where electrodynamic processes are
   influenced by the Earth's magnetic field. Scheduled for launch in 2010,
   the mission will comprise a constellation of three satellites, with two
   spacecraft flying side-by-side at lower attitude (450 km initial
   attitude), thereby measuring the East-West gradient of the magnetic
   field, and the third one flying at higher attitude (530 km).
   High-precision and high-resolution measurements of the strength,
   direction and variation of the magnetic field, complemented by precise
   navigation, accelerometer and electric field measurements, will provide
   the necessary observations that are required to separate and model the
   various Sources of the geomagnetic field. This results in it unique
   ``view{''} inside the Earth from space to study the composition and
   processes of its interior. It also allows analysing the Sun's influence
   within the Earth system. In addition practical applications in many
   different areas, such as space weather, radiation hazards, navigation
   and resource management, will benefit from the Swarm concept.}},
	author = {Friis-Christensen, E and Luhr, H and Hulot, G},
	date-added = {2016-03-10 15:48:08 +0000},
	date-modified = {2016-03-10 15:48:18 +0000},
	issn = {{1343-8832}},
	journal = {Earth Planets Space},
	number = {{4}},
	pages = {{351-358}},
	researcherid-numbers = {{Hulot, Gauthier/A-5627-2011}},
	title = {{Swarm: A constellation to study the Earth's magnetic field}},
	unique-id = {{ISI:000237185700002}},
	volume = {{58}},
	year = {{2006}}}

@article{Finlay2015IGRF,
	author = {Finlay, C. C. and Olsen, N. and Toffner-Clausen, L.},
	date-added = {2016-03-10 15:47:46 +0000},
	date-modified = {2016-03-10 15:47:46 +0000},
	journal = {Earth. Planets. Space.},
	pages = {114},
	title = {{DTU candidate field models for IGRF-12 and the CHAOS-5 geomagnetic field model}},
	volume = {67},
	year = {2015}}

@article{Bloxham1992,
	author = {Bloxham, J. and Jackson, A.},
	date-added = {2016-03-10 15:19:52 +0000},
	date-modified = {2016-03-10 15:20:13 +0000},
	doi = {{10.1029/92JB01591}},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	month = {{DEC 10}},
	number = {{B13}},
	pages = {{19537-19563}},
	title = {TIME-DEPENDENT MAPPING OF THE MAGNETIC-FIELD AT THE CORE-MANTLE BOUNDARY},
	unique-id = {{ISI:A1992KD95100001}},
	volume = {{97}},
	year = {{1992}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/92JB01591%7D}}

@article{Genevey2008,
	article-number = {{Q04038}},
	author = {Genevey, A. and Gallet, Y. and Constable, C. G. and Korte, M. and Hulot, G.},
	date-added = {2016-03-10 15:13:45 +0000},
	date-modified = {2016-03-10 15:13:55 +0000},
	doi = {{10.1029/2007GC001881}},
	issn = {{1525-2027}},
	journal = {Geochem. Geophy. Geosystems},
	month = {{APR 29}},
	orcid-numbers = {{Korte, Monika/0000-0003-2970-9075 Constable, Catherine/0000-0003-4534-4977}},
	researcherid-numbers = {{Korte, Monika/A-6086-2009 Hulot, Gauthier/A-5627-2011 Constable, Catherine/F-7784-2010}},
	title = {{ArcheoInt: An upgraded compilation of geomagnetic field intensity data for the past ten millennia and its application to the recovery of the past dipole moment}},
	unique-id = {{ISI:000255592600001}},
	volume = {{9}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2007GC001881%7D}}

@article{Gubbins1985,
	author = {Gubbins, D. and Bloxham, J.},
	date-added = {2016-03-10 15:09:36 +0000},
	date-modified = {2016-03-10 15:12:13 +0000},
	doi = {{10.1111/j.1365-246X.1985.tb05119.x}},
	issn = {{0016-8009}},
	journal = {Geophys. J. R. astr. Soc.},
	number = {{3}},
	pages = {{695-713}},
	title = {GEOMAGNETIC-FIELD ANALYSIS .3. MAGNETIC-FIELDS ON THE CORE MANTLE BOUNDARY},
	unique-id = {{ISI:A1985ADD8200009}},
	volume = {{80}},
	year = {{1985}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.1985.tb05119.x%7D}}

@article{Hellio2014,
	abstract = {We report a new method to infer continuous time-series of the declination, inclination and intensity of the magnetic field from archaeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archaeological artefacts and we use Markov chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity data sets from Mari, Syria and to intensity and directional data sets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archaeological artefacts.},
	author = {Hellio, G. and Gillet, N. and Bouligand, C. and Jault, D.},
	date-added = {2016-03-09 16:01:56 +0000},
	date-modified = {2016-03-09 16:02:07 +0000},
	doi = {10.1093/gji/ggu303},
	eprint = {http://gji.oxfordjournals.org/content/199/2/931.full.pdf+html},
	journal = {Geophys. J. Int.},
	number = {2},
	pages = {931-943},
	title = {Stochastic modelling of regional archaeomagnetic series},
	url = {http://gji.oxfordjournals.org/content/199/2/931.abstract},
	volume = {199},
	year = {2014},
	Bdsk-Url-1 = {http://gji.oxfordjournals.org/content/199/2/931.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1093/gji/ggu303}}

@article{Barraclough1974,
	author = {Barraclough, D. R.},
	date-added = {2016-03-08 16:05:28 +0000},
	date-modified = {2016-03-08 16:06:04 +0000},
	doi = {{10.1111/j.1365-246X.1974.tb00611.x}},
	issn = {{0016-8009}},
	journal = {Geophys. J. R. astr. Soc.},
	number = {{3}},
	pages = {{497-513}},
	title = {SPHERICAL HARMONIC ANALYSES OF GEOMAGNETIC-FIELD FOR 8 EPOCHS BETWEEN 1600 AND 1910},
	unique-id = {{ISI:A1974S587600001}},
	volume = {{36}},
	year = {{1974}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.1974.tb00611.x%7D}}

@article{Finlay2008,
	abstract = {The geomagnetic axial dipole (hereinafter denoted g 1 0 ) is the largest component of our planet's magnetic field. Its magnitude determines the morphology of solar-terrestrial electrical current systems and it is the most fundamental diagnostic property of the core-generated geodynamo. Elucidating past and future variations of g 1 0 ( t ) is consequently of central importance in geomagnetism. Previous historical geomagnetic field models, such as gufm1 of Jackson et al. [Jackson, A., Jonkers, A.R.T., Walker, M.R., 2000. Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. Lond. A 358, 957--990], used direct observations to constrain g 1 0 ( t ) only after 1840 A.D.; before this time a crude linear extrapolation of the post-1840 A.D. rate of change (15 nT/year) was employed. In this contribution I construct historical field models with g 1 0 ( t ) instead constrained from 1590 A.D. to 1840 A.D. by an archaeointensity dataset compiled by Korte et al. [Korte, M., Genevey, A., Constable, C.G., Frank, U., Schnepp, E., 2005. Continuous geomagnetic field models for the past 7 millennia. 1. A new global data compilation. Geochem. Geophys. Geosyst. 6, doi:10.1029/2004GC000800]. A range of possible linear models of the form g 1 0 ( t ) = g 1 0 ( 1840 ) + β ( t − 1840 ) are first explored; β = 2.74 $\pm$ 42.32  nT/year is found to explain the archaeointensity dataset with maximum likelihood, consistent with the recent findings of Gubbins et al. [Gubbins, D., Jones, A.L., Finlay, C.C., 2006. Fall in Earth's magnetic field is erratic. Science 312, 900--902]. Relaxing the linear constraint in an effort to find more physically plausible models, I find it is necessary to artificially increase the weight given to the archaeointensity data in order to obtain acceptable models. Despite satisfactorily explaining both the historical and archaeointensity data, and possessing reasonable spatial and temporal complexity, such free evolution models perform worse than the simpler linearly constrained models when tested against the independent dataset of Gallet et al. [Gallet, Y., Genevey, A., Fluteau, F., 2005. Does Earth's magnetic field secular variation control centennial climate change? Earth Plan. Sci. Lett. 236, 159--173]. Bayesian model comparison techniques indicate that a model (gufm1-g10c) involving no change in g 1 0 ( t ) between 1590 A.D. and 1840 A.D. is most probable given the presently available data and current modelling techniques. I propose that this new, empirically derived, constraint on the evolution of the geomagnetic axial dipole be incorporated into the next generation of historical field models. },
	author = {Christopher C. Finlay},
	date-added = {2016-03-08 16:04:08 +0000},
	date-modified = {2016-03-08 16:04:15 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2008.06.029},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Archaeointensity},
	number = {1--2},
	pages = {1 - 14},
	title = {Historical variation of the geomagnetic axial dipole},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920108001477},
	volume = {170},
	year = {2008},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920108001477},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2008.06.029}}

@article{Gubbins2006,
	abstract = {Earth{\textquoteright}s magnetic field has decayed by about 5\% per century since measurements began in 1840. Directional measurements predate those of intensity by more than 250 years, and we combined the global model of directions with paleomagnetic intensity measurements to estimate the fall in strength for this earlier period (1590 to 1840 A.D.). We found that magnetic field strength was nearly constant throughout this time, in contrast to the later period. Extrapolating to the core surface showed that the fall in strength originated in patches of reverse magnetic flux in the Southern Hemisphere. These patches were detectable by directional data alone; the pre-1840 model showed little or no evidence of them, supporting the conclusion of a steady dipole up to 1840.},
	author = {Gubbins, David and Jones, Adrian L. and Finlay, Christopher C.},
	date-added = {2016-03-08 16:02:11 +0000},
	date-modified = {2016-03-08 16:02:29 +0000},
	doi = {10.1126/science.1124855},
	eprint = {http://science.sciencemag.org/content/312/5775/900.full.pdf},
	issn = {0036-8075},
	journal = {Science},
	number = {5775},
	pages = {900--902},
	publisher = {American Association for the Advancement of Science},
	title = {Fall in Earth's Magnetic Field Is Erratic},
	url = {http://science.sciencemag.org/content/312/5775/900},
	volume = {312},
	year = {2006},
	Bdsk-Url-1 = {http://science.sciencemag.org/content/312/5775/900},
	Bdsk-Url-2 = {http://dx.doi.org/10.1126/science.1124855}}

@article{Genevey2009,
	abstract = {The number of reliable archeointensity determinations obtained from Western Europe for the past millennium remains limited. Moreover, the large scatter between different datasets available is puzzling. The present study analyzed 31 new groups of baked clay (ceramic or brick) fragments sampled in France (29 groups) and in Belgium (2 groups). These groups contain several fragments collected from different artefacts and are precisely dated principally from historical constraints between the \{XIIIth\} and the \{XIXth\} centuries. Additionally, we re-evaluated 14 intensity values that we previously obtained from the same time period. The fragments were analyzed using two different thermal methods: (1) the ``in field-zero field'' (IZ) or the \{IZZI\} version of the classical Thellier and Thellier method and (2) the Triaxe protocol that involves high-temperature magnetization measurements. Data were corrected for the anisotropy of thermoremanent magnetization (TRM) and the dependence of \{TRM\} acquisition on the cooling rate was taken into account in the different protocols. Archeointensity data obtained on twin specimens sampled from the same fragment and using both experimental techniques generally show a good agreement (i.e. within 5%) at the fragment and at the site level. All retained site-level averaged intensity results (43 of 45 groups) have standard deviations of less than 5 µT. Furthermore, groups of approximately the same age have very consistent archeointensity. Altogether, the data presented herein recover a detailed and smoothed geomagnetic field intensity variation curve characterized by two peaks in intensity, the first during the second half of the \{XIVth\} century and the second around \{AD\} 1600, followed by a significant decreasing trend in intensity during most the \{XVIIth\} and \{XVIIIth\} centuries. This evolution does not satisfactorily fit with the expected intensity values for France derived from geomagnetic field models relying on a different evolution of the axial dipole moment. Our results lead us to propose that the axial dipole moment decreased from \{AD\} 1600 to the end of the \{XVIIIth\} century, then slightly increased up to ~ \{AD\} 1850 before decreasing again to present day. },
	author = {Agn{\`e}s Genevey and Yves Gallet and Jean Rosen and Maxime Le Goff},
	date-added = {2016-03-08 16:00:37 +0000},
	date-modified = {2016-03-08 16:00:42 +0000},
	doi = {http://dx.doi.org/10.1016/j.epsl.2009.04.024},
	issn = {0012-821X},
	journal = {Earth and Planetary Science Letters},
	keywords = {dipole moment},
	number = {1--2},
	pages = {132 - 143},
	title = {Evidence for rapid geomagnetic field intensity variations in Western Europe over the past 800 years from new French archeointensity data},
	url = {http://www.sciencedirect.com/science/article/pii/S0012821X09002398},
	volume = {284},
	year = {2009},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012821X09002398},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.epsl.2009.04.024}}

@article{Whaler2011,
	abstract = {From 1590 to 1833, although extensive measurements of the geomagnetic field were made, no direct measurements of its intensity are available; field models for this period either make use of indirect (palaeomagnetic) intensity determinations or assume a similar change in dipole strength to that seen presently. Here, we examine the impact of different choices of field model strength on models of the core-surface flow, derived from the geomagnetic secular variation. We find that for a reasonable range of possible changes in the field strength, the variability that this unknown imposes on the flow structure is small compared with other choices in the modelling strategy, such as the degree to which the geomagnetic models are fit, the smoothness of the flows, and a priori information included to reduce non-uniqueness in the flow calculation. The flows predict variations in core angular momentum of similar magnitude to those seen in recent times. These variations are larger than seen in models from geodetic data, but do not seem inconsistent with the geodetic data themselves. We therefore suggest that it is reasonable to study core flows back at least until 1650, thereby doubling the time interval for which flows can be considered to constrain the behaviour of the geodynamo. },
	author = {K.A. Whaler and R. Holme},
	date-added = {2016-03-08 14:54:48 +0000},
	date-modified = {2016-03-08 14:54:59 +0000},
	doi = {http://dx.doi.org/10.1016/j.pepi.2011.07.006},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	keywords = {Decadal length-of-day variations},
	note = {Proceedings of the 12th Symposium of \{SEDI\}},
	number = {3--4},
	pages = {235 - 246},
	title = {The axial dipole strength and flow in the outer core},
	url = {http://www.sciencedirect.com/science/article/pii/S0031920111001476},
	volume = {188},
	year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0031920111001476},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.pepi.2011.07.006}}

@article{Cheng2013,
	author = {Cheng, M and Tapley, B. D. and Ries, J. C.},
	date-added = {2016-03-07 13:50:05 +0000},
	date-modified = {2016-03-07 13:51:08 +0000},
	journal = {{J. Geophys. Res.}},
	pages = {740-747},
	title = {{Deceleration of the Earth's oblateness}},
	volume = {118},
	year = {2013}}

@incollection{Nataf2015,
	author = {H.-C. Nataf and N. Schaeffer},
	booktitle = {Treatise on Geophysics},
	date-added = {2016-03-07 12:55:27 +0000},
	date-modified = {2016-03-07 13:55:27 +0100},
	doi = {10.1016/b978-0-444-53802-4.00142-1},
	pages = {161--181},
	publisher = {Elsevier {BV}},
	title = {Turbulence in the Core},
	url = {http://dx.doi.org/10.1016/B978-0-444-53802-4.00142-1},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/B978-0-444-53802-4.00142-1},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/b978-0-444-53802-4.00142-1}}

@article{Aubert2015,
	author = {Aubert, J.},
	date-added = {2016-02-25 15:32:21 +0000},
	date-modified = {2016-02-25 15:32:46 +0000},
	doi = {{10.1093/gji/ggv394}},
	eissn = {{1365-246X}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{DEC}},
	number = {{3}},
	pages = {{1738-1751}},
	researcherid-numbers = {{Aubert, Julien/A-5616-2011}},
	title = {{Geomagnetic forecasts driven by thermal wind dynamics in the Earth's core}},
	unique-id = {{ISI:000368426800016}},
	volume = {{203}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggv394%7D}}

@article{Jault2015,
	author = {Jault, Dominique},
	date-added = {2016-02-25 14:46:04 +0000},
	date-modified = {2016-02-25 14:46:04 +0000},
	doi = {{10.1093/gji/ggv152}},
	eissn = {{1365-246X}},
	issn = {{0956-540X}},
	journal = {Geoph. J. Int.},
	month = {{JUL}},
	number = {{1}},
	orcid-numbers = {{Jault, Dominique/0000-0001-5592-5746}},
	pages = {{482-496}},
	title = {{Illuminating the electrical conductivity of the lowermost mantle from below}},
	unique-id = {{ISI:000360623400034}},
	volume = {{202}},
	year = {{2015}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggv152%7D}}

@article{Thebault2015,
	author = {Th\'ebault, E. and others},
	date-added = {2016-02-25 14:13:43 +0000},
	date-modified = {2016-04-04 15:18:17 +0000},
	doi = {10.1186/s40623-015-0228-9},
	journal = {Earth. Planets. Space.},
	pages = {79},
	title = {International Geomagnetic Reference Field: the twelfth generation},
	volume = {67},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1186/s40623-015-0228-9}}

@incollection{Buffett2015b,
	author = {Buffett, B. A.},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2016-02-24 15:06:53 +0000},
	date-modified = {2020-09-23 17:38:19 +0200},
	pages = {213--224},
	publisher = {Elsevier},
	title = {Core--Mantle Interactions},
	volume = {8 - Core Dynamics},
	year = {2015}}

@article{Finlay2016,
	article-number = {{10422}},
	author = {Finlay, C. C. and Aubert, Julien and Gillet, Nicolas},
	date-added = {2016-02-24 14:58:26 +0000},
	date-modified = {2017-12-14 10:06:00 +0000},
	doi = {{10.1038/ncomms10422}},
	issn = {{2041-1723}},
	journal = {Nature comm.},
	month = {{JAN}},
	title = {{Gyre-driven decay of the Earth's magnetic dipole}},
	unique-id = {{ISI:000369022600005}},
	volume = {{7:10422}},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms10422%7D}}

@incollection{Hulot2015,
	author = {Hulot, G. and Sabaka, T. J. and Olsen, N. and Fournier, A.},
	booktitle = {Treatise on Geophysics (Second Edition)},
	date-added = {2016-02-24 14:55:50 +0000},
	date-modified = {2016-02-24 15:08:09 +0000},
	pages = {33-78},
	publisher = {Elsevier},
	title = {The Present and Future Geomagnetic Field},
	volume = {5 - Geomagnetism},
	year = {2015}}

@article{Holme2013,
	author = {Holme, R. and de Viron, O.},
	date-added = {2016-02-24 14:55:18 +0000},
	date-modified = {2017-01-27 13:23:57 +0000},
	doi = {{10.1038/nature12282}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{JUL 11}},
	number = {{7457}},
	orcid-numbers = {{de Viron, Olivier/0000-0003-3112-9686}},
	pages = {{202-204}},
	researcherid-numbers = {{de Viron, Olivier/N-6647-2014}},
	title = {{Characterization and implications of intradecadal variations in length of day}},
	unique-id = {{ISI:000321557600060}},
	volume = {{499}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature12282%7D}}

@article{Buffett2014,
	author = {Buffett, B. A.},
	date-added = {2015-10-14 14:11:20 +0000},
	date-modified = {2016-11-14 13:40:20 +0000},
	doi = {{10.1038/nature13122}},
	eissn = {{1476-4687}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{MAR 27}},
	number = {{7493}},
	pages = {{484-487}},
	title = {{Geomagnetic fluctuations reveal stable stratification at the top of the Earth's core}},
	unique-id = {{ISI:000333402000037}},
	volume = {{507}},
	year = {{2014}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature13122%7D}}

@article{Fournier2015,
	author = {Fournier, A. and Aubert, J. and Th\'ebault, E.},
	date-added = {2015-10-13 12:59:09 +0000},
	date-modified = {2015-10-13 12:59:09 +0000},
	doi = {10.1186/s40623-015-0245-8},
	journal = {Earth. Planets. Space.},
	pages = {81},
	title = {{A candidate secular variation model for IGRF-12 based on Swarm data and inverse geodynamo modelling}},
	volume = {67},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1186/s40623-015-0245-8}}

@article{Pichon2016,
	author = {Pichon, G. and Aubert, J. and Fournier, A.},
	date-added = {2015-10-12 14:17:16 +0000},
	date-modified = {2016-11-14 13:51:43 +0000},
	journal = {Earth Planet. Sci. Lett.},
	pages = {114-126},
	title = {{Coupled dynamics of Earth's geomagnetic westward drift and inner core super-rotation}},
	volume = {437},
	year = {2016}}

@article{Aubert2014,
	author = {Aubert, J.},
	date-added = {2014-10-16 12:53:28 +0000},
	date-modified = {2016-11-14 13:37:40 +0000},
	doi = {{10.1093/gji/ggu064}},
	eissn = {{1365-246X}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUN}},
	number = {{3}},
	pages = {{1321-1334}},
	researcherid-numbers = {{Aubert, Julien/A-5616-2011}},
	title = {{Earth's core internal dynamics 1840-2010 imaged by inverse geodynamo modelling}},
	unique-id = {{ISI:000337041100004}},
	volume = {{197}},
	year = {{2014}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggu064%7D}}

@article{Nerger2013,
	author = {Nerger, Lars and Hiller, Wolfgang},
	date-added = {2013-10-14 14:53:13 +0000},
	date-modified = {2013-10-14 14:53:26 +0000},
	doi = {{10.1016/j.cageo.2012.03.026}},
	issn = {{0098-3004}},
	journal = {Computers and Geosciences},
	month = {{JUN}},
	number = {{SI}},
	pages = {{110-118}},
	researcherid-numbers = {{Nerger, Lars/G-4845-2013}},
	title = {{Software for ensemble-based data assimilation systems-Implementation strategies and scalability}},
	unique-id = {{ISI:000318384600010}},
	volume = {{55}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cageo.2012.03.026%7D}}

@inproceedings{Nerger2005,
	author = {Nerger, L and Hiller, W and Schroter, J},
	booktitle = {{Use of High Performance Computing in Meteorology}},
	date-added = {2013-10-14 11:08:49 +0000},
	date-modified = {2013-10-14 11:08:49 +0000},
	doi = {{10.1142/9789812701831\_0006}},
	editor = {{Zwieflhofer, W and Mozdzynski, G}},
	isbn = {{981-256-354-7}},
	note = {{11th Workshop on the Use of High Performance Computing in Meteorology, European Ctr Medium Range Weather Forecasts, Reading, ENGLAND, OCT 25-29, 2004}},
	pages = {{63-83}},
	title = {{PDAF - The parallel data assimilation framework: Experiences with Kalman filtering}},
	unique-id = {{ISI:000234714600006}},
	year = {{2005}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1142/9789812701831%5C_0006%7D}}

@article{Schaeffer2013,
	author = {Schaeffer, N.},
	date-added = {2013-10-14 10:08:40 +0000},
	date-modified = {2016-11-14 13:53:02 +0000},
	doi = {{10.1002/ggge.20071}},
	issn = {{1525-2027}},
	journal = {Geophys. Geochem. Geosystems.},
	month = {{MAR}},
	number = {{3}},
	pages = {{751-758}},
	researcherid-numbers = {{Schaeffer, Nathanael/F-4162-2012}},
	title = {{Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations}},
	unique-id = {{ISI:000317825000015}},
	volume = {{14}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/ggge.20071%7D}}

@article{Gross2001,
	author = {Gross, R. S.},
	date-added = {2013-09-25 08:04:41 +0000},
	date-modified = {2013-09-25 08:05:00 +0000},
	doi = {{10.1016/S0031-9201(00)00217-X}},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	month = {{MAR}},
	number = {{1}},
	pages = {{65-76}},
	title = {{A combined length-of-day series spanning 1832-1997: LUNAR97}},
	unique-id = {{ISI:000167478700005}},
	volume = {{123}},
	year = {{2001}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0031-9201(00)00217-X%7D}}

@article{Finlay2010IGRF,
	author = {Finlay, C. C. and Maus, S. and Beggan, C. D. and Bondar, T. N. and Chambodut, A. and Chernova, T. A. and Chulliat, A. and Golovkov, V. P. and Hamilton, B. and Hamoudi, M. and Holme, R. and Hulot, G. and Kuang, W. and Langlais, B. and Lesur, V. and Lowes, F. J. and Luehr, H. and Macmillan, S. and Mandea, M. and McLean, S. and Manoj, C. and Menvielle, M. and Michaelis, I. and Olsen, N. and Rauberg, J. and Rother, M. and Sabaka, T. J. and Tangborn, A. and Toffner-Clausen, L. and Thebault, E. and Thomson, A. W. P. and Wardinski, I. and Wei, Z. and Zvereva, T. I. and Int Assoc Geomagnetism Aeronomy Wo},
	date-added = {2013-09-24 08:36:10 +0000},
	date-modified = {2013-09-24 08:36:53 +0000},
	doi = {{10.1111/j.1365-246X.2010.04804.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{DEC}},
	number = {{3}},
	orcid-numbers = {{Olsen, Nils/0000-0003-1132-6113 Langlais, Benoit/0000-0001-5207-304X Kuang, Weijia/0000-0001-7786-6425 }},
	pages = {{1216-1230}},
	researcherid-numbers = {{Hulot, Gauthier/A-5627-2011 Chulliat, Arnaud/A-5747-2011 Olsen, Nils/H-1822-2011 Sabaka, Terence/D-5618-2012 MANDEA, Mioara/E-4892-2012 Lesur, Vincent/H-1031-2012 Langlais, Benoit/K-5366-2012 Kuang, Weijia/K-5141-2012 Thebault, Erwan/A-5670-2011}},
	title = {{International Geomagnetic Reference Field: the eleventh generation}},
	unique-id = {{ISI:000284274700010}},
	volume = {{183}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2010.04804.x%7D}}

@article{Fournier2013,
	author = {Fournier, A. and Nerger, L. and Aubert, J.},
	date-added = {2013-09-13 14:10:01 +0000},
	date-modified = {2013-10-14 10:55:15 +0000},
	journal = {Geophys. Geochem. Geosystems.},
	note = {doi: 10.1002/ggge.20252},
	title = {An ensemble {K}alman filter for the time-dependent analysis of the geomagnetic field},
	volume = {14},
	year = {2013}}

@article{Christensen2012,
	author = {Christensen, U. R. and Wardinski, I. and Lesur, V.},
	date-added = {2013-09-13 13:08:45 +0000},
	date-modified = {2013-09-13 13:08:57 +0000},
	doi = {{10.1111/j.1365-246X.2012.05508.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUL}},
	number = {{1}},
	pages = {{243-254}},
	researcherid-numbers = {{Lesur, Vincent/H-1031-2012}},
	title = {{Timescales of geomagnetic secular acceleration in satellite field models and geodynamo models}},
	unique-id = {{ISI:000305080900017}},
	volume = {{190}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2012.05508.x%7D}}

@article{Aubert2013b,
	author = {Aubert, J. and Finlay, C. C. and Fournier, A.},
	date-added = {2013-09-13 13:02:18 +0000},
	date-modified = {2017-03-06 17:01:28 +0000},
	journal = {{Nature}},
	pages = {219-223},
	title = {{Bottom-up control of geomagnetic secular variation by the Earth's inner core}},
	volume = {502},
	year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature12574%7D}}

@article{Gillet2013,
	abstract = {{Inferring the core dynamics responsible for the observed geomagnetic
   secular variation requires knowledge of the magnetic field at the
   core-mantle boundary together with its associated model covariances.
   However, most currently available field models have been built using
   regularization conditions, which force the expansions in the spatial and
   time domains to converge but also hinder the calculation of reliable
   second-order statistics. To tackle this issue, we propose a stochastic
   approach that integrates, through time covariance functions, some prior
   information on the time evolution of the geomagnetic field. We consider
   the time series of spherical harmonic coefficients as realizations of a
   continuous and differentiable stochastic process. Our specific choice of
   process, such that it is not twice differentiable, mainly relies on two
   properties of magnetic observatory records (time spectra, existence of
   geomagnetic jerks). In addition, the required characteristic times for
   the low degree coefficients are obtained from available models of the
   magnetic field and its secular variation based on satellite data. We
   construct the new family COV-OBS of field models spanning the
   observatory and satellite era of 18402010. These models include the
   external dipole and permit sharper time changes of the internal field
   compared to previous regularized reconstructions. The a posteriori
   covariance matrix displays correlations in both space and time, which
   should be accounted for through the secular variation error model in
   core flow inversions and geomagnetic data assimilation studies.}},
	author = {Gillet, N. and Jault, D. and Finlay, C. C. and Olsen, N.},
	date-added = {2013-09-13 11:14:02 +0000},
	date-modified = {2013-09-13 11:14:02 +0000},
	doi = {{10.1002/ggge.20041}},
	issn = {{1525-2027}},
	journal = {{Geochem. Geophys. Geosyst.}},
	month = {{APR}},
	number = {{4}},
	orcid-numbers = {{Olsen, Nils/0000-0003-1132-6113}},
	pages = {{766-786}},
	researcherid-numbers = {{Olsen, Nils/H-1822-2011}},
	title = {{Stochastic modeling of the Earth's magnetic field: Inversion for covariances over the observatory era}},
	unique-id = {{ISI:000319410100002}},
	volume = {{14}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/ggge.20041%7D}}

@article{Finlay2012,
	author = {Finlay, C. C. and Jackson, A. and Gillet, N. and Olsen, N.},
	date-added = {2013-08-13 15:26:07 +0000},
	date-modified = {2013-08-13 15:26:34 +0000},
	doi = {{10.1111/j.1365-246X.2012.05395.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{MAY}},
	number = {{2}},
	orcid-numbers = {{Olsen, Nils/0000-0003-1132-6113}},
	pages = {{761-781}},
	researcherid-numbers = {{Olsen, Nils/H-1822-2011}},
	title = {{Core surface magnetic field evolution 2000-2010}},
	unique-id = {{ISI:000302623600005}},
	volume = {{189}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2012.05395.x%7D}}

@book{Ahrens:1995aa,
	abstract = {The purpose of this Handbook is to provide, in highly accessible form, selected critical data for professional and student solid Earth and planetary geophysicists. Coverage of topics and authors were carefully chosen to fulfill these objectives.These volumes represent the third version of the &#8220;Handbook of Physical Constants. &#8221; Several generations of solid Earth scientists have found these handbooks to be the most frequently used item in their personal library. The first version of this Handbook was edited by F. Birch, J. F. Schairer, and H. Cecil Spicer and published in 1942 by the Geological Society of America (GSA) as Special Paper 36. The second edition, edited by Sydney P. Clark, Jr., was also published by GSA as Memoir 92 in 1966. Since 1966, our scientific knowledge of the Earth and planets has grown enormously, spurred by the discovery and verification of plate tectonics and the systematic exploration of the solar system.},
	address = {Washington, DC},
	author = {Ahrens, T. J.},
	date = {1995///},
	date-added = {2013-03-22 14:53:50 +0000},
	date-modified = {2013-03-22 14:55:02 +0000},
	doi = {10.1029/RF001},
	ep = {376},
	isbn = {0-87590-851-9},
	keywords = {1200 Geodesy and Gravity; 1500 Geomagnetism and Paleomagnetism; 5400 Planetology: Solid Surface Planets; 7200 Seismology; Physical constants\&{\#}8212;Handbooks, manuals, etc.; Geophysics\&{\#}8212;Handbooks, manuals, etc.},
	publisher = {AGU},
	title = {Global Earth Physics: A Handbook of Physical Constants},
	title1 = {AGU Ref. Shelf},
	ty = {BOOK},
	volume = {1},
	year = {1995},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/RF001}}

@article{Lesur2010,
	abstract = {{We present the second generation of the GFZ Reference Internal Magnetic
   Model (GRIMM-2), that was derived for the preparation of the GFZ
   candidate for the 11th generation of the IGRF. The model is built by
   fitting a vector data set made of CHAMP satellite and observatory data,
   spanning the period 2001.0 to 2009.5. The data selection technique and
   the model parametrization are similar to that used for the derivation of
   the GRIMM model (Lesur et al., 2008). The obtained model is robust over
   the time span of the data. However, the secular variation above
   spherical harmonic degree 13 becomes less controlled by the data and is
   constrained by the applied regularization before 2002 and after 2008.5.
   At best, only the spherical harmonic degrees 3 to 6 are robustly
   estimated for the secular acceleration. The problem associated with the
   first two spherical harmonic degrees of the secular acceleration model
   arise from the difficulty in separating the core field signal from the
   external fields and their internally induced counterparts. The
   regularization technique applied smoothes the magnetic field model in
   time. This affects all spherical harmonic degrees, but starts to be
   significant at spherical harmonic degree 5.}},
	author = {Lesur, V. and Wardinski, I. and Hamoudi, M. and Rother, M.},
	date-added = {2013-03-18 16:38:10 +0000},
	date-modified = {2013-03-18 16:38:19 +0000},
	doi = {{10.5047/eps.2010.07.007}},
	issn = {{1343-8832}},
	journal = {Earth Planets Space},
	number = {{10}},
	pages = {{765-773}},
	researcherid-numbers = {{Lesur, Vincent/H-1031-2012}},
	times-cited = {{18}},
	title = {{The second generation of the GFZ Reference Internal Magnetic Model: GRIMM-2}},
	unique-id = {{ISI:000287478500007}},
	volume = {{62}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.5047/eps.2010.07.007%7D}}

@article{Olsen2006,
	abstract = {{We have derived a model of the near-Earth magnetic field (up to
   spherical harmonic degree n= 50 for the static field, and up to n = 18
   for the first time derivative) using more than 6.5 yr of high-precision
   geomagnetic measurements from the three satellites Orsted, CHAMP and
   SAC-C taken between 1999 March and 2005 December.
   Our modelling approach goes in several aspects beyond that used for
   recent models: (i) we use different data selection criteria and allow
   for higher geomagnetic activity (index Kp <= 2o), thus we include more
   data than previous models; (ii) we describe the temporal variation of
   the core field by splines (for n <= 14); (iii) we take magnetometer
   vector data in the instrument frame and co-estimate the Euler angles
   that describe the transformation from the magnetometer frame to the star
   imager frame, avoiding the inconsistency of using vector data that have
   been aligned using a different (pre-existing) field model; (iv) we
   account for the bending of the CHAMP optical bench connecting
   magnetometer and star imager by estimating Euler angles in 10 day
   segments and (v) we co-estimate degree-1 external fields separately for
   every 12 hr interval.
   The model provides a reliable representation of the static (core and
   crustal) field up to spherical harmonic degree n = 40, and of the first
   time derivative up to n = 15.}},
	author = {Olsen, N and Luhr, H and Sabaka, TJ and Mandea, M and Rother, M and Tofner-Clausen, L and Choi, S},
	date-added = {2013-03-14 10:10:39 +0000},
	date-modified = {2013-03-14 10:10:51 +0000},
	doi = {{10.1111/j.1365-246X.2006.02959.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUL}},
	number = {{1}},
	pages = {{67-75}},
	researcherid-numbers = {{Olsen, Nils/H-1822-2011 Sabaka, Terence/D-5618-2012 MANDEA, Mioara/E-4892-2012}},
	times-cited = {{86}},
	title = {{CHAOS-a model of the Earth's magnetic field derived from CHAMP, Orsted, and SAC-C magnetic satellite data}},
	unique-id = {{ISI:000238748300006}},
	volume = {{166}},
	year = {{2006}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2006.02959.x%7D}}

@phdthesis{Finlay2005,
	address = {University of Leeds},
	author = {Finlay, Christopher C.},
	date-added = {2013-03-07 14:35:54 +0000},
	date-modified = {2013-03-25 15:11:42 +0000},
	school = {School of {E}arth and {E}nvironment},
	title = {Hydromagnetic waves in {E}arth's core and their influence on geomagnetic secular variation},
	year = {2005}}

@article{Miyagoshi2010,
	abstract = {{Zonal jets are very common in nature. Well-known examples are those in
   the atmospheres of giant planets and the alternating jet streams found
   in the Earth's world ocean(1). Zonal flow formation in nuclear fusion
   devices is also well studied(2). A common feature of these zonal flows
   is that they are spontaneously generated in turbulent systems. Because
   the Earth's outer core is believed to be in a turbulent state, it is
   possible that there is zonal flow in the liquid iron of the outer core.
   Here we report an investigation at the current low-viscosity limit of
   numerical simulations of the geodynamo. We find a previously unknown
   convection regime of the outer core that has a dual structure comprising
   inner, sheet-like radial plumes and an outer, westward cylindrical zonal
   flow. We numerically confirm that the dual-convection structure with
   such a zonal flow is stable under a strong, self-generated dipole
   magnetic field.}},
	author = {Miyagoshi, T. and Kageyama, A. and Sato, T.},
	date-added = {2013-03-07 12:37:39 +0000},
	date-modified = {2016-11-14 13:50:20 +0000},
	doi = {{10.1038/nature08754}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{FEB 11}},
	number = {{7282}},
	pages = {{793-796}},
	times-cited = {{12}},
	title = {{Zonal flow formation in the Earth's core}},
	unique-id = {{ISI:000274394300036}},
	volume = {{463}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature08754%7D}}

@article{Glatzmaier1995,
	abstract = {{A three-dimensional, self-consistent numerical model of the geodynamo is
   described, that maintains a magnetic field for over 40,000 years. The
   model, which Incorporates a finitely conducting inner core, undergoes
   several polarity excursions and then, near the end of the simulation, a
   successful reversal of the dipole moment. This simulated magnetic field
   reversal shares some features with real reversals of the geomagnetic
   field, and may provide insight into the geomagnetic reversal mechanism.}},
	author = {Glatzmaier, G.A. and Roberts, P.H.},
	date-added = {2013-03-01 15:54:20 +0000},
	date-modified = {2013-03-01 16:05:11 +0000},
	doi = {{10.1038/377203a0}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{SEP 21}},
	number = {{6546}},
	pages = {{203-209}},
	times-cited = {{427}},
	title = {A 3-DIMENSIONAL SELF-CONSISTENT COMPUTER-SIMULATION OF A GEOMAGNETIC-FIELD REVERSAL},
	unique-id = {{ISI:A1995RV87200030}},
	volume = {{377}},
	year = {{1995}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/377203a0%7D}}

@article{Kuang1997,
	abstract = {{The mechanism by which the Earth and other planets maintain their
   magnetic fields against ohmic decay is among the longest standing
   problems in planetary science. Although it is widely acknowledged that
   these fields are maintained by dynamo action, the mechanism by which the
   dynamo operates is in large part not understood. Numerical simulations
   of the dynamo process in the Earth's core(1-4) have produced magnetic
   fields that resemble the Earth's field, but it is unclear whether these
   models accurately represent the extremely low values of viscosity
   believed to be appropriate to the core. Here we describe the results of
   a numerical investigation of the dynamo process that adopts an
   alternative approach(5) to this problem in which, through the judicious
   choice of boundary conditions, the effects of viscosity are rendered
   unimportant. We thereby obtain a solution that at leading order operates
   in an Earth-like dynamical regime. The morphology and evolution of the
   magnetic field and the fluid flow at the tore-mantle boundary are
   similar to those of the Earth, and the field within the core is
   qualitatively similar to that proposed on theoretical grounds(6).}},
	author = {Kuang, WL and Bloxham, J},
	date-added = {2013-03-01 15:54:02 +0000},
	date-modified = {2013-03-19 12:12:33 +0000},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{SEP 25}},
	number = {{6649}},
	pages = {{371-374}},
	times-cited = {{266}},
	title = {{An Earth-like numerical dynamo model}},
	unique-id = {{ISI:A1997XX67500049}},
	volume = {{389}},
	year = {{1997}}}

@article{Aubert2013a,
	abstract = {{This paper introduces inverse geodynamo modelling, a framework imaging
   flow throughout the Earth's core from observations of the geomagnetic
   field and its secular variation. The necessary prior information is
   provided by statistics from 3-D and self-consistent numerical
   simulations of the geodynamo. The core method is a linear estimation (or
   Kalman filtering) procedure, combined with standard frozen-flux core
   surface flow inversions in order to handle the non-linearity of the
   problem. The inversion scheme is successfully validated using synthetic
   test experiments. A set of four numerical dynamo models of increasing
   physical complexity and similarity to the geomagnetic field is then used
   to invert for flows at single epochs within the period 1970-2010, using
   data from the geomagnetic field models CM4 and gufm-sat-Q3. The
   resulting core surface flows generally provide satisfactory fits to the
   secular variation within the level of modelled errors, and robustly
   reproduce the most commonly observed patterns while additionally
   presenting a high degree of equatorial symmetry. The corresponding deep
   flows present a robust, highly columnar structure once rotational
   constraints are enforced to a high level in the prior models, with
   patterns strikingly similar to the results of quasi-geostrophic
   inversions. In particular, the presence of a persistent planetary scale,
   eccentric westward columnar gyre circling around the inner core is
   confirmed. The strength of the approach is to uniquely determine the
   trade-off between fit to the data and complexity of the solution by
   clearly connecting it to first principle physics; statistical deviations
   observed between the inverted flows and the standard model behaviour can
   then be used to quantitatively assess the shortcomings of the physical
   modelling. Such deviations include the (i) westwards and (ii)
   hemispherical character of the eccentric gyre. A prior model with
   angular momentum conservation of the core-mantle inner-core system, and
   gravitational coupling of reasonable strength between the mantle and the
   inner core, is shown to produce enough westward drift to resolve
   statistical deviation (i). Deviation (ii) is resolved by a prior with an
   hemispherical buoyancy release at the inner-core boundary, with excess
   buoyancy below Asia. This latter result suggests that the recently
   proposed inner-core translational instability presently transports the
   solid inner-core material westwards, opposite to the seismologically
   inferred long-term trend but consistently with the eccentricity of the
   geomagnetic dipole in recent times.}},
	address = {{GREAT CLARENDON ST, OXFORD OX2 6DP, ENGLAND}},
	affiliation = {{Aubert, J (Reprint Author), Univ Paris Diderot, UMR CNRS 7154, Inst Phys Globe Paris, Sorbonne Paris Cite, 1 Rue Jussieu, F-75005 Paris, France. Univ Paris Diderot, UMR CNRS 7154, Inst Phys Globe Paris, Sorbonne Paris Cite, F-75005 Paris, France.}},
	author = {Aubert, Julien},
	author-email = {{aubert@ipgp.fr}},
	date-added = {2013-02-21 14:19:29 +0000},
	date-modified = {2013-09-13 13:02:16 +0000},
	doc-delivery-number = {{071VG}},
	doi = {{10.1093/gji/ggs051}},
	funding-acknowledgement = {{French Institut National des Sciences de l'Univers (INSU) of CNRS; French Agence Nationale de la Recherche {[}ANR-2011-BS56-011]; GENCI-IDRIS {[}2011-042122, 2012-042122]}},
	funding-text = {{JA wishes to thank Ingo Wardinski and an anonymous referee for insightful reviews. This work was supported by programs PNP/SEDI-TPS of French Institut National des Sciences de l'Univers (INSU) of CNRS, and by the French Agence Nationale de la Recherche under the grant ANR-2011-BS56-011. Numerical computations were performed at S-CAPAD, IPGP, France and using HPC resources from GENCI-IDRIS (Grants 2011-042122 and 2012-042122). This is IPGP contribution 3345.}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	journal-iso = {{Geophys. J. Int.}},
	keywords = {{Inverse theory; Dynamo: theories and simulations; Rapid time variations}},
	keywords-plus = {{BOUNDARY HEAT-FLOW; MAGNETIC-FIELD; INNER-CORE; SECULAR VARIATION; GEODYNAMO MODELS; ANGULAR-MOMENTUM; SPHERICAL-SHELL; SURFACE; MANTLE; CONVECTION}},
	language = {{English}},
	month = {{FEB}},
	number = {{2}},
	number-of-cited-references = {{44}},
	pages = {{537-556}},
	publisher = {{OXFORD UNIV PRESS}},
	research-areas = {{Geochemistry \& Geophysics}},
	times-cited = {{0}},
	title = {{Flow throughout the Earth's core inverted from geomagnetic observations and numerical dynamo models}},
	type = {{Article}},
	unique-id = {{ISI:000313623100006}},
	volume = {{192}},
	web-of-science-categories = {{Geochemistry \& Geophysics}},
	year = {{2013}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/gji/ggs051%7D}}

@article{Deguen2011,
	abstract = {{The dynamics of Earth's inner core depends critically on whether it is
   stably stratified or unstably stratified. We propose here a general
   analysis of the thermal evolution of the inner core. Whether the
   geotherm in the inner core is superadiabatic or not depends on the inner
   core solidification rate, on the thermal diffusivity of iron at inner
   core conditions, and on the ratio of the Clapeyron slope to the
   adiabatic gradient in the inner core. The temperature field within the
   inner core can be destabilizing-and could drive convection-if the growth
   of the inner core is fast enough. The effect of radiogenic heating is
   probably small, and, perhaps surprisingly, can even stabilize the inner
   core against convection. The uncertainties are such that it is not
   possible at present to conclude about the likelihood of thermal
   convection in the inner core, but recent estimates of the Core-Mantle
   Boundary (CMB) heat flux and inner core conductivity favour convection.
   Thermal convection is more likely early in the inner core history, a
   consequence of the secular decrease in cooling rate of the core. In
   addition, solidification-induced partitioning of the light elements may
   induce a stable density stratification within the inner core.
   We develop a numerical model of thermochemical convection in a growing
   inner core, which couples the evolution and dynamics of the inner core
   with the thermal and compositional evolution of the outer core. Melting
   and crystallization associated with deformation of the Inner Core
   Boundary (ICB) would be of importance for the style of convection if the
   viscosity is large, but we focus here on the case of low viscosity for
   which phase change associated with dynamic topography at the ICB is
   expected to play a secondary role. In this regime, convection is typical
   of high Rayleigh number internally heated convection, with cold plumes
   falling from the ICB.
   Several possible scenarios can lead to a layered inner core, either
   because of cessation of thermal convection due to the decrease in
   cooling rate of the core, or because of a compositional stratification
   which can confine convection in the deep inner core, or stabilize the
   whole inner core. For each of these scenarios, it is possible to find
   plausible sets of parameters (inner core age, viscosity, magnitude of
   the compositional stratification) for which the radius at which
   convection stops corresponds to the radius of the seismically inferred
   innermost inner core.}},
	author = {Deguen, Renaud and Cardin, Philippe},
	date-added = {2013-01-30 15:06:00 +0000},
	date-modified = {2013-01-30 15:06:10 +0000},
	doi = {{10.1111/j.1365-246X.2011.05222.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{DEC}},
	number = {{3}},
	pages = {{1101-1118}},
	researcherid-numbers = {{CARDIN, Philippe/A-2625-2012}},
	times-cited = {{5}},
	title = {{Thermochemical convection in Earth's inner core}},
	unique-id = {{ISI:000297114400004}},
	volume = {{187}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2011.05222.x%7D}}

@article{Gubbins2013,
	author = {Gubbins, D. and Alfe, D. and Davies, Chris J.},
	date-added = {2013-01-29 10:27:47 +0000},
	date-modified = {2013-07-17 15:22:51 +0000},
	doi = {10.1002/grl.50186},
	journal = {Geophys. Res. Lett.},
	number = {6},
	pages = {1084-1088},
	title = {Compositional Instability of {E}arth's Solid Inner Core},
	volume = {40},
	year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/grl.50186}}

@article{Aubert2011assim,
	abstract = {{Over the past decades, direct three-dimensional numerical modelling has
   been successfully used to reproduce the main features of the geodynamo.
   Here we report on efforts to solve the associated inverse problem,
   aiming at inferring the underlying properties of the system from the
   sole knowledge of surface observations and the first principle dynamical
   equations describing the convective dynamo. To this end we rely on twin
   experiments. A reference model time sequence is first produced and used
   to generate synthetic data, restricted here to the large-scale component
   of the magnetic field and its rate of change at the outer boundary.
   Starting from a different initial condition, a second sequence is next
   run and attempts are made to recover the internal magnetic, velocity and
   buoyancy anomaly fields from the sparse surficial data. In order to
   reduce the vast underdetermination of this problem, we use stochastic
   inversion, a linear estimation method determining the most likely
   internal state compatible with the observations and some prior
   knowledge, and we also implement a sequential evolution algorithm in
   order to invert time-dependent surface observations. The prior is the
   multivariate statistics of the numerical model, which are directly
   computed from a large number of snapshots stored during a preliminary
   direct run. The statistics display strong correlation between different
   harmonic degrees of the surface observations and internal fields,
   provided they share the same harmonic order, a natural consequence of
   the linear coupling of the governing dynamical equations and of the
   leading influence of the Coriolis force. Synthetic experiments performed
   with a weakly nonlinear model yield an excellent quantitative retrieval
   of the internal structure. In contrast, the use of a strongly nonlinear
   (and more realistic) model results in less accurate static estimations,
   which in turn fail to constrain the unobserved small scales in the time
   integration of the evolution scheme. Evaluating the quality of forecasts
   of the system evolution against the reference solution, we show that our
   scheme can improve predictions based on linear extrapolations on
   forecast horizons shorter than the system e-folding time. Still, in the
   perspective of forthcoming data assimilation activities, our study
   underlines the need of advanced estimation techniques able to cope with
   the moderate to strong nonlinearities present in the geodynamo.}},
	author = {Aubert, J. and Fournier, A.},
	date-added = {2013-01-25 14:00:05 +0000},
	date-modified = {2013-01-25 14:00:21 +0000},
	doi = {{10.5194/npg-18-657-2011}},
	issn = {{1023-5809}},
	journal = {Nonlin. Processes Geophys.},
	number = {{5}},
	pages = {{657-674}},
	researcherid-numbers = {{Fournier, Alexandre/A-5774-2011 Aubert, Julien/A-5616-2011}},
	times-cited = {{1}},
	title = {{Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model}},
	unique-id = {{ISI:000296743300013}},
	volume = {{18}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.5194/npg-18-657-2011%7D}}

@article{Buffett1992,
	abstract = {{Observations of the Earth's nutations are used to explore the possible
   presence of a conducting layer at the base of the mantle. The existence
   of such a layer is suggested by recent experiments on iron and silicate
   mixtures at high pressures and temperatures (Knittle and Jeanloz, 1986,
   1989), which indicate that iron may react with silicate minerals to
   produce metallic compounds. Nutations provide an ideal tool for
   investigating the existence of such a layer because they are sensitive
   to the electrical properties within a thin magnetic boundary layer along
   the core-mantle boundary (CMB). Evidence in favor of a conducting layer
   is found in the effects of ohmic dissipation which cause the amplitude
   of the Earth's nutation to be out-of-phase with tidal forcings. Although
   out-of-phase components in the Earth's nutations are conventionally
   attributed to the dissipative influences of ocean tides and mantle
   anelasticity, these effects appear incapable of explaining nutation
   amplitudes determined from very long baseline interferometry (VLBI)
   observations. The additional effects of ohmic dissipation, enhanced by
   the presence of a thin conducting layer at the CMB, are sufficient to
   reconcile theory and observation. The largest mismatch between
   observations and theory, taking account of ocean tides and mantle
   anelasticity, is a discrepancy of 0.39 +/- 0.04 milliarcseconds in the
   out-of-phase component of the retrograde annual nutation. This
   discrepancy can be eliminated if the lowermost 200 m of the mantle has a
   conductivity of 5 x 10(5)S m-1, and the magnetic energy in the spherical
   harmonic components of the field at the CMB in degrees l > 12 is
   approximately 4 times greater than the energy inferred in degrees l
   less-than-or-equal-to 12 from surface observations. Unfortunately, the
   VLBI observations do not uniquely resolve the mantle conductivity and
   magnetic energy, so that trade-offs exist between these two parameters.
   Nevertheless, a high mantle conductivity is favored on the grounds that
   the alternative, involving high levels of magnetic energy, yields an
   excessive amount of ohmic heating. Other interpretations of the VLBI
   discrepancy are also discussed. One such alternative involves viscous
   dissipation at the CMB, requiring a kinematic viscosity of nu = 0.1 m2
   s-1.}},
	author = {Buffett, B.A.},
	date-added = {2013-01-25 13:55:30 +0000},
	date-modified = {2013-01-25 13:56:04 +0000},
	doi = {{10.1029/92JB00977}},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	month = {{DEC 10}},
	number = {{B13}},
	pages = {{19581-19597}},
	times-cited = {{66}},
	title = {CONSTRAINTS ON MAGNETIC ENERGY AND MANTLE CONDUCTIVITY FROM THE FORCED NUTATIONS OF THE {E}ARTH},
	unique-id = {{ISI:A1992KD95100003}},
	volume = {{97}},
	year = {1992},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/92JB00977%7D}}

@article{Gubbins2008,
	abstract = {{Recent seismological observations suggest the existence of a approximate
   to 150-km-thick density-stratified layer with a P-wave velocity gradient
   that differs slightly from PREM. Such a structure can only be caused by
   a compositional gradient, effects of a slurry or temperature being too
   small and probably the wrong sign. We propose a stably stratified,
   variable concentration layer on the liquidus. Heat is transported by
   conduction down the liquidus while the light and heavy components
   migrate through the layer by a process akin to zone refining, similar to
   the one originally proposed by Braginsky. The layer remains static in a
   frame of reference moving upwards with the expanding inner core
   boundary. We determine the gradient using estimates of c(o), the
   concentration in the main body of the outer core, and c(b), the
   concentration of the liquid at the inner core boundary. We determine the
   depression of the melting point and concentrations using ideal solution
   theory and seismologically determined density jumps at the inner core
   boundary. We suppose that co determines Delta rho(mod), the jump from
   normal mode eigenfrequencies that have long resolution lengths
   straddling the entire layer, and that cb determines Delta rho(bod), the
   jump determined from body waves, which have fine resolution. A simple
   calculation then yields the seismic, temperature, and concentration
   profiles within the layer. Comparison with the distance to the C-cusp of
   PKP and normal mode eigenfrequencies constrain the model. We explore a
   wide range of possible input parameters; many fail to predict sensible
   seismic properties and heat fluxes. A model with Delta rho(mod) = 0.8 gm
   cc(-1), Delta rho(bod) = 0.6 gm cc(-1), and layer thickness 200 km is
   consistent with the seismic observations and can power the geodynamo
   with a reasonable inner core heat flux of approximate to 2 TW and
   nominal inner core age of approximate to 1 Ga. It is quite remarkable
   and encouraging that a model based on direct seismic observations and
   simple chemistry can predict heat fluxes that are comparable with those
   derived from recent core thermal history calculations. The model also
   provides plausible explanations of the observed seismic layer and
   accounts for the discrepancy between estimates of the inner core density
   jumps derived from body waves and normal modes.}},
	author = {Gubbins, David and Masters, Guy and Nimmo, Francis},
	date-added = {2013-01-25 12:03:21 +0000},
	date-modified = {2013-01-25 12:13:54 +0000},
	doi = {{10.1111/j.1365-246X.2008.03879.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{SEP}},
	number = {{3}},
	pages = {{1007-1018}},
	times-cited = {{14}},
	title = {{A thermochemical boundary layer at the base of Earth's outer core and independent estimate of core heat flux}},
	unique-id = {{ISI:000258684400020}},
	volume = {{174}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2008.03879.x%7D}}

@article{Soderlund2012,
	abstract = {{The magnetic fields of planets and stars are thought to play an
   important role in the fluid motions responsible for their field
   generation, as magnetic energy is ultimately derived from kinetic
   energy. We investigate the influence of magnetic fields on convective
   dynamo models by contrasting them with non-magnetic, but otherwise
   identical, simulations. This survey considers models with Prandtl number
   Pr=1; magnetic Prandtl numbers up to Pm=5; Ekman numbers in the range
   10(-3) >= E >= 10(-5); and Rayleigh numbers from near onset to more than
   1000 times critical.
   Two major points are addressed in this letter. First, we find that the
   characteristics of convection, including convective flow structures and
   speeds as well as heat transfer efficiency, are not strongly affected by
   the presence of magnetic fields in most of our models. While Lorentz
   forces must alter the flow to limit the amplitude of magnetic field
   growth, we find that dynamo action does not necessitate a significant
   change to the overall flow field. By directly calculating the forces in
   each of our simulations, we show that the traditionally defined Elsasser
   number, Lambda(i), overestimates the role of the Lorentz force in
   dynamos. The Coriolis force remains greater than the Lorentz force even
   in cases with Lambda(i) approximate to 100, explaining the persistence
   of columnar flows in Lambda(i) > 1 dynamo simulations. We argue that a
   dynamic Elsasser number, Lambda(d), better represents the Lorentz to
   Coriolis force ratio. By applying the Ad parametrization to planetary
   settings, we predict that the convective dynamics (excluding zonal
   flows) in planetary interiors are only weakly influenced by their
   large-scale magnetic fields.
   The second major point addressed here is the observed transition between
   dynamos with dipolar and multipolar magnetic fields. We find that the
   breakdown of dipolar field generation is due to the degradation of
   helicity in the flow. This helicity change does not coincide with the
   destruction of columnar convection and is not strongly influenced by the
   presence of magnetic fields. Force calculations suggest that this
   transition may be related to a competition between inertial and viscous
   forces. If viscosity is indeed important for large-scale field
   generation, such moderate Ekman number models may not adequately
   simulate the dynamics of planetary dynamos, where viscous effects are
   expected to be negligible. (C) 2012 Elsevier B.V. All rights reserved.}},
	author = {Soderlund, K. M. and King, E. M. and Aurnou, J. M.},
	date-added = {2013-01-25 11:22:07 +0000},
	date-modified = {2016-11-14 13:58:55 +0000},
	doi = {{10.1016/j.epsl.2012.03.038}},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Lett.},
	month = {{JUN 1}},
	pages = {{9-20}},
	times-cited = {{2}},
	title = {{The influence of magnetic fields in planetary dynamo models}},
	unique-id = {{ISI:000306884000002}},
	volume = {{333}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2012.03.038%7D}}

@article{DeKoker2012,
	abstract = {{Earth's magnetic field is sustained by magnetohydrodynamic convection
   within the metallic liquid core. In a thermally advecting core, the
   fraction of heat available to drive the geodynamo is reduced by heat
   conducted along the core geotherm, which depends sensitively on the
   thermal conductivity of liquid iron and its alloys with candidate light
   elements. The thermal conductivity for Earth's core is very poorly
   constrained, with current estimates based on a set of scaling relations
   that were not previously tested at high pressures. We perform
   first-principles electronic structure computations to determine the
   thermal conductivity and electrical resistivity for Fe, Fe-Si, and Fe-O
   liquid alloys. Computed resistivity agrees very well with existing shock
   compression measurements and shows strong dependence on light element
   concentration and type. Thermal conductivity at pressure and temperature
   conditions characteristic of Earth's core is higher than previous
   extrapolations. Conductive heat flux near the core-mantle boundary is
   comparable to estimates of the total heat flux from the core but
   decreases with depth, so that thermally driven flow would be constrained
   to greater depths in the absence of an inner core.}},
	author = {De Koker, Nico and Steinle-Neumann, Gerd and Vlcek, Vojtech},
	date-added = {2013-01-24 16:09:05 +0000},
	date-modified = {2013-01-25 10:20:46 +0000},
	doi = {{10.1073/pnas.1111841109}},
	issn = {{0027-8424}},
	journal = {PNAS},
	month = {{MAR 13}},
	number = {{11}},
	pages = {{4070-4073}},
	researcherid-numbers = {{Steinle-Neumann, Gerd/D-8805-2012}},
	times-cited = {{5}},
	title = {{Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core}},
	unique-id = {{ISI:000301426700017}},
	volume = {{109}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.1111841109%7D}}

@article{Gubbins2012,
	author = {Gubbins, D. and Davies, Chris J.},
	date-added = {2013-01-24 15:13:31 +0000},
	date-modified = {2013-03-25 15:15:15 +0000},
	doi = {10.1016/j.pepi.2012.11.001},
	journal = {Phys. Earth. Planet. Int.},
	pages = {21-28},
	title = {The stratified layer at the core-mantle boundary caused by barodiffusion of oxygen, sulphur and silicon},
	volume = {215},
	year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2012.11.001}}

@article{Mizzon2013,
	author = {Mizzon, H. and Monnereau, Marc},
	date-added = {2013-01-24 13:23:38 +0000},
	date-modified = {2013-01-24 13:25:08 +0000},
	doi = {10.1016/j.epsl.2012.11.005},
	journal = {Earth Planet. Sci. Lett.},
	pages = {391-401},
	title = {Implications of the lopsided growth for the viscosity of {E}arth's inner core},
	volume = {361},
	year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2012.11.005}}

@article{Pozzo2012,
	abstract = {{The Earth acts as a gigantic heat engine driven by the decay of
   radiogenic isotopes and slow cooling, which gives rise to plate
   tectonics, volcanoes and mountain building. Another key product is the
   geomagnetic field, generated in the liquid iron core by a dynamo running
   on heat released by cooling and freezing (as the solid inner core
   grows), and on chemical convection (due to light elements expelled from
   the liquid on freezing). The power supplied to the geodynamo, measured
   by the heat flux across the core-mantle boundary (CMB), places
   constraints on Earth's evolution(1). Estimates of CMB heat flux(2-5)
   depend on properties of iron mixtures under the extreme pressure and
   temperature conditions in the core, most critically on the thermal and
   electrical conductivities. These quantities remain poorly known because
   of inherent experimental and theoretical difficulties. Here we use
   density functional theory to compute these conductivities in liquid iron
   mixtures at core conditions from first principles-unlike previous
   estimates, which relied on extrapolations. The mixtures of iron, oxygen,
   sulphur and silicon are taken from earlier work(6) and fit the
   seismologically determined core density and inner-core boundary density
   jump(7,8). We find both conductivities to be two to three times higher
   than estimates in current use. The changes are so large that core
   thermal histories and power requirements need to be reassessed. New
   estimates indicate that the adiabatic heat flux is 15 to 16 terawatts at
   the CMB, higher than present estimates of CMB heat flux based on mantle
   convection(1); the top of the core must be thermally stratified and any
   convection in the upper core must be driven by chemical convection
   against the adverse thermal buoyancy or lateral variations in CMB heat
   flow. Power for the geodynamo is greatly restricted, and future models
   of mantle evolution will need to incorporate a high CMB heat flux and
   explain the recent formation of the inner core.}},
	author = {Pozzo, M. and Davies, C. J. and Gubbins, D. and Alf{\`e}, D.},
	date-added = {2013-01-24 13:22:19 +0000},
	date-modified = {2016-11-14 13:52:05 +0000},
	doi = {{10.1038/nature11031}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{MAY 17}},
	number = {{7398}},
	pages = {{355-358}},
	researcherid-numbers = {{Alfe`, Dario/C-1521-2008 Pozzo, Monica/C-4965-2011 Davies, Chris/I-7652-2012}},
	times-cited = {{6}},
	title = {{Thermal and electrical conductivity of iron at Earth's core conditions}},
	unique-id = {{ISI:000304099100039}},
	volume = {{485}},
	year = {{2012}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature11031%7D}}

@article{Davies2013,
	author = {Davies, Chris J. and Silva, L. and Mound, J. E.},
	date-added = {2013-01-24 11:11:20 +0000},
	date-modified = {2013-03-25 15:15:22 +0000},
	doi = {10.1016/j.pepi.2012.10.001},
	journal = {Phys. Earth Planet. Inter.},
	pages = {104-115},
	title = {On the influence of a translating inner core in models of outer core convection},
	volume = {214},
	year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2012.10.001}}

@article{Gubbins2011,
	abstract = {{The Earth's magnetic field is generated by a dynamo in the liquid iron
   core, which convects in response to cooling of the overlying rocky
   mantle. The core freezes from the innermost surface outward, growing the
   solid inner core and releasing light elements that drive compositional
   convection(1-3). Mantle convection extracts heat from the core at a rate
   that has enormous lateral variations(4). Here we use geodynamo
   simulations to show that these variations are transferred to the
   inner-core boundary and can be large enough to cause heat to flow into
   the inner core. If this were to occur in the Earth, it would cause
   localized melting. Melting releases heavy liquid that could form the
   variable-composition layer suggested by an anomaly in seismic velocity
   in the 150 kilometres immediately above the inner-core boundary(5-7).
   This provides a very simple explanation of the existence of this layer,
   which otherwise requires additional assumptions such as locking of the
   inner core to the mantle, translation from its geopotential centre(7,8)
   or convection with temperature equal to the solidus but with composition
   varying from the outer to the inner core(9). The predominantly narrow
   downwellings associated with freezing and broad upwellings associated
   with melting mean that the area of melting could be quite large despite
   the average dominance of freezing necessary to keep the dynamo going.
   Localized melting and freezing also provides a strong mechanism for
   creating seismic anomalies in the inner core itself, much stronger than
   the effects of variations in heat flow so far considered(10).}},
	author = {Gubbins, David and Sreenivasan, Binod and Mound, Jon and Rost, Sebastian},
	date-added = {2013-01-24 11:04:45 +0000},
	date-modified = {2013-08-13 15:40:52 +0000},
	doi = {{10.1038/nature10068}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{MAY 19}},
	number = {{7347}},
	pages = {{361-363}},
	times-cited = {{12}},
	title = {{Melting of the Earth's inner core}},
	unique-id = {{ISI:000290722400045}},
	volume = {{473}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature10068%7D}}

@article{Olson2012-2,
	author = {Olson, P. and Deguen, R.},
	date-added = {2012-09-03 14:02:23 +0000},
	date-modified = {2012-09-03 14:04:01 +0000},
	doi = {10.1038/NGEO1506},
	journal = {Nature Geosci.},
	pages = {565-569},
	title = {Eccentricity of the geomagnetic dipole caused by lopsided inner core growth},
	volume = {5},
	year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/NGEO1506}}

@article{Aubert2011_2,
	abstract = {{We present a systematic survey of numerical geodynamo simulations where
   the inner core is allowed to differentially rotate in the longitudinal
   direction with respect to the mantle. We focus on the long-term
   behaviour of inner core rotation, on timescales much longer than the
   overturn time of the fluid outer core, including the steady component of
   rotation. The inner core is subject to viscous and magnetic torques
   exerted by the fluid outer core, and a gravitational restoring torque
   exerted by the mantle. We show that the rate of steady inner core
   rotation is limited by the differential rotation between spherical
   surfaces that the convective dynamics can sustain across the fluid outer
   core. We further show that this differential rotation is determined by a
   torque balance between the resistive Lorentz force and the Coriolis
   force on spherical surfaces within the fluid core. We derive a scaling
   law on the basis of this equilibrium suggesting that the ratio of the
   steady inner core rotation to typical angular velocity within the fluid
   core should be proportional to the square root of the Ekman number, in
   agreement with our numerical results. The addition of gravitational
   coupling does not alter this scaling, though it further reduces the
   amplitude of inner core rotation. In contrast, the long-term
   fluctuations in inner core rotation remain proportional to the fluid
   core angular velocity, with no apparent dependency on the Ekman number.
   If the same torque balance pertains to the Earth's core conditions, the
   inner core rotation then consists in a very slow super rotation of a few
   degrees per million years, superimposed over large fluctuations (at
   about a tenth of a degree per year). This suggests that the present-day
   seismically inferred inner core rotation is a fragment of a time-varying
   signal, rather than a steady super rotation. For the inner core rotation
   fluctuations not to cause excessive variations in the length-of-day, the
   strength of the gravitational coupling between the inner core and the
   mantle must be smaller than previously published values. We finally
   explore how the torque balance which we observe in our models could be
   altered in planetary cores, yielding possibly larger values of the
   steady rotation.}},
	author = {Aubert, Julien and Dumberry, Mathieu},
	date-added = {2012-08-27 10:19:22 +0000},
	date-modified = {2012-08-27 10:19:37 +0000},
	doi = {{10.1111/j.1365-246X.2010.04842.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JAN}},
	number = {{1}},
	pages = {{162-170}},
	title = {{Steady and fluctuating inner core rotation in numerical geodynamo models}},
	unique-id = {{ISI:000285357300010}},
	volume = {{184}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2010.04842.x%7D}}

@article{Olson2012,
	author = {Olson, P. and Christensen, U.R. and Driscoll, P.},
	date-added = {2012-05-30 15:09:27 +0200},
	date-modified = {2012-05-30 15:11:31 +0200},
	doi = {10.1016/j.epsl.2011.12.008},
	journal = {Earth. Plan. Sci. Let.},
	pages = {75-82},
	title = {From superchrons to secular variation: A broadband dynamo frequency spectrum for the geomagnetic dipole},
	volume = {319-320},
	year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2011.12.008}}

@article{Christensen2003,
	author = {Christensen, Ulrich R. and Olson, P.},
	date-added = {2012-04-19 13:53:11 +0200},
	date-modified = {2013-03-25 15:14:21 +0000},
	journal = {Phys. Earth Planet. Int.},
	note = {doi: 10.1016/S0031-9201(03)00064-5},
	pages = {39-54},
	title = {Secular variation in numerical geodynamo models with lateral variations of boundary heat flux},
	volume = {138},
	year = {2003}}

@article{Monnereau2010,
	author = {Monnereau, Marc and Calvet, Marie and Margerin, Ludovic and Souriau, Annie},
	date-added = {2012-04-16 14:41:59 +0200},
	date-modified = {2012-04-16 21:52:21 +0200},
	doi = {{10.1126/science.1186212}},
	issn = {{0036-8075}},
	journal = {Science},
	month = {{MAY 21}},
	number = {{5981}},
	pages = {{1014-1017}},
	title = {{Lopsided Growth of Earth's Inner Core}},
	unique-id = {{ISI:000277877100037}},
	volume = {{328}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1186212%7D}}

@article{Alboussiere2010,
	author = {Alboussi\`ere, Thierry and Deguen, Renaud and Melzani, Mickael},
	date-added = {2012-04-16 14:41:49 +0200},
	date-modified = {2013-03-13 17:14:59 +0000},
	doi = {{10.1038/nature09257}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{AUG 5}},
	number = {{7307}},
	pages = {{744-747}},
	title = {{Melting-induced stratification above the Earth's inner core due to convective translation}},
	unique-id = {{ISI:000280562500036}},
	volume = {{466}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature09257%7D}}

@article{Holme2011,
	abstract = {{Data from recent satellite missions have vastly increased the resolution
   of models of the geomagnetic field, and its first and second time
   derivatives-secular variation (SV) and secular acceleration (SA). The
   spectra of both SV and SA are `blue' at the core-mantle boundary, both
   well-fit by functions proportional to l(l + 1) where l is the spherical
   harmonic degree. The ratio of the two spectra defines a timescale for
   geomagnetic variations of approximately 10 yrs for all resolvable
   harmonic degrees. The blue spectra should prevent meaningful maps of the
   SV being generated; nevertheless, the coherence of the maps up to
   harmonic degree 13 suggests that it is possible to obtain useful insight
   from their examination. Low SV is confirmed under the Pacific, but also
   revealed under the North Atlantic and Antarctica. These features are
   more readily explained in terms of dynamo control through thermal
   core-mantle coupling than by electromagnetic screening. Comparison with
   maps from measurements prior to the recent satellites, using the
   `Comprehensive Model', suggests that models back to at least 1970 are
   sufficiently good to enable direct comparison of the SV.}},
	author = {Holme, R. and Olsen, N. and Bairstow, F. L.},
	date-added = {2012-03-13 13:16:46 +0100},
	date-modified = {2012-03-13 13:17:00 +0100},
	doi = {{10.1111/j.1365-246X.2011.05066.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{AUG}},
	number = {{2}},
	pages = {{521-528}},
	title = {{Mapping geomagnetic secular variation at the core-mantle boundary}},
	unique-id = {{ISI:000292742700010}},
	volume = {{186}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2011.05066.x%7D}}

@article{Helffrich2010,
	abstract = {{Light elements must be present in the nearly pure iron core of the Earth
   to match the remotely observed properties of the outer and inner
   cores(1,2). Crystallization of the inner core excludes light elements
   from the solid, concentrating them in liquid near the inner-core
   boundary that potentially rises and collects at the top of the core(3),
   and this may have a seismically observable signal. Here we present
   array-based observations of seismic waves sensitive to this part of the
   core whose wave speeds require there to be radial compositional
   variation in the topmost 300 km of the outer core. The velocity profile
   significantly departs from that of compression of a homogeneous liquid.
   Total light-element enrichment is up to five weight per cent at the top
   of the core if modelled in the Fe-O-S system. The stratification
   suggests the existence of a subadiabatic temperature gradient at the top
   of the outer core.}},
	author = {Helffrich, George and Kaneshima, Satoshi},
	date-added = {2012-03-09 11:39:44 +0100},
	date-modified = {2013-08-13 15:40:23 +0000},
	doi = {{10.1038/nature09636}},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{DEC 9}},
	number = {{7325}},
	pages = {{807-810}},
	title = {{Outer-core compositional stratification from observed core wave speed profiles}},
	unique-id = {{ISI:000285093700042}},
	volume = {{468}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature09636%7D}}

@article{Takehiro2001,
	abstract = {{Penetration of columnar convection in a rapidly rotating spherical shell
   into a stably stratified fluid layer near the outer boundary is
   investigated. An analytical expression for the penetration thickness is
   derived by considering perturbations to a stably stratified rotating
   Boussinesq fluid in a semi-infinite region with the rotation axis tilted
   relative to the gravity axis. Solutions for the response to vortical
   motion applied at the bottom boundary show that the penetration
   thickness is proportional to the angular velocity of the system and to
   the horizontal scale of the vortices, and inversely proportional to the
   Brunt-Vaisala frequency in the stratified layer. Thus the stratification
   acts as a lowpass filter to forcing from below. The analytic expression
   for the penetration thickness gives good agreement with numerical
   results for critical convection in a rotating spherical shell with a
   stably stratified outer layer. The results suggest that if deep
   convection is to penetrate the stratified layer observed by the Galileo
   probe then the horizontal scale needs to be more than several thousand
   kilometers. Parameter values from recent studies of the thermal history
   of the Earth's core also suggest that any convection columns with
   horizontal scale larger than several hundred kilometers would be
   expected to penetrate into any stable layer in the outer part of the
   Earth's fluid outer core when the Lorentz force plays a subdominant
   role. (C) 2001 Elsevier Science B.V. All rights reserved.}},
	author = {Takehiro, S and Lister, JR},
	date-added = {2012-03-09 11:39:40 +0100},
	date-modified = {2012-03-09 11:39:58 +0100},
	doi = {{10.1016/S0012-821X(01)00283-7}},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Let.},
	month = {{MAY 15}},
	number = {{3-4}},
	pages = {{357-366}},
	title = {{Penetration of columnar convection into an outer stably stratified layer in rapidly rotating spherical fluid shells}},
	unique-id = {{ISI:000168799600011}},
	volume = {{187}},
	year = {{2001}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0012-821X(01)00283-7%7D}}

@article{Gubbins2007strat,
	abstract = {{The geodynamo requires that at least part of the Earth's liquid core be
   convecting so vigorously as to mix it thoroughly to uniform composition
   and adiabatic temperature. It is possible, however, that part of liquid
   core is stably stratified, either thermally because of a low temperature
   gradient or compositionally because light material has separated out.
   The top of the outer core is the most likely site for stability because
   the adiabat is steepest there and because light material will rise to
   the surface. Here I show that part of the observed secular variation,
   that associated with flux expulsion in the southern hemisphere, can only
   be caused by fluid upwelling in the electromagnetic boundary layer at
   the top of the core or by very strong poloidal field gradients at the
   top of the core. Any stratified layer is limited to roughly the
   uppermost 100 km if flux expulsion is the mechanism; if the layer is any
   thicker the region in the southern hemisphere where reverse flux patches
   are growing must also be the site of very strong field gradients caused
   by very strong near-surface shear flows.}},
	author = {Gubbins, David},
	date-added = {2012-03-09 11:39:40 +0100},
	date-modified = {2012-03-09 11:40:32 +0100},
	issn = {{1343-8832}},
	journal = {Earth. Planets. Space.},
	note = {{International Session on Perspectives Geomagnetism - Geodynamo, Paleomagnetis, and Rock Magnetism, Chiba City, JAPAN, MAY 14-18, 2006}},
	number = {{7}},
	organization = {{Japan Geosci Union}},
	pages = {{661-664}},
	title = {{Geomagnetic constraints on stratification at the top of Earth's core}},
	unique-id = {{ISI:000248613700003}},
	volume = {{59}},
	year = {{2007}}}

@article{Sreenivasan2010,
	abstract = {{It is widely accepted that the Earth's magnetic field is powered by a
   convection-driven dynamo operating in its liquid iron core. The
   twentieth century witnessed remarkable advances in the field of
   magnetohydrodynamics, which eventually led to three-dimensional computer
   simulations of the geodynamo. In this review we look at the significant
   developments that shaped our present understanding of magnetic field
   generation in the Earth's core. We also examine the successes and
   shortcomings of current geodynamo models.}},
	author = {Sreenivasan, Binod},
	date-added = {2012-03-08 20:43:07 +0100},
	date-modified = {2012-03-08 20:43:20 +0100},
	issn = {{0011-3891}},
	journal = {Current Science},
	month = {{DEC 25}},
	number = {{12}},
	pages = {{1739-1750}},
	title = {{Modelling the geodynamo: progress and challenges}},
	unique-id = {{ISI:000286028200021}},
	volume = {{99}},
	year = {{2010}}}

@incollection{Holme2007,
	author = {Holme, R.},
	booktitle = {Treatise on Geophysics. 8- Core dynamics},
	date-added = {2012-03-05 14:12:54 +0100},
	date-modified = {2012-03-05 14:14:46 +0100},
	editor = {Olson, P.},
	publisher = {Elsevier},
	title = {Large-scale flow in the core},
	volume = {8},
	year = {2007}}

@article{Olsen2010AGU,
	author = {Olsen, N. and L{\"u}hr, H. and Sabaka, T. J. and Michaelis, I. and Rauberg, J. and Toffner-Clausen, L.},
	date-added = {2012-02-14 14:17:10 +0100},
	date-modified = {2012-03-13 13:20:38 +0100},
	journal = {Abstract GP21A-0992, Fall Meeting, AGU, San Francisco, CA},
	note = {http://www.spacecenter.dk/files/magnetic-models/CHAOS-4/},
	title = {{CHAOS-4 - A high-resolution geomagnetic field model derived from low-altitude CHAMP data}},
	year = {2010}}

@article{Holme2006,
	abstract = {{Data from the Orsted and CHAMP satellites have allowed modelling of the
   geomagnetic secular variation (SV) with unprecedented accuracy. The
   spectrum of the SV is consistent with generation by advectively
   dominated processes. Based on the SV model, it is not possible to reject
   the frozen-flux hypothesis, but the spectrum of the SV implies that a
   conclusive test of frozen-flux is not possible. We parametrize the
   effects of diffusion as an expected misfit in the flow prediction due to
   departure from the frozen-flux hypothesis; at low spherical harmonic
   degrees, this contribution dominates the expected departure of the SV
   predictions from flow to the observed SV, while at high degrees the SV
   model uncertainty is dominant. We construct fine-scale core surface
   flows to model the SV. Flow non-uniqueness is a serious problem because
   the flows are sufficiently small scale to allow flow around
   non-uniqueness contours. Nevertheless, we find evidence to support
   previously suggested polar vortices. For this model of field and SV,
   predicted variations in length of day from modelled core angular
   momentum vary over a large range, although there is evidence that this
   effect is reduced with longer time-series of magnetic data and better
   parametrization of the external magnetic field.}},
	author = {Holme, R. and Olsen, N.},
	date-added = {2012-02-07 13:42:35 +0100},
	date-modified = {2012-02-07 13:42:46 +0100},
	doi = {{10.1111/j.1365-246X.2006.03033.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{AUG}},
	number = {{2}},
	pages = {{518-528}},
	title = {{Core surface flow modelling from high-resolution secular variation}},
	unique-id = {{ISI:000239004900003}},
	volume = {{166}},
	year = {{2006}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2006.03033.x%7D}}

@article{Rau2000,
	abstract = {{We test inversion methods of geomagnetic secular variation data for the
   pattern of fluid flow near the surface of the core with synthetic data.
   These are taken from self-consistent 3-D models of convection-driven
   magnetohydrodynamic dynamos in rotating spherical shells, which generate
   dipole-dominated magnetic fields with an Earth-like morphology. We find
   that the frozen-flux approximation, which is fundamental to all
   inversion schemes, is satisfied to a fair degree in the models. In order
   to alleviate the non-uniqueness of the inversion, usually a priori
   conditions are imposed on the flow; for example, it is required to be
   purely toroidal or geostrophic. Either condition is nearly satisfied by
   our model flows near the outer surface. However, most of the surface
   velocity field lies in the nullspace of the inversion problem.
   Nonetheless, the a priori constraints reduce the nullspace, and by
   inverting the magnetic data with either one of them we recover a
   significant part of the flow. With the geostrophic condition the
   correlation coefficient between the inverted and the true velocity field
   can reach values of up to 0.65, depending on the choice of the damping
   parameter. The correlation is significant at the 95 per cent level for
   most spherical harmonic degrees up to l = 26. However, it degrades
   substantially, even at long wavelengths, when we truncate the magnetic
   data sets to l less than or equal to 14, that is, to the resolution of
   core-field models. In some of the latter inversions prominent zonal
   currents, similar to those seen in core-flow models derived from
   geomagnetic data, occur in the equatorial region. However, the true flow
   does not contain this flow component. The results suggest that some
   meaningful information on the core-flow pattern can be retrieved from
   secular variation data, but also that the limited resolution of the
   magnetic core field could produce serious artefacts.}},
	author = {Rau, S and Christensen, U and Jackson, A and Wicht, J},
	date-added = {2012-02-02 15:48:09 +0100},
	date-modified = {2012-02-02 15:48:21 +0100},
	doi = {{10.1046/j.1365-246x.2000.00097.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{MAY}},
	number = {{2}},
	pages = {{485-497}},
	title = {{Core flow inversion tested with numerical dynamo models}},
	unique-id = {{ISI:000086981500017}},
	volume = {{141}},
	year = {{2000}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1046/j.1365-246x.2000.00097.x%7D}}

@article{Amit2008,
	abstract = {{We use numerical dynamos to investigate the possible role of magnetic
   diffusion at the top of the core. We find that the contribution of
   radial magnetic diffusion to the secular variation is correlated with
   that of tangential magnetic diffusion for a wide range of control
   parameters. The correlation between the two diffusive terms is
   interpreted in terms of the variation in the strength of poloidal flow
   along a columnar flow tube. The amplitude ratio of the two diffusive
   terms is used to estimate the probable contribution of radial magnetic
   diffusion to the secular variation at Earth-like conditions. We then
   apply a model where radial magnetic diffusion is proportional to
   tangential diffusion to core flow inversions of geomagnetic secular
   variation data. We find that including magnetic diffusion does not
   change dramatically the global flow but some significant local
   variations appear. In the non frozen-flux core flow models (termed
   `diffusive'), the hemispherical dichotomy between the active Atlantic
   and quiet Pacific is weaker, a cyclonic vortex below North America
   emerges and the vortex below Asia is stronger. Our results have several
   important geophysical implications. First, our diffusive flow models
   contain some flow activity at low latitudes in the Pacific, suggesting a
   local balance between magnetic field advection and diffusion in that
   region. Second, the cyclone below North America in our diffusive flows
   reconciles the difference between mantle-driven thermal wind predictions
   and frozen-flux core flow models, and is consistent with the prominent
   intense magnetic flux patch below North America in geomagnetic field
   models. Finally, we hypothesize that magnetic diffusion near the core
   surface plays a larger role in the geomagnetic secular variation than
   usually assumed.}},
	author = {Amit, Hagay and Christensen, Ulrich R.},
	date-added = {2012-02-02 15:21:40 +0100},
	date-modified = {2012-02-02 15:21:51 +0100},
	doi = {{10.1111/j.1365-246X.2008.03948.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{DEC}},
	number = {{3}},
	pages = {{913-924}},
	title = {{Accounting for magnetic diffusion in core flow inversions from geomagnetic secular variation}},
	unique-id = {{ISI:000261185000010}},
	volume = {{175}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2008.03948.x%7D}}

@article{Amit2007,
	abstract = {{We test the quality of a new core flow imaging method that incorporates
   constraints on flow helicity, using synthetic magnetic secular variation
   data from 3-D self-consistent numerical dynamo models. Comparison with
   the dynamo model flows reveals that our imaging method delineates most
   of the main large-scale flow features, both in pattern and magnitude.
   The dynamo model flows are characterized by high-latitude vortices, some
   equatorial symmetry, columnar convection and a significant amount of
   flow along radial magnetic field contours. Our inversion method
   correctly images these aspects of the flows. The correlation coefficient
   between the dynamo velocity and the imaged velocity exceeds 0.5 in cases
   with large-scale flow and magnetic field pattern, but degrades
   substantially in more complex cases when the scale of the secular
   variation is small. The magnitude of the imaged velocity depends on the
   a priori-assumed ratio of tangential divergence to radial vorticity k,
   in some resemblance to the damping parameter in spectral methods,
   although with our method the misfit is insensitive to k-values.
   Including tangential magnetic diffusion in core flow inversion improves
   the quality of the imaged velocity pattern. The largest artefacts in the
   imaged velocities are due to unmodelled radial magnetic diffusion and
   truncation of the input magnetic field.}},
	author = {Amit, Hagay and Olson, Peter and Christensen, Ulrich},
	date-added = {2012-02-01 16:26:03 +0100},
	date-modified = {2012-02-01 16:26:16 +0100},
	doi = {{10.1111/j.1365-246X.2006.03175.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JAN}},
	number = {{1}},
	pages = {{27-39}},
	title = {{Tests of core flow imaging methods with numerical dynamos}},
	unique-id = {{ISI:000243295300003}},
	volume = {{168}},
	year = {{2007}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2006.03175.x%7D}}

@article{Moon1979,
	author = {Moon, W.},
	date-added = {2012-01-27 16:30:24 +0100},
	date-modified = {2012-01-27 16:31:54 +0100},
	doi = {{10.1016/0010-4655(79)90092-4}},
	issn = {{0010-4655}},
	journal = {Comp. Phys. Comm.},
	number = {{2}},
	pages = {{267-271}},
	title = {Numerical evaluation of geomagnetic dynamo integrals ({E}lsasser and {A}dams-{G}aunt integrals).},
	unique-id = {{ISI:A1979GM71000010}},
	volume = {{16}},
	year = {{1979}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0010-4655(79)90092-4%7D}}

@article{James1973,
	author = {James, R.W.},
	date-added = {2012-01-27 16:22:27 +0100},
	date-modified = {2012-01-27 16:23:29 +0100},
	doi = {{10.1098/rspa.1973.0003}},
	issn = {{1364-5021}},
	journal = {Proc. Roy. Soc. A},
	number = {{1587}},
	pages = {{469-478}},
	title = {{A}dams and {E}lsasser dynamo integrals},
	unique-id = {{ISI:A1973O522700003}},
	volume = {{331}},
	year = {{1973}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1098/rspa.1973.0003%7D}}

@article{Whaler1986,
	author = {Whaler, K. A.},
	date-added = {2012-01-27 15:51:27 +0100},
	date-modified = {2012-01-27 15:52:52 +0100},
	doi = {{10.1111/j.1365-246X.1986.tb03844.x}},
	issn = {{0016-8009}},
	journal = {Geophys. J. R. astr. Soc.},
	month = {{AUG}},
	number = {{2}},
	pages = {{563-588}},
	title = {Geomagnetic evidence for fluid upwelling at the core-mantle boundary},
	unique-id = {{ISI:A1986D446600019}},
	volume = {{86}},
	year = {{1986}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.1986.tb03844.x%7D}}

@article{Olsen2010CHAOS,
	abstract = {{As a part of the 11th generation IGRF defined by IAGA, we propose a
   candidate model for the DGRF 2005, a candidate model for IGRF 2010 and a
   candidate model for the mean secular variation between 2010 and 2015.
   These candidate models, the derivation of which is described in the
   following, are based on the latest model in the CHAOS model series,
   called ``CHAOS-3{''}. This model is derived from more than 10 years of
   satellite and ground observatory data. Maximum spherical harmonic degree
   of the static field is n = 60. The core field time changes are expressed
   by spherical harmonic expansion coefficients up to n = 20, described by
   order 6 splines (with 6-month knot spacing) spanning the time interval
   1997.0-2010.0. The third time derivative of the squared magnetic field
   intensity is regularized at the core-mantle boundary. No spatial
   regularization is applied.}},
	author = {Olsen, Nils and Mandea, Mioara and Sabaka, Terence J. and Toffner-Clausen, Lars},
	date-added = {2012-01-24 15:06:52 +0100},
	date-modified = {2012-01-24 15:09:40 +0100},
	doi = {{10.5047/eps.2010.07.003}},
	issn = {{1343-8832}},
	journal = {Earth Planets Space},
	number = {{10}},
	pages = {{719-727}},
	title = {{The CHAOS-3 geomagnetic field model and candidates for the 11th generation IGRF}},
	unique-id = {{ISI:000287478500002}},
	volume = {{62}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.5047/eps.2010.07.003%7D}}

@article{Sabaka2004,
	abstract = {{A new model of the quiet-time, near-Earth magnetic field has been
   derived using a comprehensive approach, which includes not only POGO and
   Magsat satellite data, but also data from the Orsted and CHAMP
   satellites. The resulting model shows great improvement over its
   predecessors in terms of completeness of sources, time span and noise
   reduction in parameters. With its well separated fields and extended
   time domain of 1960 to mid-2002, the model is able to detect the known
   sequence of geomagnetic jerks within this frame and gives evidence for
   an event of interest around 1997. Because all sources are coestimated in
   a comprehensive approach, intriguing north-south features typically
   filtered out with other methods are being discovered in the lithospheric
   representation of the model, such as the S Atlantic spreading ridge and
   Andean subduction zone lineations. In addition, this lithospheric field
   exhibits significantly less noise than previous models as a result of
   improved data selection. The F-region currents, through which the
   satellites pass, are now treated as lying within meridional planes, as
   opposed to being purely radial. Results are consistent with those found
   previously for Magsat, but an analysis at Orsted altitude shows exciting
   evidence that the meridional currents associated with the equatorial
   electrojet likely close beneath the satellite. Besides the model, a new
   analysis technique has been developed to infer the portion of a model
   parameter state resolved by a particular data subset. This has proven
   very useful in diagnosing the cause of peculiar artefacts in the Magsat
   vector data, which seem to suggest the presence of a small misalignment
   bias in the vector magnetometer.}},
	author = {Sabaka, Terence J. and Olsen, N and Purucker, ME},
	date-added = {2012-01-24 15:06:35 +0100},
	date-modified = {2013-05-31 09:06:18 +0000},
	doi = {{10.1111/j.1365-246X.2004.02421.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{NOV}},
	number = {{2}},
	pages = {{521-547}},
	title = {{Extending comprehensive models of the Earth's magnetic field with Oersted and CHAMP data}},
	unique-id = {{ISI:000224634500009}},
	volume = {{159}},
	year = {{2004}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2004.02421.x%7D}}

@article{Busse1970,
	author = {Busse, F. H.},
	date-added = {2012-01-17 14:58:15 +0100},
	date-modified = {2012-01-17 14:58:15 +0100},
	journal = {J. Fluid. Mech.},
	number = {3},
	pages = {441-460},
	title = {Thermal instabilities in rapidly rotating systems},
	volume = {44},
	year = {1970}}

@article{Aubert2011,
	abstract = {{Over the past decades, direct three-dimensional numerical modelling has
   been successfully used to reproduce the main features of the geodynamo.
   Here we report on efforts to solve the associated inverse problem,
   aiming at inferring the underlying properties of the system from the
   sole knowledge of surface observations and the first principle dynamical
   equations describing the convective dynamo. To this end we rely on twin
   experiments. A reference model time sequence is first produced and used
   to generate synthetic data, restricted here to the large-scale component
   of the magnetic field and its rate of change at the outer boundary.
   Starting from a different initial condition, a second sequence is next
   run and attempts are made to recover the internal magnetic, velocity and
   buoyancy anomaly fields from the sparse surficial data. In order to
   reduce the vast underdetermination of this problem, we use stochastic
   inversion, a linear estimation method determining the most likely
   internal state compatible with the observations and some prior
   knowledge, and we also implement a sequential evolution algorithm in
   order to invert time-dependent surface observations. The prior is the
   multivariate statistics of the numerical model, which are directly
   computed from a large number of snapshots stored during a preliminary
   direct run. The statistics display strong correlation between different
   harmonic degrees of the surface observations and internal fields,
   provided they share the same harmonic order, a natural consequence of
   the linear coupling of the governing dynamical equations and of the
   leading influence of the Coriolis force. Synthetic experiments performed
   with a weakly nonlinear model yield an excellent quantitative retrieval
   of the internal structure. In contrast, the use of a strongly nonlinear
   (and more realistic) model results in less accurate static estimations,
   which in turn fail to constrain the unobserved small scales in the time
   integration of the evolution scheme. Evaluating the quality of forecasts
   of the system evolution against the reference solution, we show that our
   scheme can improve predictions based on linear extrapolations on
   forecast horizons shorter than the system e-folding time. Still, in the
   perspective of forthcoming data assimilation activities, our study
   underlines the need of advanced estimation techniques able to cope with
   the moderate to strong nonlinearities present in the geodynamo.}},
	author = {Aubert, J. and Fournier, A.},
	date-added = {2012-01-17 14:18:43 +0100},
	date-modified = {2012-01-17 14:18:55 +0100},
	doi = {{10.5194/npg-18-657-2011}},
	issn = {{1023-5809}},
	journal = {Nonlin. Processes Geophys.},
	number = {{5}},
	pages = {{657-674}},
	title = {{Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model}},
	unique-id = {{ISI:000296743300013}},
	volume = {{18}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.5194/npg-18-657-2011%7D}}

@article{Wicht2010,
	abstract = {{P>Cylinders aligned with the planetary rotation axis have a special
   significance in the dynamics of planetary dynamo regions. The azimuthal
   Lorentz forces on these geostrophic cylinders is expected to cancel to a
   large degree, establishing the so-called Taylor state. Deviations from
   this state take the form of torsional oscillations (TOs) that are
   supposed to represent important fast flow variations. These oscillations
   have reportedly been identified in the secular variation signal from the
   top of Earth's core. We have performed several dynamo simulations at
   different parameters to check whether Taylor state and TOs can also be
   identified in a numerical model. Taylor states are approached when
   viscous effects are small at Ekman numbers of E = 3 x 10-5 or below and
   Reynolds stresses are kept low by choosing moderate Rayleigh numbers.
   One-dimensional magnetic Alfven waves that travel towards the boundaries
   then become prominent in the motion of the geostrophic cylinders. These
   waves obey the TO theory but are also damped and modified by other
   effects. For example, fast variations of likely convective origin remain
   important in all our simulations. Reynolds stresses may play a more
   sizable role for the dynamics in Earth's dynamo region than commonly
   assumed. They may also contribute to the motions of geostrophic
   cylinders and severely reduce the significance of TOs for the fast core
   dynamics. The amplitude of TOs amounts to not more than a few percent of
   the total flow amplitude in the simulations, which renders these motions
   insignificant for the long-term dynamo process.}},
	author = {Wicht, J. and Christensen, U. R.},
	date-added = {2012-01-17 13:56:07 +0100},
	date-modified = {2016-11-14 13:59:55 +0000},
	doi = {{10.1111/j.1365-246X.2010.04581.x}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUN}},
	number = {{3}},
	pages = {{1367-1380}},
	title = {{Torsional oscillations in dynamo simulations}},
	unique-id = {{ISI:000277716400012}},
	volume = {{181}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2010.04581.x%7D}}

@article{Sreenivasan2005,
	abstract = {{Observations of the Earth's magnetic field suggest that there are
   anticyclonic polar vortices in the core (Olson and Aurnou, 1999; Hulot
   et al., 2002). Some geodynamo simulations have also shown the existence
   of an anticyclonic flow in the polar region of the Earth's outer core.
   The polar vortices are investigated using a spherical convection-driven
   dynamo model. In a fully three-dimensional model where no longitudinal
   symmetry is imposed, we find that the polar vortex core is offset from
   the pole itself by approximately 10 degrees from the axis of rotation.
   It is therefore non-axisymmetric, and can drift considerably in
   longitude during a magnetic diffusion time. We also find that the strong
   polar vortex depends crucially on the magnetic field in the core. The
   simulation results are compared with the polar core flow reconstructed
   from secular variation observations.}},
	article-number = {{L20301}},
	author = {Sreenivasan, B and Jones, CA},
	date-added = {2012-01-17 13:18:43 +0100},
	date-modified = {2012-01-17 13:18:55 +0100},
	doi = {{10.1029/2005GL023841}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	month = {{OCT 18}},
	number = {{20}},
	title = {{Structure and dynamics of the polar vortex in the Earth's core}},
	unique-id = {{ISI:000232828200005}},
	volume = {{32}},
	year = {{2005}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2005GL023841%7D}}

@article{Bloxham1991,
	abstract = {{Maps of the fluid flow at the core surface are important for a number of
   reasons:  foremost they may provide some insight into the workings of
   the geodynamo and may place useful constraints on geodynamo models; from
   the flow, the force balance at the top of the core can, at least in
   part, be deduced; the flow can provide short-term predictions of the
   secular variation; the flow is important in understanding changes in the
   length of day; and constraints on lateral temperature variations and
   topography at the core-mantle boundary may be derived.  Unlike the case
   of mantle convection, only very small lateral variations in core density
   are required to drive the flow; these density variations are too small
   (by several orders of magnitude) to be imaged seismically, so instead we
   use the geomagnetic secular variation to infer the flow.  Despite
   considerable recent progress in mapping the core flow, substantial
   differences exist between maps produced by different researchers.  Here
   we examine the possible underlying reasons for these differences, paying
   particular attention to the inherent problems of nonuniqueness.  We
   focus on the aspects of the flow which do seem to be well determined and
   discuss their geophysical implications.}},
	author = {Bloxham, J. and Jackson, A.},
	date-added = {2012-01-17 11:26:46 +0100},
	date-modified = {2012-10-18 12:21:36 +0000},
	doi = {10.1029/90RG02470},
	issn = {{8755-1209}},
	journal = {Rev. Geophysics},
	month = {{FEB}},
	number = {{1}},
	pages = {{97-120}},
	title = {Fluid flow near the surface of {E}arth's outer core},
	unique-id = {{ISI:A1991EY10300005}},
	volume = {{29}},
	year = {{1991}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/90RG02470%7D}}

@article{Lhuillier2011a,
	author = {Lhuillier, F. and Aubert, J. and Hulot, G.},
	date-added = {2011-10-05 16:18:16 +0200},
	date-modified = {2011-10-05 16:31:13 +0200},
	doi = {10.1111/j.1365-246X.2011.05081.x},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{AUG}},
	number = {{2}},
	pages = {{492-508}},
	title = {{Earth's dynamo limit of predictability controlled by magnetic dissipation}},
	unique-id = {{ISI:000292742700008}},
	volume = {{186}},
	year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2011.05081.x%7D}}

@article{Hulot2010review,
	author = {Hulot, G. and Finlay, C. C. and Constable, C. G. and Olsen, N. and Mandea, M.},
	date-added = {2011-10-05 16:11:13 +0200},
	date-modified = {2011-10-05 16:11:47 +0200},
	doi = {{10.1007/s11214-010-9644-0}},
	issn = {{0038-6308}},
	journal = {Space. Sci. Rev.},
	month = {{MAY}},
	number = {{1-4}},
	pages = {{159-222}},
	title = {{The Magnetic Field of Planet Earth}},
	unique-id = {{ISI:000279486600006}},
	volume = {{152}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9644-0%7D}}

@article{Fournier2011,
	author = {Fournier, Alexandre and Aubert, Julien and Th\'ebault, Erwan},
	date-added = {2011-10-05 16:04:26 +0200},
	date-modified = {2011-10-05 16:07:06 +0200},
	doi = {10.1111/j.1365-246X.2011.05037.x},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUL}},
	number = {{1}},
	pages = {{118-136}},
	title = {{Inference on core surface flow from observations and 3-D dynamo modelling}},
	unique-id = {{ISI:000292741800012}},
	volume = {{186}},
	year = {{2011}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2011.05037.x%7D}}

@article{Gillet2010,
	author = {Gillet, N. and Jault, D. and Canet, E. and Fournier, A.},
	date-added = {2011-10-05 16:03:18 +0200},
	date-modified = {2016-11-14 13:45:33 +0000},
	doi = {10.1038/nature09010},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{MAY 6}},
	number = {{7294}},
	pages = {{74-77}},
	title = {{Fast torsional waves and strong magnetic field within the Earth's core}},
	unique-id = {{ISI:000277311900033}},
	volume = {{465}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature09010%7D}}

@article{Korte2011,
	author = {Korte, M. and Constable, C. G.},
	date-added = {2011-09-23 11:35:23 +0200},
	date-modified = {2011-10-05 16:15:57 +0200},
	doi = {10.1016/j.pepi.2011.06.017},
	journal = {Phys. Earth Planet. Inter.},
	title = {Improving geomagnetic field reconstructions for 0-3 ka},
	year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2011.06.017}}

@inproceedings{kalnay2010ensemble,
	address = {Berlin Heidelberg},
	author = {Eugenia Kalnay},
	booktitle = {Data Assimilation},
	date-modified = {2011-10-05 16:12:58 +0200},
	doi = {10.1007/978-3-540-74703-1_4},
	editor = {William Lahoz and Boris Khattatov and Richard M\'enard},
	pages = {69--92},
	publisher = {Springer},
	title = {Ensemble Kalman Filter: Current Status and Potential},
	year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-74703-1_4}}

@inproceedings{houser2010land,
	address = {Berlin Heidelberg},
	author = {Paul R. Houser and Gabri\"{e}lle J. M. {De Lannoy} and Jeffrey P. Walker},
	booktitle = {Data Assimilation},
	date-modified = {2011-10-05 16:09:26 +0200},
	doi = {10.1007/978-3-540-74703-1_21},
	editor = {William Lahoz and Boris Khattatov and Richard M\'enard},
	pages = {549--597},
	publisher = {Springer},
	title = {Land Surface Data Assimilation},
	year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-74703-1_21}}

@inproceedings{elbern2010inverse,
	address = {Berlin Heidelberg},
	author = {Hendrik Elbern and Achim Strunk and Lars Nieradzik},
	booktitle = {Data Assimilation},
	date-modified = {2011-10-05 15:53:27 +0200},
	doi = {10.1007/978-3-540-74703-1_19},
	editor = {William Lahoz and Boris Khattatov and Richard M\'enard},
	pages = {491--513},
	publisher = {Springer},
	title = {Inverse Modelling and Combined State-Source Estimation for Chemical Weather},
	year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-74703-1_19}}

@book{kalnay2003amd,
	address = {Cambridge},
	author = {Kalnay, E.},
	publisher = {Cambridge University Press},
	title = {{Atmospheric modeling, data assimilation, and predictability}},
	year = {2003}}

@book{evensen2009dae,
	address = {Berlin},
	author = {Evensen, G.},
	doi = {10.1007/978-3-642-03711-5},
	edition = 2,
	publisher = {Springer},
	title = {{Data assimilation: The ensemble Kalman filter}},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-03711-5}}

@inproceedings{brasseur06,
	author = {Brasseur, P.},
	booktitle = {Ocean Weather Forecasting: An Integrated View of Oceanography},
	editor = {Chassignet, E. and Verron, J.},
	pages = {271--316},
	publisher = {Springer},
	title = {Ocean Data Assimilation using Sequential Methods based on the {K}alman Filter},
	year = {2006}}

@article{Finlay2010CANDIDATES,
	abstract = {{The eleventh generation of the International Geomagnetic Reference
   Field (IGRF) was agreed in December 2009 by a task force appointed by
   the International Association of Geomagnetism and Aeronomy (IAGA)
   Division V Working Group V-MOD. New spherical harmonic main field
   models for epochs 2005.0 (DGRF-2005) and 2010.0 (IGRF-2010), and
   predictive linear secular variation for the interval 2010.0-2015.0
   (SV-2010-2015) were derived from weighted averages of candidate models
   submitted by teams led by DTU Space, Denmark (team A); NOAA/NGDC,
   U.S.A. (team B); BGS, U. K. (team C); IZMIRAN, Russia (team D); EOST,
   France (team E); IPGP, France (team F); GFZ, Germany (team G) and
   NASA-GSFC, U. S. A. (team H). Here, we report the evaluations of
   candidate models carried out by the IGRF-11 task force during
   October/November 2009 and describe the weightings used to derive the
   new IGRF-11 model. The evaluations include calculations of root mean
   square vector field differences between the candidates, comparisons of
   the power spectra, and degree correlations between the candidates and a
   mean model. Coefficient by coefficient analysis including determination
   of weighting factors used in a robust estimation of mean coefficients
   is also reported. Maps of differences in the vertical field intensity
   at Earth's surface between the candidates and weighted mean models are
   presented. Candidates with anomalous aspects are identified and efforts
   made to pinpoint both troublesome coefficients and geographical regions
   where large variations between candidates originate. A retrospective
   analysis of IGRF-10 main field candidates for epoch 2005.0 and
   predictive secular variation candidates for 2005.0-2010.0 using the new
   IGRF-11 models as a reference is also reported. The high quality and
   consistency of main field models derived using vector satellite data is
   demonstrated; based on internal consistency DGRF-2005 has a formal root
   mean square vector field error over Earth's surface of 1.0 nT.
   Difficulties nevertheless remain in accurately forecasting field
   evolution only five years into the future.}},
	address = {{2003 SANSEI JIYUGAOKA HAIMU, 5-27-19 OKUSAWA, SETAGAYA-KU, TOKYO, 158-0083, JAPAN}},
	affiliation = {{Finlay, CC (Reprint Author), ETH, Earth \& Planetary Magnetism Grp, Inst Geophys, Sonneggstr 5, CH-8092 Zurich, Switzerland. {[}Finlay, C. C.] ETH, Earth \& Planetary Magnetism Grp, Inst Geophys, CH-8092 Zurich, Switzerland. {[}Maus, S.] NOAA, NGDC, Silver Spring, MD USA. {[}Maus, S.] Univ Colorado, CIRES, Boulder, CO 80309 USA. {[}Beggan, C. D.] British Geol Survey, Edinburgh EH9 3LA, Midlothian, Scotland. {[}Hamoudi, M.] GFZ German Res Ctr Geosci, Helmholtz Ctr Potsdam, D-14473 Telegrafenberg, Germany. {[}Lowes, F. J.] Newcastle Univ, Sch Chem, Newcastle Upon Tyne NE1 7RU, Tyne \& Wear, England. {[}Olsen, N.] DTU Space, DK-2100 Copenhagen, Denmark. {[}Thebault, E.] Univ Paris Diderot, CNRSINSU, Inst Phys Globe Paris, Equipe Geomagnetisme,UMR 7154, Paris, France.}},
	author = {Finlay, Christopher C. and Maus, S. and Beggan, C. D. and Hamoudi, M. and Lowes, F. J. and Olsen, N. and Thebault, E.},
	author-email = {{cfinlay@erdw.ethz.ch}},
	date-added = {2011-06-28 15:44:07 +0200},
	date-modified = {2013-09-24 08:36:42 +0000},
	doc-delivery-number = {{723AP}},
	doi = {10.5047/eps.2010.11.005},
	issn = {{1343-8832}},
	journal = {Earth Planets Space},
	journal-iso = {{Earth Planets Space}},
	keywords = {{Geomagnetism; field modelling; reference field; secular variation}},
	keywords-plus = {{POWER SPECTRUM}},
	language = {{English}},
	number = {{10}},
	number-of-cited-references = {{28}},
	pages = {{787-804}},
	publisher = {{TERRA SCIENTIFIC PUBL CO}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{4}},
	title = {{Evaluation of candidate geomagnetic field models for IGRF-11}},
	type = {{Article}},
	unique-id = {{ISI:000287478500009}},
	volume = {{62}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.5047/eps.2010.11.005%7D}}

@article{Aubert2010,
	abstract = {{The geomagnetic signal contains an enormous temporal range-from
   geomagnetic jerks on time scales of less than a year to the evolution
   of Earth's dipole moment over billions of years. This review compares
   observations and numerical models of the long-term range of that
   signal, for periods much larger than the typical overturn time of
   Earth's core. On time scales of 10(5)-10(9) years, the geomagnetic
   field reveals the control of mantle thermodynamic conditions on core
   dynamics. We first briefly describe the general formalism of numerical
   dynamo simulations and available paleomagnetic data sets that provide
   insight into paleofield behavior. Models for the morphology of the
   time-averaged geomagnetic field over the last 5 million years are
   presented, with emphasis on the possible departures from the geocentric
   axial dipole hypothesis and interpretations in terms of core dynamics.
   We discuss the power spectrum of the dipole moment, as it is a
   well-constrained aspect of the geomagnetic field on the million year
   time scale. We then summarize paleosecular variation and intensity over
   the past 200 million years, with emphasis on the possible dynamical
   causes for the occurrence of superchrons. Finally, we highlight the
   geological evolution of the geodynamo in light of the oldest
   paleomagnetic records available. A summary is given in the form of a
   tentative classification of well-constrained observations and robust
   numerical modeling results.}},
	address = {{VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS}},
	affiliation = {{Aubert, J (Reprint Author), Inst Phys Globe, Bur 459, 1 Rue Jussieu, F-75238 Paris 05, France. {[}Aubert, Julien] Inst Phys Globe, Bur 459, F-75238 Paris 05, France. {[}Tarduno, John A.] Univ Rochester, Dept Earth \& Environm Sci, Rochester, NY 14627 USA. {[}Johnson, Catherine L.] Univ British Columbia, Vancouver, BC V5Z 1M9, Canada.}},
	author = {Aubert, Julien and Tarduno, John A. and Johnson, Catherine L.},
	author-email = {{aubert@ipgp.fr john@earth.rochester.edu cjohnson@eos.ubc.ca}},
	date-added = {2011-06-07 15:21:36 +0200},
	date-modified = {2011-10-05 23:05:26 +0200},
	doc-delivery-number = {{682TX}},
	doi = {10.1007/s11214-010-9684-5},
	issn = {{0038-6308}},
	journal = {Space. Sci. Rev.},
	journal-iso = {{Space Sci. Rev.}},
	keywords = {{Geomagnetism; Paleomagnetism; Paleointensity; Geodynamo; Core Processes; Core-Mantle Interactions}},
	keywords-plus = {{GEOMAGNETIC SECULAR VARIATION; CORE-MANTLE BOUNDARY; AVERAGED PALEOMAGNETIC FIELD; CRETACEOUS NORMAL SUPERCHRON; SINGLE PLAGIOCLASE CRYSTALS; DRIVEN NUMERICAL DYNAMOS; BILLION YEARS AGO; 983 GARDAR DRIFT; INNER-CORE; PALEOSECULAR VARIATION}},
	language = {{English}},
	month = {{AUG}},
	number = {{1-4}},
	number-of-cited-references = {{140}},
	organization = {{Int Space Sci Inst}},
	pages = {{337-370}},
	publisher = {{SPRINGER}},
	subject-category = {{Astronomy \& Astrophysics}},
	times-cited = {{1}},
	title = {{Observations and Models of the Long-Term Evolution of Earth's Magnetic Field}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000284427000012}},
	volume = {{155}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9684-5%7D}}

@article{Aubert2009,
	abstract = {{Although it is known that the geodynamo has been operating for at least
   3.2 Ga, it remains difficult to infer the intensity, dipolarity and
   stability (occurrence of reversals) of the Precambrian magnetic field
   of the Earth. In order to assist the interpretation of palaeomagnetic
   data, we produce models for the long-term evolution of the geodynamo by
   combining core thermodynamics with a systematic scaling analysis of
   numerical dynamo simulations. We update earlier dynamo scaling results
   by exploring a parameter space, which has been extended in order to
   account for core aspect ratios and buoyancy source distributions
   relevant to Earth in the Precambrian. Our analysis highlights the
   central role of the convective power, which is an output of core
   thermodynamics and the main input of our updated scalings. As the
   thermal evolution of the Earth's core is not well known, two end-member
   models of heat flow evolution at the core-mantle boundary (CMB) are
   used, respectively, terminating at present heat flows of 11 TW
   (high-power scenario) and 3 TW(low power scenario). The resulting
   models predict that until the appearance of the inner core, a thermal
   dynamo driven only by secular cooling, and without any need for
   radioactive heating, can produce a dipole moment of strength comparable
   to that of the present field, thus precluding an interpretation of the
   oldest palaeomagnetic records as evidence of the inner core presence.
   The observed lack of strong long-term trends in palaeointensity data
   throughout the Earth's history can be rationalized by the weakness of
   palaeointensity variations predicted by our models relatively to the
   data scatter. Specifically, the most significant internal magnetic
   field increase which we predict is associated to the sudden power
   increase resulting from inner core nucleation, but the dynamo becomes
   deeper-seated in the core, thus largely cancelling the increase at the
   core and Earth surface, and diminishing the prospect of observing this
   event in palaeointensity data. Our models additionally suggest that the
   geodynamo has lied close to the transition to polarity reversals
   throughout its history. In the Precambrian, we predict a dynamo with
   similar dipolarity and less frequent reversals than at present times,
   due to conditions of generally lower convective forcing. Quantifying
   the typical CMB heat flow variation needed for the geodynamo to cross
   the transition from a reversing to a non-reversing state, we find that
   it is unlikely that such a variation may have caused superchrons in the
   last 0.5 Ga without shutting down dynamo action altogether.}},
	address = {{COMMERCE PLACE, 350 MAIN ST, MALDEN 02148, MA USA}},
	affiliation = {{Aubert, J (Reprint Author), Univ Paris Diderot, Inst Phys Globe Paris, CNRS, INSU, 4 Pl Jussieu, F-75252 Paris 05, France. {[}Aubert, Julien; Poitou, Charles] Univ Paris Diderot, Inst Phys Globe Paris, CNRS, INSU, F-75252 Paris 05, France. {[}Labrosse, Stephane] Univ Lyon, Ecole Normale Super Lyon, Lab Sci Terre, CNRS,UMR 5570, F-69364 Lyon, France.}},
	author = {Aubert, Julien and Labrosse, Stephane and Poitou, Charles},
	author-email = {{aubert@ipgp.jussieu.fr}},
	date-added = {2011-06-07 15:15:52 +0200},
	date-modified = {2011-06-07 15:16:22 +0200},
	doc-delivery-number = {{517RH}},
	doi = {{10.1111/j.1365-246X.2009.04361.x}},
	funding-acknowledgement = {{CNRS ; programs Programme National de Planetologie (PNP) and Structure et Dynamique de l'Interieur de la Terre (SEDIT) ; French Institut National des Sciences de l'Univers (INSU) ; French Agence Nationale de la Recherche }},
	funding-text = {{We thank U. R. Christensen for providing the numerical data relative to published dynamo models. JA was supported by CNRS and programs Programme National de Planetologie (PNP) and Structure et Dynamique de l'Interieur de la Terre (SEDIT) of the French Institut National des Sciences de l'Univers (INSU). SL was supported by program ANR BEGDy from French Agence Nationale de la Recherche. Numerical calculations were performed at the MesoCentre de Calcul et de donnees (MCCD) of IPGP, and at IDRIS, France. This is IPGP contribution 2547.}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	journal-iso = {{Geophys. J. Int.}},
	keywords = {{Dynamo: theories and simulations; Palaeointensity; Palaeomagnetic secular variation; Reversals: process, timescale, magnetostratigraphy}},
	keywords-plus = {{GEOMAGNETIC SECULAR VARIATION; IAGA PALEOINTENSITY DATABASE; EARTHS CORE; INNER-CORE; NUMERICAL DYNAMOS; THERMAL EVOLUTION; MAGNETIC-FIELD; DIPOLE-MOMENT; CONVECTION; MANTLE}},
	language = {{English}},
	month = {{DEC}},
	number = {{3}},
	number-of-cited-references = {{53}},
	pages = {{1414-1428}},
	publisher = {{WILEY-BLACKWELL PUBLISHING, INC}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{17}},
	title = {{Modelling the palaeo-evolution of the geodynamo}},
	type = {{Article}},
	unique-id = {{ISI:000271634300011}},
	volume = {{179}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2009.04361.x%7D}}

@article{Jault2008,
	abstract = {{Geostrophic jets propagating as Alfven waves are shown to arise in a
   rapidly rotating spherical shell permeated by a magnetic field among
   the transient motions set up by an impulsive rotation of the inner
   core. These axially invariant motions evolve on a time-scale which is
   short compared to the magnetic diffusion time. The numerical study is
   taken as illustrative of a more general point: on such a fast
   time-scale the dimensionless number appropriate to compare the rotation
   and magnetic forces is independent of the magnetic diffusivity in
   contrast with the often used Elsasser number. Extension of the analysis
   to non-axisymmetrical motions is supported by published studies of
   dynamo models and magnetic instabilities. (C) 2007 Elsevier B.V. All
   rights reserved.}},
	address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}},
	affiliation = {{Jault, D (Reprint Author), Univ Grenoble 1, CNRS, LGIT, BP 53, F-38041 Grenoble, France. Univ Grenoble 1, CNRS, LGIT, F-38041 Grenoble, France.}},
	author = {Jault, Dominique},
	author-email = {{Dominique.Jault@obs.ujf-grenoble.fr}},
	date-added = {2011-06-07 12:18:43 +0200},
	date-modified = {2011-06-07 15:23:55 +0200},
	doc-delivery-number = {{268YW}},
	doi = {10.1016/j.pepi.2007.11.001},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	journal-iso = {{Phys. Earth Planet. Inter.}},
	keywords = {{Earth's core; magneto-hydrodynamic waves; geomagnetic field; core flow}},
	keywords-plus = {{ROTATING SPHERICAL-SHELL; TOROIDAL MAGNETIC-FIELD; TORSIONAL OSCILLATIONS; INNER-CORE; CONVECTION; GEODYNAMO; WAVES; MODEL; FLOW; MAGNETOCONVECTION}},
	language = {{English}},
	month = {{JAN}},
	number = {{1-2}},
	number-of-cited-references = {{32}},
	pages = {{67-76}},
	publisher = {{ELSEVIER SCIENCE BV}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{15}},
	title = {{Axial invariance of rapidly varying diffusionless motions in the Earth's core interior}},
	type = {{Article}},
	unique-id = {{ISI:000253617500006}},
	volume = {{166}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2007.11.001%7D}}

@article{Kuang2010,
	author = {Kuang, W. and Wei, Z. and Holme, R. and Tangborn, A.},
	date-added = {2011-06-07 12:15:13 +0200},
	date-modified = {2011-06-07 12:17:05 +0200},
	journal = {Earth Planets Space},
	pages = {775-785},
	title = {Prediction of geomagnetic field with data assimilation: a candidate secular variation model for IGRF-11},
	volume = {62},
	year = {2010}}

@article{Livermore2010,
	abstract = {{The geodynamo mechanism, responsible for sustaining Earth's magnetic
   field, is believed to be strongly influenced by the solid inner core
   through its influence on the structure of convection within the tangent
   cylinder. In the rapidly rotating low-viscosity regime of the geodynamo
   equations relevant to the Earth's core, the magnetic field must satisfy
   a continuum of conditions known as Taylor's constraint. Magnetic fields
   that satisfy this constraint, termed Taylor states, have the property
   that their axial magnetic torque vanishes when averaged over any
   geostrophic contour, cylinders of fluid coaxial with the rotational
   axis. In recent theoretical developments, we proved that when adopting
   a truncated spherical harmonic expansion, the continuous constraint in
   space reduced to a finite spectral set of conditions. Furthermore, an
   expedient choice of regular radial basis presents an under-determined
   problem when constructing Taylor states in a full-sphere showing the
   ubiquity of such solutions. A spherical-shell geometry, with a
   conducting inner core, complicates the formulation of Taylor's
   constraint due to the partitioning of the geostrophic contours into
   three distinct regions, ostensibly trebling the stringency of the
   constraint. This raises questions as to the admissible structures of
   such Taylor states, and their relation to those in a full-sphere. In
   this paper, we address these issues in two stages. First, we present a
   mathematical characterisation of the structure of Taylor's constraint
   in a spherical-shell. We then enumerate the effective number of
   conditions that must be satisfied by any magnetic field that is
   everywhere C-infinity inside the core, and show that, assuming an equal
   truncation in radial and solid angle representation, the number of
   conditions is approximately 5/3 times that for a full-sphere Taylor
   state. Second, we investigate the influence of the inner core on the
   structure of admissible Taylor states by constructing a low-degree
   family of optimally smooth observationally consistent examples in both
   a spherical-shell and a full-sphere. We show that the introduction of
   an inner core into a full-sphere increases the minimum magnetic field
   complexity, simply by virtue of the increased potency of Taylor's
   constraint, a trait more pronounced in our quasi-axisymmetric models.
   We speculate that axisymmetric dynamo-generated exact Taylor states,
   particularly those generated in a spherical-shell, in general have
   small radial length scales that may be difficult to resolve. (C) 2009
   Elsevier B.V. All rights reserved.}},
	address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}},
	affiliation = {{Livermore, PW (Reprint Author), Univ Calif San Diego, Scripps Inst Oceanog, Inst Geophys \& Planetary Phys, La Jolla, CA 92093 USA. {[}Livermore, Philip W.; Ierley, Glenn R.] Univ Calif San Diego, Scripps Inst Oceanog, Inst Geophys \& Planetary Phys, La Jolla, CA 92093 USA. {[}Jackson, Andrew] ETH, Inst Geophys, CH-8093 Zurich, Switzerland.}},
	author = {Livermore, Philip W. and Ierley, Glenn R. and Jackson, Andrew},
	author-email = {{phil@ucsd.edu}},
	date-added = {2011-06-07 12:12:14 +0200},
	date-modified = {2011-10-05 16:20:31 +0200},
	doc-delivery-number = {{547NV}},
	doi = {10.1016/j.pepi.2009.07.015},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	journal-iso = {{Phys. Earth Planet. Inter.}},
	keywords = {{Taylor's constraint; Inner core}},
	keywords-plus = {{PLANETARY MAGNETIC-FIELDS; EARTHS CORE; GEODYNAMO SIMULATIONS; GEOMAGNETIC-FIELD; CONVECTION; REVERSALS; DYNAMOS; CONSTRAINT}},
	language = {{English}},
	month = {{JAN}},
	number = {{1-2, Sp. Iss. SI}},
	number-of-cited-references = {{29}},
	organization = {{Int Union Geol \& Geophys}},
	pages = {{16-26}},
	publisher = {{ELSEVIER SCIENCE BV}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{1}},
	title = {{The construction of exact Taylor states. II: The influence of an inner core}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000273897200004}},
	volume = {{178}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2009.07.015%7D}}

@article{Canet2009,
	abstract = {{We introduce a quasi-geostrophic model of core dynamics, which aims at
   describing core processes on geomagnetic secular variation timescales.
   It extends the formalism of Alfven torsional oscillations by
   incorporating nonzonal motions. Within this framework, the
   magnetohydrodynamics takes place in the equatorial plane; it involves
   quadratic magnetic quantities, which are averaged along the direction
   of rotation of the Earth. In addition, the equatorial flow is projected
   on the core-mantle boundary. It interacts with the magnetic field at
   the core surface, through the radial component of the magnetic
   induction equation. That part of the model connects the dynamics and
   the observed secular variation, with the radial component of the
   magnetic field acting as a passive tracer. We resort to variational
   data assimilation to formally construct the relationship between model
   predictions and observations. Variational data assimilation seeks to
   minimize an objective function by computing its sensitivity to its
   control variables. The sensitivity is efficiently calculated after
   integration of the adjoint model. We illustrate that framework with
   twin experiments, performed first in the case of the kinematic core
   flow inverse problem and then in the case of Alfven torsional
   oscillations. In both cases, using the adjoint model allows us to
   retrieve core state variables which, while taking part in the dynamics,
   are not directly sampled at the core surface. We study the effect of
   several factors on the solution (width of the assimilation time window,
   amount and quality of data), and we discuss the potential of the model
   to deal with real geomagnetic observations.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Canet, E (Reprint Author), Univ Grenoble 1, CNRS, LGIT, BP 53, F-38041 Grenoble 9, France. {[}Canet, Elisabeth; Jault, Dominique] Univ Grenoble 1, CNRS, LGIT, F-38041 Grenoble 9, France. {[}Fournier, Alexandre] Univ Paris Diderot, CNRS, INSU, Inst Phys Globe, F-75252 Paris, France.}},
	article-number = {{B11101}},
	author = {Canet, Elisabeth and Fournier, Alexandre and Jault, Dominique},
	author-email = {{ecanet@obs.ujf-grenoble.fr fournier@ipgp.fr djault@obs.ujf-grenoble.fr}},
	date-added = {2011-06-07 12:11:03 +0200},
	date-modified = {2011-10-05 15:50:47 +0200},
	doc-delivery-number = {{517AI}},
	doi = {10.1029/2008JB006189},
	funding-acknowledgement = {{Agence Nationale de la Recherche {[}BLAN06-2 155316]; INSU }},
	funding-text = {{We thank the reviewers A. Tangborn and A. De Santis for their constructive comments on the manuscript. We thank E. Cosme, C. Finlay, M. Nodet, and O. Talagrand for fruitful discussions. We also thank N. Gillet, N. Schaeffer, and A. Pais for many exchanges at different stages of this work. The manuscript has benefited from the suggestions received from C. Finlay and N. Gillet, who read an earlier draft of the manuscript. A. Pais has provided a core flow model {[}Pais et al., 2004]. The M1QN3 routine has been provided by Gilbert and Lemarechal {[}1989]. Maps have been produced with GMT free software {[}Wessel and Smith, 1991]. This work has been supported by a grant from the Agence Nationale de la Recherche ({''}white'' research program VS-QG, grant reference BLAN06-2 155316) and by INSU, under the LEFE\_ASSIM program (Les Enveloppes Fluides et l'Environnement volet Assimilation).}},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	journal-iso = {{J. Geophys. Res.-Solid Earth}},
	keywords-plus = {{EARTHS MAGNETIC-FIELD; METEOROLOGICAL OBSERVATIONS; DATA ASSIMILATION; TORSIONAL OSCILLATIONS; VORTICITY EQUATION; MHD SYSTEM; CORE; FLOWS; MOTIONS; ALGORITHMS}},
	language = {{English}},
	month = {{NOV 6}},
	number-of-cited-references = {{52}},
	pages = {{B11101}},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{6}},
	title = {{Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation}},
	type = {{Article}},
	unique-id = {{ISI:000271584700001}},
	volume = {{114}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2008JB006189%7D}}

@article{Dormy1998,
	abstract = {{Motion is generated in a rotating spherical shell, by a slight
   differential rotation of the inner core. We show how the numerical
   solution tends, with decreasing Ekman number, to the asymptotic limit
   of Proudman {[}J. Fluid Mech. 1 (1956) 505-516]. Starting from
   geophysically large values, we show that the main qualitative features
   of the asymptotic solution show up only when the Ekman number is
   decreased below 10(-6). Then, we impose a dipolar and force-free
   magnetic field with internal sources. Both the inner core and the
   liquid shell are electrically conducting. The first effect of the
   Lorentz force is to smooth out the change in angular velocity at the
   tangent cylinder. As the Elsasser number is further increased, the
   Proudman-Taylor constraint is violated, Ekman layers are changed into
   Hartmann type layers, shear at the inner sphere boundary vanishes, and
   the flow tends to a bulk rotation together with the inner sphere.
   Unexpectedly, for increasing strength of the field, there is a
   super-rotation (the angular velocity does not reach a maximum at the
   inner core boundary but in the interior of the fluid) localized in an
   equatorial torus. At a given field strength, the amplitude of this
   phenomenon depends on the Ekman number and tends to vanish in the
   magnetostrophic limit. (C) 1998 Elsevier Science B.V. All rights
   reserved.}},
	address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}},
	affiliation = {{Dormy, E (Reprint Author), Univ Calif Los Angeles, Inst Geophys \& Planetary Phys, Los Angeles, CA 90024 USA. IPGP, F-75252 Paris, France. ENS, F-75231 Paris, France.}},
	author = {Dormy, E and Cardin, P and Jault, D},
	date-added = {2011-06-06 11:18:46 +0200},
	date-modified = {2011-06-06 11:18:46 +0200},
	doc-delivery-number = {{104GB}},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Let.},
	journal-iso = {{Earth Planet. Sci. Lett.}},
	keywords = {{dynamos; Earth; magnetic field; induction; models}},
	language = {{English}},
	month = {{JUL}},
	number = {{1-2}},
	number-of-cited-references = {{15}},
	pages = {{15-30}},
	publisher = {{ELSEVIER SCIENCE BV}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{54}},
	title = {{MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field}},
	type = {{Article}},
	unique-id = {{ISI:000075005400002}},
	volume = {{160}},
	year = {{1998}}}

@article{Liu2007,
	abstract = {{Observing System Simulation Experiments (OSSEs) have been carried out
   for a geomagnetic data assimilation system. The purpose of these
   experiments is to demonstrate how new algorithms for assimilating
   geomagnetic observations into a geodynamo model can be evaluated. A
   ``nature'' run is carried out to establish a ``true'' evolution of the
   Earth's core state, from which synthetic surface geomagnetic field
   observations are created. These observations are then assimilated into
   the geodynamo model using an optimal interpolation (OI) scheme. Model
   error is simulated by using a different Rayleigh number in the nature
   and model runs. Because the true core state evolution is known
   completely, the assimilation results can be evaluated in terms of any
   state variable and at any point in the computational domain. In this
   work we focus on the poloidal (observed) and toroidal (unobserved)
   components of the magnetic field throughout the outer core. Experiments
   are carried out using observations of different degrees and varying
   forecast error correlation length scales. We also investigate the
   impact of model error on the assimilation and on the accuracy of
   geomagnetic forecasts. Assimilation runs lasting about 90\% of the
   magnetic free decay time show a positive impact on both components of
   magnetic field deep within the outer core. Forecasts of the surface
   magnetic field show much lower error growth, indicating that the
   initial condition used for the forecasts has been substantially
   improved through assimilation.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Liu, D (Reprint Author), Univ Maryland, Joint Ctr Earth Syst Technol, Baltimore, MD 21250 USA. Univ Maryland, Joint Ctr Earth Syst Technol, Baltimore, MD 21250 USA. NASA, Goddard Space Flight Ctr, Planetary Geodynam Lab, Greenbelt, MD 20771 USA.}},
	author = {Liu, Don and Tangborn, Andrew and Kuang, Weijia},
	author-email = {{donliu@umbc.edu tangborn@umbc.edu weijia.kuang-1@nasa.gov}},
	date-added = {2011-06-06 11:12:57 +0200},
	date-modified = {2011-10-05 16:19:28 +0200},
	doc-delivery-number = {{208SB}},
	doi = {10.1029/2006JB004691},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	journal-iso = {{J. Geophys. Res.-Solid Earth}},
	keywords-plus = {{ERROR STATISTICS; MHD SYSTEM; FIELD; MODEL; DYNAMO; MANTLE}},
	language = {{English}},
	month = {{AUG 29}},
	number = {{B8}},
	number-of-cited-references = {{23}},
	pages = {B08103},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{8}},
	title = {{Observing system simulation experiments in geomagnetic data assimilation}},
	type = {{Article}},
	unique-id = {{ISI:000249338400002}},
	volume = {{112}},
	year = {{2007}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2006JB004691%7D}}

@article{Christensen2011,
	author = {Christensen, U. R.},
	date-added = {2011-06-06 10:23:09 +0200},
	date-modified = {2016-05-04 12:38:13 +0000},
	journal = {Phys. Earth Planet. Int.},
	note = {doi:10.1016/j.pepi.2011.03.012},
	pages = {157-169},
	title = {Geodynamo models: Tools for understanding properties of {E}arth's magnetic field},
	volume = {187},
	year = {2011}}

@article{Roberts1965,
	author = {Roberts, P. H. and Scott, S.},
	date-added = {2011-06-06 10:18:59 +0200},
	date-modified = {2016-04-04 14:42:04 +0000},
	journal = {J. Geomag. Geoelectr.},
	pages = {137-151},
	title = {On the analysis of the secular variation. 1. {A} hydromagnetic constraint: theory.},
	volume = {17},
	year = {1965}}

@article{Olsen2010,
	abstract = {{Observations of the Earth's magnetic field from low-Earth orbiting
   (LEO) satellites started very early on, more than 50 years ago.
   Continuous such observations, relying on more advanced technology and
   mission concepts, have however only been available since 1999. The
   unprecedented time-space coverage of this recent data set opened
   revolutionary new possibilities for monitoring, understanding and
   exploring the Earth's magnetic field. In the near future, the
   three-satellite Swarm constellation concept to be launched by ESA, will
   not only ensure continuity of such measurements, but also provide
   enhanced possibilities to improve on our ability to characterize and
   understand the many sources that produce this field. In the present
   paper we review and discuss the advantages and drawbacks of the various
   LEO space magnetometry concepts that have been used so far, and report
   on the motivations that led to the latest Swarm constellation concept.
   We conclude with some considerations about future concepts that could
   possibly be implemented to ensure the much needed continuity of LEO
   space magnetometry, possibly with enhanced scientific return, by the
   time the Swarm mission ends.}},
	address = {{VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS}},
	affiliation = {{Olsen, N (Reprint Author), Tech Univ Denmark, DTU Space, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark. {[}Olsen, N.] Tech Univ Denmark, DTU Space, DK-2100 Copenhagen, Denmark. {[}Hulot, G.] Univ Paris Diderot, Equipe Geomagnetisme, Inst Phys Globe Paris, INSU,CNRS, F-75252 Paris 05, France. {[}Sabaka, T. J.] NASA, Goddard Space Flight Ctr, Geodynam Branch, Greenbelt, MD 20771 USA.}},
	author = {Olsen, N. and Hulot, G. and Sabaka, T. J.},
	author-email = {{nio@space.dtu.dk}},
	date-added = {2011-05-10 12:31:36 +0200},
	date-modified = {2011-10-05 16:20:54 +0200},
	doc-delivery-number = {{682TX}},
	doi = {10.1007/s11214-010-9676-5},
	issn = {{0038-6308}},
	journal = {Space. Sci. Rev.},
	journal-iso = {{Space Sci. Rev.}},
	keywords = {{Low earth-orbiting satellites; Magnetic field modeling; POGO; Magsat; Orsted; SAC-C; ST-5; CHAMP; Swarm}},
	keywords-plus = {{GEOMAGNETIC-FIELD; SWARM CONSTELLATION; ALIGNED CURRENTS; ANOMALY MAP; MAGSAT DATA; ELECTROMAGNETIC INDUCTION; SATELLITE ALTITUDE; SECULAR VARIATION; GLOBAL VECTOR; MODEL}},
	language = {{English}},
	month = {{AUG}},
	number = {{1-4}},
	number-of-cited-references = {{97}},
	organization = {{Int Space Sci Inst}},
	pages = {{65-93}},
	publisher = {{SPRINGER}},
	subject-category = {{Astronomy \& Astrophysics}},
	times-cited = {{1}},
	title = {{Measuring the Earth's Magnetic Field from Space: Concepts of Past, Present and Future Missions}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000284427000004}},
	volume = {{155}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9676-5%7D}}

@article{Bloxham1989,
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009}},
	affiliation = {{BLOXHAM, J (Reprint Author), HARVARD UNIV,DEPT EARTH \& PLANETARY SCI,20 OXFORD ST,CAMBRIDGE,MA 02138.}},
	author = {Bloxham, J and Jackson, A.},
	date-added = {2011-05-10 12:29:22 +0200},
	date-modified = {2011-06-07 15:18:31 +0200},
	doc-delivery-number = {{CA470}},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	language = {{English}},
	month = {{NOV 10}},
	number = {{B11}},
	number-of-cited-references = {{22}},
	pages = {{15753-15769}},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{43}},
	title = {Simultaneous stochastic inversion for geomagnetic main field and secular variation .2. 1820-1980},
	type = {{Article}},
	unique-id = {{ISI:A1989CA47000022}},
	volume = {{94}},
	year = {{1989}}}

@article{Lister2003,
	author = {Lister, J. R.},
	date-added = {2011-05-10 11:22:47 +0200},
	date-modified = {2011-06-07 15:25:17 +0200},
	doi = {10.1016/j.pepi.2003.07.007},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	month = {{NOV 28}},
	number = {{1-3}},
	pages = {{145-158}},
	title = {{Expressions for the dissipation driven by convection in the Earth's core}},
	unique-id = {{ISI:000187226100010}},
	volume = {{140}},
	year = {{2003}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2003.07.007%7D}}

@inproceedings{Talagrand2003,
	address = {Dordrecht, the Netherlands},
	affiliation = {{Talagrand, O (Reprint Author), Ecole Normale Super, Meteorol Dynam Lab, CNRS, 24 Rue Lhomond, F-72531 Paris 05, France. Ecole Normale Super, Meteorol Dynam Lab, CNRS, F-72531 Paris 05, France.}},
	author = {Talagrand, O},
	booktitle = {Data Assimilation for the {E}arth system},
	date-added = {2011-05-09 12:20:15 +0200},
	date-modified = {2011-05-09 12:23:49 +0200},
	doc-delivery-number = {{BAY45}},
	editor = {Swinbank, R. and Shutyaev, V. and Lahoz, W.A.},
	isbn = {{1-4020-1592-5}},
	issn = {{1568-1238}},
	journal-iso = {{NATO Sci. Series IV Earth Environ. Sciences}},
	keywords-plus = {{ATMOSPHERIC DATA ASSIMILATION; WHITE NOISE; PART II; FORECAST; PERFORMANCE; STATISTICS; COVARIANCE; PARAMETERS; FILTER}},
	language = {{English}},
	number-of-cited-references = {{20}},
	pages = {{85-95}},
	publisher = {Springer},
	series = {{NATO Science Series IV Earth and Environmental Sciences}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{4}},
	title = {{A posteriori validation of assimilation algorithms}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000224214500008}},
	volume = {{26}},
	year = {{2003}}}

@article{Evensen1994,
	abstract = {{A new sequential data assimilation method is discussed. It is based on
   forecasting the error statistics using Monte Carlo methods, a better
   alternative than solving the traditional and computationally extremely
   demanding approximate error covariance equation used in the extended
   Kalman filter. The unbounded error growth found in the extended Kalman
   filter, which is caused by an overly simplified closure in the error
   covariance equation, is completely eliminated. Open boundaries can be
   handled as long as the ocean model is well posed. Well-known numerical
   instabilities associated with the error covariance equation are avoided
   because storage and evolution of the error covariance matrix itself are
   not needed. The results are also better than what is provided by the
   extended Kalman filter since there is no closure problem and the
   quality of the forecast error statistics therefore improves. The method
   should be feasible also for more sophisticated primitive equation
   models. The computational load for reasonable accuracy is only a
   fraction of what is required for the extended Kalman filter and is
   given by the storage of, say, 100 model states for an ensemble size of
   100 and thus CPU requirements of the order of the cost of 100 model
   integrations. The proposed method can therefore be used with realistic
   nonlinear ocean models on large domains on existing computers, and it
   is also well suited for parallel computers and clusters of workstations
   where each processor integrates a few members of the ensemble.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009}},
	affiliation = {{EVENSEN, G (Reprint Author), NANSEN ENVIRONM \& REMOTE SENSING CTR,EDVARD GRIEGSVEJ 3A,N-5037 SOLHEIMSVIKEN,NORWAY.}},
	author = {Evensen, G.},
	date-added = {2011-03-14 14:56:49 +0100},
	date-modified = {2011-06-07 15:19:39 +0200},
	doc-delivery-number = {{NL930}},
	issn = {{0148-0227}},
	journal = {J. Geophys. Res.},
	journal-iso = {{J. Geophys. Res.-Oceans}},
	keywords-plus = {{METEOROLOGICAL DATA ASSIMILATION; STOCHASTIC DYNAMIC PREDICTION; EXTENDED KALMAN FILTER; OCEAN MODEL; PREDICTABILITY; CIRCULATION}},
	language = {{English}},
	month = {{MAY 15}},
	number = {{C5}},
	number-of-cited-references = {{28}},
	pages = {{10143-10162}},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Oceanography}},
	times-cited = {{790}},
	title = {Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics},
	type = {{Article}},
	unique-id = {{ISI:A1994NL93000029}},
	volume = {{99}},
	year = {{1994}}}

@article{Buffett2010,
	abstract = {{Magnetic fields at the Earth's surface represent only a fraction of the
   field inside the core(1). The strength and structure of the internal
   field are poorly known(2-5), yet the details are important for our
   understanding of the geodynamo. Here I obtain an indirect estimate for
   the field strength from measurements of tidal dissipation. Tidally
   driven flow in the Earth's liquid core develops internal shear layers,
   which distort the internal magnetic field and generate electric
   currents. Ohmic losses damp the tidal motions and produce detectable
   signatures in the Earth's nutations. Previously reported evidence of
   anomalous dissipation in nutations(3,6) can be explained with a
   core-averaged field of 2.5 mT, eliminating the need for high fluid
   viscosity(6) or a stronger magnetic field at the inner-core
   boundary(3). Estimates for the internal field constrain the power
   required for the geodynamo(7,8).}},
	author = {Buffett, B. A.},
	date-added = {2011-03-11 11:54:48 +0100},
	date-modified = {2016-11-14 13:40:26 +0000},
	doi = {10.1038/nature09643},
	issn = {{0028-0836}},
	journal = {Nature},
	month = {{DEC 16}},
	number = {{7326}},
	pages = {{952-955}},
	title = {{Tidal dissipation and the strength of the Earth's internal magnetic field}},
	unique-id = {{ISI:000285344600044}},
	volume = {{468}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature09643%7D}}

@article{Buffett2009,
	abstract = {{Oscillations in Earth's liquid core with periods of several decades are
   inferred from variations in the magnetic field. The observed periods
   are consistent with a type of hydromagnetic wave known as torsional
   oscillations. These oscillations represent a set of very-low-frequency
   normal modes in which the internal magnetic field provides the primary
   restoring force. By adapting the methods of normal-mode seismology, we
   construct estimates for the internal structure of the magnetic field
   and several other key parameters, including the viscosity of the inner
   core. The structure of the recovered field provides useful insights
   into the nature of convection. We find evidence of columnar convection
   in the core, and estimate the strength of the field generated by these
   flows (approximate to 0.3 mT). We also use the normal modes to recover
   the excitation source for the oscillations. Much of the excitation
   appears to originate near the surface of a cylinder that is tangent to
   the equator of the inner core. Distinct events rise above a background
   level of excitation, and may be related to instabilities in the
   geodynamo.}},
	author = {Buffett, Bruce A. and Mound, Jon E. and Jackson, Andrew},
	date-added = {2011-03-11 11:54:48 +0100},
	date-modified = {2013-03-25 15:20:14 +0000},
	doi = {10.1111/j.1365-246X.2009.04129.x},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{JUN}},
	number = {{3}},
	pages = {{878-890}},
	title = {{Inversion of torsional oscillations for the structure and dynamics of Earth's core}},
	unique-id = {{ISI:000266025200005}},
	volume = {{177}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2009.04129.x%7D}}

@article{Kuang2009,
	abstract = {{To constrain numerical geodynamo models with surface geomagnetic
   observations, we develop an assimilation scheme for mapping surface
   geomagnetic data into numerical dynamo solutions. This approach is
   similar to the optimal interpolation that has been used in atmospheric
   data assimilation for many years. The scheme is numerically stable and
   computationally efficient, and has been tested in a series of observing
   system simulation experiments with either simplified MHD systems or
   synthetic data from numerical dynamo simulations. In this study, the
   algorithm is integrated with our MoSST core dynamics model and is
   tested with 100-yr surface geomagnetic observations, starting in 1900.
   These experiments use 5 and 20-yr analysis intervals, and forecasts are
   made every 5 yr starting from 1905. We show that forecast errors
   gradually reduce over the course of the assimilation. Shorter
   assimilation runs (starting in 1960 and 1980) result in much larger
   forecast errors. We investigate the causes of the error reduction by
   examining how the assimilation impacts the unobserved variables. We
   discuss the implications for the ability of much longer assimilation
   runs to constrain the physical fields within the Earth's outer core.}},
	author = {Kuang, Weijia and Tangborn, Andrew and Wei, Zigang and Sabaka, Terence},
	date-added = {2011-03-07 18:12:51 +0100},
	date-modified = {2011-06-07 15:24:36 +0200},
	doi = {10.1111/j.1365-246X.2009.04376.x},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{DEC}},
	number = {{3}},
	pages = {{1458-1468}},
	title = {{Constraining a numerical geodynamo model with 100 years of surface observations}},
	unique-id = {{ISI:000271634300013}},
	volume = {{179}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2009.04376.x%7D}}

@article{Gubbins1983,
	author = {Gubbins, D.},
	date-added = {2011-02-03 14:43:53 +0100},
	date-modified = {2011-02-03 14:44:43 +0100},
	journal = {Geophys. J. R. astr. Soc.},
	pages = {641-652},
	title = {Geomagnetic field analysis - I. Stochastic inversion},
	volume = {73},
	year = {1983}}

@article{Hulot2010,
	abstract = {{Earth's magnetic field is currently decreasing, reducing the protection
   it offers against charged particles coming from space and increasing
   space weather hazards within the near-Earth environment. Modeling the
   future evolution of the field is thus of considerable interest. But how
   far in the future this can conceivably be done is still an open
   question. Here we report on the first systematic investigation of the
   limit of predictability of fully consistent 3D numerical dynamo
   simulations, and suggest that the Earth's dynamo is likely
   unpredictable beyond a century, making decade timescale forecasts of
   the main magnetic field conceivable, but rendering longer-term
   predictions, such as the timing of the next reversal, totally
   unpredictable. Citation: Hulot, G., F. Lhuillier, and J. Aubert (2010),
   Earth's dynamo limit of predictability, Geophys. Res. Lett., 37,
   L06305, doi: 10.1029/2009GL041869.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Hulot, G (Reprint Author), Univ Paris Diderot, Equipe Geomagnetisme, Inst Phys Globe Paris, INSU,CNRS, 4 Pl Jussieu,Case 89, F-75252 Paris 05, France. {[}Hulot, G.; Lhuillier, F.] Univ Paris Diderot, Equipe Geomagnetisme, Inst Phys Globe Paris, INSU,CNRS, F-75252 Paris 05, France. {[}Lhuillier, F.; Aubert, J.] Univ Paris Diderot, Equipe Dynam Fluides Geol, Inst Phys Globe Paris, INSU,CNRS, F-75252 Paris, France.}},
	author = {Hulot, G. and Lhuillier, F. and Aubert, J.},
	author-email = {{gh@ipgp.fr}},
	date-added = {2011-02-02 13:34:23 +0100},
	date-modified = {2011-10-05 16:10:23 +0200},
	doc-delivery-number = {{574WR}},
	doi = {10.1029/2009GL041869},
	funding-acknowledgement = {{CNRS-INSU ; GENCI-CINES/IDRIS {[}2009-042122]}},
	funding-text = {{Very helpful comments by Andrew Tangborn and an anonymous reviewer are gratefully acknowledged. This study was supported by the SEDIT programme of CNRS-INSU. Numerical computations were performed at S-CAPAD, IPGP, France and at HPC resources from GENCI-CINES/IDRIS (grant 2009-042122). This is IPGP contribution 2604.}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	journal-iso = {{Geophys. Res. Lett.}},
	keywords-plus = {{GEOMAGNETIC DATA ASSIMILATION; PLANETARY MAGNETIC-FIELDS; GEODYNAMO; SYSTEM; SPACE}},
	language = {{English}},
	month = {{MAR 25}},
	number-of-cited-references = {{26}},
	pages = {L06305},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{1}},
	title = {{Earth's dynamo limit of predictability}},
	type = {{Article}},
	unique-id = {{ISI:000276025400002}},
	volume = {{37}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2009GL041869%7D}}

@article{Lhuillier2011b,
	author = {Lhuillier, F. and Fournier, A. and Hulot, G and Aubert, J.},
	date-added = {2011-02-02 13:28:35 +0100},
	date-modified = {2011-06-07 15:25:04 +0200},
	doi = {10.1029/2011GL047356},
	journal = {Geophys. Res. Lett.},
	pages = {L09306},
	title = {The geomagnetic secular-variation timescale in observations and numerical dynamo models},
	volume = {38},
	year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2011GL047356,%202011}}

@article{Kalman1960,
	author = {Kalman, R. E.},
	date-added = {2011-02-01 15:01:55 +0100},
	date-modified = {2011-02-01 15:02:14 +0100},
	journal = {Transactions of the ASME--Journal of Basic Engineering},
	number = {Series D},
	pages = {35--45},
	title = {A New Approach to Linear Filtering and Prediction Problems},
	volume = {82},
	year = {1960}}

@incollection{Christensen2007,
	address = {Amsterdam},
	author = {Christensen, Ulrich R. and Wicht, J.},
	booktitle = {Treatise on Geophysics. 8- Core Dynamics},
	date-added = {2011-02-01 14:44:11 +0100},
	date-modified = {2013-03-26 13:05:51 +0000},
	editor = {Schubert, G.},
	publisher = {Elsevier},
	title = {Numerical dynamo simulations},
	volume = {8},
	year = {2007}}

@article{Fournier2010,
	abstract = {{Data assimilation in geomagnetism designates the set of inverse methods
   for geomagnetic data analysis which rely on an underlying prognostic
   numerical model of core dynamics. Within that framework, the
   time-dependency of the magnetohydrodynamic state of the core need no
   longer be parameterized: The model trajectory (and the secular
   variation it generates at the surface of the Earth) is controlled by
   the initial condition, and possibly some other static control
   parameters. The primary goal of geomagnetic data assimilation is then
   to combine in an optimal fashion the information contained in the
   database of geomagnetic observations and in the dynamical model, by
   adjusting the model trajectory in order to provide an adequate fit to
   the data.
   The recent developments in that emerging field of research are
   motivated mostly by the increase in data quality and quantity during
   the last decade, owing to the ongoing era of magnetic observation of
   the Earth from space, and by the concurrent progress in the numerical
   description of core dynamics.
   In this article we review briefly the current status of our knowledge
   of core dynamics, and elaborate on the reasons which motivate
   geomagnetic data assimilation studies, most notably (a) the prospect to
   propagate the current quality of data backward in time to construct
   dynamically consistent historical core field and flow models, (b) the
   possibility to improve the forecast of the secular variation, and (c)
   on a more fundamental level, the will to identify unambiguously the
   physical mechanisms governing the secular variation. We then present
   the fundamentals of data assimilation (in its sequential and
   variational forms) and summarize the observations at hand for data
   assimilation practice. We present next two approaches to geomagnetic
   data assimilation: The first relies on a three-dimensional model of the
   geodynamo, and the second on a quasi-geostrophic approximation. We also
   provide an estimate of the limit of the predictability of the
   geomagnetic secular variation based upon a suite of three-dimensional
   dynamo models. We finish by discussing possible directions for future
   research, in particular the assimilation of laboratory observations of
   liquid metal analogs of Earth's core.}},
	address = {{VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS}},
	affiliation = {{Fournier, A (Reprint Author), Univ Paris Diderot, Inst Phys Globe Paris, CNRS, 4 Pl Jussieu, F-75252 Paris 5, France. {[}Fournier, Alexandre; Hulot, Gauthier] Univ Paris Diderot, Inst Phys Globe Paris, CNRS, F-75252 Paris 5, France. {[}Jault, Dominique; Gillet, Nicolas; Canet, Elisabeth] Univ Grenoble 1, CNRS, Lab Geophys Interne \& Tectonophys, Grenoble, France. {[}Kuang, Weijia] NASA, Goddard Space Flight Ctr, Planetary Geodynam Lab, Greenbelt, MD 20771 USA. {[}Tangborn, Andrew] Univ Maryland Baltimore Cty, Joint Ctr Earth Syst Technol, Baltimore, MD 21228 USA. {[}Canet, Elisabeth] ETH, Inst Geophys, CH-8093 Zurich, Switzerland.}},
	author = {Fournier, Alexandre and Hulot, Gauthier and Jault, Dominique and Kuang, Weijia and Tangborn, Andrew and Gillet, Nicolas and Canet, Elisabeth and Aubert, Julien and Lhuillier, Florian},
	author-email = {{fournier@ipgp.fr}},
	date-added = {2011-02-01 14:38:15 +0100},
	date-modified = {2011-10-05 16:07:36 +0200},
	doc-delivery-number = {{682TX}},
	doi = {10.1007/s11214-010-9669-4},
	issn = {{0038-6308}},
	journal = {Space. Sci. Rev.},
	journal-iso = {{Space Sci. Rev.}},
	keywords = {{Geomagnetic secular variation; Dynamo: theories and simulations; Earth's core dynamics; Inverse theory; Data assimilation; Satellite magnetics; Predictability}},
	keywords-plus = {{EARTHS MAGNETIC-FIELD; ADJOINT VORTICITY EQUATION; SPHERICAL COUETTE-FLOW; SECULAR VARIATION; METEOROLOGICAL OBSERVATIONS; SATELLITE DATA; SURFACE FLOWS; VARIATIONAL ASSIMILATION; TORSIONAL OSCILLATIONS; SEISMIC TOMOGRAPHY}},
	language = {{English}},
	month = {{AUG}},
	number = {{1-4}},
	number-of-cited-references = {{154}},
	organization = {{Int Space Sci Inst}},
	pages = {{247-291}},
	publisher = {{SPRINGER}},
	subject-category = {{Astronomy \& Astrophysics}},
	times-cited = {{2}},
	title = {{An Introduction to Data Assimilation and Predictability in Geomagnetism}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000284427000010}},
	volume = {{155}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9669-4%7D}}

@article{Gillet2009,
	abstract = {{Quasi-geostrophic core flow models are built from two secular variation
   models spanning the periods 1960-2002 and 1997-2008. We rely on an
   ensemble method to account for the contributions of the unresolved
   small-scale magnetic field interacting with core surface flows to the
   observed magnetic field changes. The different core flow members of the
   ensemble solution agree up to spherical harmonic degree l similar or
   equal to 10, and this resolved component varies only weakly with
   regularization. Taking into account the finite correlation time of the
   small-scale concealed magnetic field, we find that the time variations
   of the magnetic field occurring over short time scales, such as the
   geomagnetic jerks, can be accounted for by the resolved (large-scale)
   part of the flow to a large extent. Residuals from our flow models are
   30\% smaller for recent epochs, after 1995. This result is attributed
   to an improvement in the quality of geomagnetic data. The magnetic
   field models show little frozen flux violation for the most recent
   epochs, within our estimate of the apparent magnetic flux changes at
   the core-mantle boundary arising from spatial resolution errors. We
   associate the more important flux changes detected at earlier epochs
   with uncertainties in the field models at large harmonic degrees. Our
   core flow models show, at all epochs, an eccentric and planetary-scale
   anticyclonic gyre circling around the cylindrical surface tangent to
   the inner core, at approximately 30 and 60 latitude under the Indian
   and Pacific oceans, respectively. They account well for the changes in
   core angular momentum for the most recent epochs.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Gillet, N (Reprint Author), Univ Grenoble 1, CNRS, LGIT, BP 53, F-38041 Grenoble 9, France. {[}Gillet, N.; Jault, D.] Univ Grenoble 1, CNRS, LGIT, F-38041 Grenoble 9, France. {[}Pais, M. A.] Univ Coimbra, Dept Phys, CFC, P-3004516 Coimbra, Portugal.}},
	article-number = {{Q06004}},
	author = {Gillet, N. and Pais, M. A. and Jault, D.},
	author-email = {{nicolas.gillet@obs.ujf-grenoble.fr pais@teor.fis.uc.pt dominique.jault@obs.ujf-grenoble.fr}},
	date-added = {2011-02-01 14:34:28 +0100},
	date-modified = {2011-10-05 16:08:28 +0200},
	doc-delivery-number = {{458FB}},
	doi = {10.1029/2008GC002290},
	funding-acknowledgement = {{French Agence Nationale de la Recherche {[}BLAN06-2.155316]; Cooperation Program PESSOA, between the Portuguese and French scientific agencies GRICES/EGIDE }},
	funding-text = {{We are indebted to Nils Olsen who provided us the magnetic field model xCHAOS. We are grateful to Andy Jackson for useful discussions and for providing the original B spline code for core flow inversions. We thank Henri-Claude Nataf and Thierry Alboussiere for useful comments on the manuscript and Vincent Lesur, Gauthier Hulot, and an anonymous referee for reviews that helped improve the quality of the present work. The integrals of a scalar function over the sphere used John Burkardt's STRI-QUAD FORTRAN90 library(https://people.scs.fsu.edu/similar to burkardt). N.G. has been funded by a grant from the French Agence Nationale de la Recherche, Research program VS-QG (grant BLAN06-2.155316). This work has also been supported by the Cooperation Program PESSOA, between the Portuguese and French scientific agencies GRICES/EGIDE.}},
	issn = {{1525-2027}},
	journal = {Geochem. Geophy. Geosystems},
	journal-iso = {{Geochem. Geophys. Geosyst.}},
	keywords = {{geomagnetic secular variation; core flows}},
	keywords-plus = {{GEOMAGNETIC-FIELD ANALYSIS; EARTHS MAGNETIC-FIELD; SECULAR VARIATION; MANTLE BOUNDARY; TORSIONAL OSCILLATIONS; SATELLITE DATA; SURFACE; MOTIONS; ASSIMILATION; CONSTRAINTS}},
	language = {{English}},
	month = {{JUN 10}},
	number-of-cited-references = {{54}},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{10}},
	title = {{Ensemble inversion of time-dependent core flow models}},
	type = {{Article}},
	unique-id = {{ISI:000266999300001}},
	volume = {{10}},
	year = {{2009}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1029/2008GC002290%7D}}

@article{Finlay2010,
	abstract = {{Fluid motions in the Earth's core produce changes in the geomagnetic
   field (secular variation) and are also an important ingredient in the
   planet's rotational dynamics. In this article we review current
   understanding of core dynamics focusing on short timescales of years to
   centuries. We describe both theoretical models and what may be inferred
   from geomagnetic and geodetic observations. The kinematic concepts of
   frozen flux and magnetic diffusion are discussed along with relevant
   dynamical regimes of magnetostrophic balance, tangential geostrophy,
   and quasi-geostrophy. An introduction is given to free modes and waves
   that are expected to be present in Earth's core including axisymmetric
   torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We
   focus on important recent developments and promising directions for
   future investigations.}},
	address = {{VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS}},
	affiliation = {{Finlay, CC (Reprint Author), ETH, Inst Geophys, 5 Sonneggstr, CH-8092 Zurich, Switzerland. {[}Finlay, C. C.] ETH, Inst Geophys, CH-8092 Zurich, Switzerland. {[}Dumberry, M.] Univ Alberta, Dept Phys, Edmonton, AB T6G 2G7, Canada. {[}Chulliat, A.] Inst Phys Globe, Equipe Geomagnetisme, F-75252 Paris, France. {[}Pais, M. A.] Univ Coimbra, Dept Phys, P-3004516 Coimbra, Portugal.}},
	author = {Finlay, Christopher C. and Dumberry, M. and Chulliat, A. and Pais, M. A.},
	author-email = {{cfinlay@erdw.ethz.ch dumberry@phys.ualberta.ca chulliat@ipgp.jussieu.fr pais@fis.uc.pt}},
	date-added = {2011-02-01 14:32:09 +0100},
	date-modified = {2013-03-25 15:11:57 +0000},
	doc-delivery-number = {{682TX}},
	doi = {10.1007/s11214-010-9691-6},
	issn = {{0038-6308}},
	journal = {Space. Sci. Rev.},
	journal-iso = {{Space Sci. Rev.}},
	keywords = {{Geomagnetism; Secular variation; Core dynamics; Core-mantle coupling}},
	keywords-plus = {{GEOMAGNETIC SECULAR VARIATION; ROTATING SPHERICAL-SHELLS; EARTHS MAGNETIC-FIELD; TANGENTIALLY GEOSTROPHIC FLOW; FINITE-AMPLITUDE CONVECTION; FROZEN-FLUX APPROXIMATION; BOUNDARY HEAT-FLOW; TORSIONAL OSCILLATIONS; THERMAL-CONVECTION; NUMERICAL DYNAMOS}},
	language = {{English}},
	month = {{AUG}},
	number = {{1-4}},
	number-of-cited-references = {{185}},
	organization = {{Int Space Sci Inst}},
	pages = {{177-218}},
	publisher = {{SPRINGER}},
	subject-category = {{Astronomy \& Astrophysics}},
	times-cited = {{0}},
	title = {{Short Timescale Core Dynamics: Theory and Observations}},
	type = {{Proceedings Paper}},
	unique-id = {{ISI:000284427000008}},
	volume = {{155}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11214-010-9691-6%7D}}

@article{Pais2008,
	abstract = {{We present core flows constructed from high resolution secular
   variation (SV) models for the epochs 2001, 2002.5 and 2004, assuming
   that these flows are quasi-geostrophic in the core interior and that
   they do not cross the axial cylindrical surface tangent to the inner
   core. A large jet encircling the inner core and carrying a significant
   part of the core angular momentum and axial vortices of similar to 700
   km diameter mainly clustering around the cylinder tangent to the solid
   inner core, are inferred from geomagnetic SV. New regularizations are
   suggested from dynamic considerations. It is found that medium and
   small-scale velocity fields contribute significantly to the large-scale
   SV. Accordingly, final models of core flows are calculated after an
   iterative process, whereby the magnetic field variation produced by
   small-scale stochastic magnetic fields and medium to small-scale
   computed velocity fields are incorporated into the inversion itself as
   modelling errors. This study represents a significant step in an effort
   to join geomagnetic observations and the fluid core dynamics on short
   timescales.}},
	author = {Pais, M. A. and Jault, D.},
	date-added = {2011-02-01 14:30:21 +0100},
	date-modified = {2011-06-07 15:26:13 +0200},
	doi = {10.1111/j.1365-246X.2008.03741.x},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	month = {{MAY}},
	number = {{2}},
	pages = {{421-443}},
	title = {{Quasi-geostrophic flows responsible for the secular variation of the Earth's magnetic field}},
	unique-id = {{ISI:000254949700006}},
	volume = {{173}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2008.03741.x%7D}}

@article{Christensen2010,
	abstract = {{For many published dynamo models an Earth-like magnetic field has been
   claimed. However, it has also been noted that as the Ekman number
   (viscosity) is lowered to less unrealistic values, the magnetic field
   tends to become less Earth-like. Here we define quantitative criteria
   for the degree of semblance of a model field with the geomagnetic
   field, based on the field morphology at the core mantle boundary. We
   consider the ratio of the power in the axial dipole component to that
   in the rest if the field, the ratios between equatorially symmetric and
   antisymmetric and between zonal and non-zonal non-dipole components,
   and a measure for the degree of spatial concentration of magnetic flux
   at the core surface. We also briefly discuss shortcomings of possible
   other criteria for an Earth-like model. We test the compliance with our
   criteria for a large number of dynamo models driven by imposed
   temperatures at their inner and outer boundaries that cover the
   accessible parameter space. We order models according to their magnetic
   Reynolds number Rm (ratio of advection to diffusion of magnetic field)
   and magnetic Ekman number E-eta (ratio between rotation period and
   magnetic diffusion time). Requirements for an Earth-like field
   morphology are that E-eta<10(-4) and that Rm falls into a limited range
   that depends on E-eta. Higher values of Rm are required at low values
   of E-eta. Extrapolating the boundaries of compliant dynamos in this
   parameter space to the Earth's value of E-eta suggests that Earth-like
   dynamos exist all the way between present model values and parameter
   values of the geodynamo. We also study a more limited set of dynamo
   models with flux boundary conditions. The nature of the boundary
   condition and the distribution of sources and sinks of buoyancy have a
   secondary influence on the field morphology. (C) 2010 Elsevier B.V. All
   rights reserved.}},
	address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}},
	affiliation = {{Christensen, UR (Reprint Author), Max Planck Inst Solar Syst Res, Katlenburg Lindau, Germany. {[}Christensen, Ulrich R.] Max Planck Inst Solar Syst Res, Katlenburg Lindau, Germany. {[}Aubert, Julien; Hulot, Gauthier] Univ Paris Diderot, Inst Phys Globe Paris, CNRS, INSU, Paris, France.}},
	author = {Christensen, U. R. and Aubert, J. and Hulot, G.},
	author-email = {{christensen@mps.mpg.de}},
	date-added = {2011-02-01 14:19:17 +0100},
	date-modified = {2016-11-14 13:42:42 +0000},
	doc-delivery-number = {{638ZJ}},
	doi = {10.1016/j.epsl.2010.06.009},
	issn = {{0012-821X}},
	journal = {Earth. Plan. Sci. Let.},
	journal-iso = {{Earth Planet. Sci. Lett.}},
	keywords = {{geomagnetic field; dynamo models}},
	keywords-plus = {{GEOMAGNETIC SECULAR VARIATION; CONVECTION-DRIVEN DYNAMOS; BOUNDARY HEAT-FLOW; MAGNETIC-FIELD; NUMERICAL DYNAMOS; PALEOSECULAR VARIATION; COMPUTER-SIMULATION; REVERSALS; MANTLE; CORE}},
	language = {{English}},
	month = {{AUG 1}},
	number = {{3-4}},
	number-of-cited-references = {{50}},
	pages = {{487-496}},
	publisher = {{ELSEVIER SCIENCE BV}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{0}},
	title = {{Conditions for Earth-like geodynamo models}},
	type = {{Article}},
	unique-id = {{ISI:000280940300033}},
	volume = {{296}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2010.06.009%7D}}

@article{Finlay2003,
	author = {Finlay, Christopher C. and Jackson, A.},
	date-added = {2010-06-03 15:24:20 +0200},
	date-modified = {2013-03-25 15:11:32 +0000},
	journal = {Science},
	pages = {2084-2086},
	title = {Equatorially dominated magnetic field change at the surface of {E}arth's core.},
	volume = {300},
	year = {2003}}

@article{Dumberry2010_2,
	author = {Dumberry, M.},
	date-added = {2010-06-03 14:45:29 +0200},
	date-modified = {2010-06-03 14:46:01 +0200},
	journal = {Earth Planet. Sci. Lett.},
	title = {Gravitationally driven inner core differential rotation},
	year = {submitted}}

@article{Olsen2008,
	abstract = {{A large part of the Earth's magnetic field is generated by fluid motion
   in the molten outer core(1). As a result of continuous satellite
   measurements since 1999, the core magnetic field and its recent
   variations can now be described with a high resolution in space and
   time(2). These data have recently been used to investigate small-scale
   core flow(3,4), but no advantage has yet been taken of the improved
   temporal resolution, partly because the filtering effect of the
   electrically conducting mantle was assumed to mask short-period
   magnetic variations(5). Here we show that changes in the magnetic field
   occurring over only a few months, indicative of fluid flow at the top
   of the core, can in fact be resolved. Using nine years of magnetic
   field data obtained by satellites as well as Earth-based observatories,
   we determine the temporal changes in the core magnetic field and flow
   in the core. We find that the core flow is spatially localized and
   involves rapid variations over a few months, with surprisingly large
   local accelerations. Our results suggest that short-term fluctuations
   of the core magnetic field are robust features of rapid core dynamics
   and should be considered in the development of future numerical models
   of the geodynamo.}},
	address = {{75 VARICK STREET, 9TH FLOOR, NEW YORK, NY 10013-1917 USA}},
	affiliation = {{Olsen, N (Reprint Author), Univ Copenhagen, Danish Natl Space Ctr, DTU, Juliane Maries Vej 30, Copenhagen 2100, Denmark. {[}Olsen, Nils] Univ Copenhagen, Danish Natl Space Ctr, DTU, Copenhagen 2100, Denmark. {[}Olsen, Nils] Univ Copenhagen, Niels Bohr Inst, DK-2100 Copenhagen, Denmark. {[}Mandea, Mioara] Geoforschungszentrum Potsdam, D-14473 Potsdam, Germany.}},
	author = {Olsen, Nils and Mandea, Mioara},
	author-email = {{nio@space.dtu.dk}},
	date-added = {2010-06-03 14:28:45 +0200},
	date-modified = {2010-06-03 14:28:58 +0200},
	doc-delivery-number = {{309BC}},
	doi = {{10.1038/ngeo203}},
	issn = {{1752-0894}},
	journal = {Nature Geosci.},
	journal-iso = {{Nat. Geosci.}},
	keywords-plus = {{SECULAR VARIATION; MAGNETIC-FIELD; SATELLITE DATA; ELECTRICAL-CONDUCTIVITY; GEOMAGNETIC JERKS; MANTLE BOUNDARY; MOTIONS; SURFACE}},
	language = {{English}},
	month = {{JUN}},
	number = {{6}},
	number-of-cited-references = {{27}},
	pages = {{390-394}},
	publisher = {{NATURE PUBLISHING GROUP}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{24}},
	title = {{Rapidly changing flows in the Earth's core}},
	type = {{Article}},
	unique-id = {{ISI:000256433700017}},
	volume = {{1}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/ngeo203%7D}}

@article{Taylor1963,
	address = {{6 CARLTON HOUSE TERRACE, LONDON SW1Y 5AG, ENGLAND}},
	author = {Taylor, J.B.},
	date-added = {2010-06-03 12:17:32 +0200},
	date-modified = {2010-06-03 12:18:15 +0200},
	doc-delivery-number = {{9980B}},
	journal = {Proc. Roy. Soc. A},
	language = {{English}},
	number-of-cited-references = {{11}},
	pages = {274-283},
	publisher = {{ROYAL SOC LONDON}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{181}},
	title = {MAGNETO-HYDRODYNAMICS OF A ROTATING FLUID AND {E}ARTHS DYNAMO PROBLEM},
	type = {{Article}},
	unique-id = {{ISI:A19639980B00037}},
	volume = {9},
	year = {1963}}

@book{Moffatt1978,
	author = {Moffatt, K.},
	date-added = {2010-06-03 11:52:30 +0200},
	date-modified = {2010-06-03 11:53:32 +0200},
	editor = {Batchelor, G. K. and Miles, J. W.},
	publisher = {Cambridge University Press},
	title = {Magnetic field generation in electrically conducting fluids},
	year = {1978}}

@incollection{Gubbins1987,
	author = {Gubbins, D. and Roberts, P. H.},
	booktitle = {Geomagnetism},
	date-added = {2010-05-27 16:57:38 +0200},
	date-modified = {2010-05-27 16:57:38 +0200},
	editor = {J. A. Jacobs},
	title = {Magnetohydrodynamics of the {E}arth's core},
	volume = {2},
	year = {1987}}

@article{Dumberry2010,
	abstract = {{P>Seismological observations suggest that the Earth's solid inner core
   has been rotating faster than the mantle over the past several decades,
   consistent with the results of some numerical geodynamo models.
   However, the hemispherical anisotropy structure of the inner core, also
   seismically observed, may require the inner core to remain at a
   relatively fixed longitudinal alignment with respect to the mantle,
   perhaps due to gravitational locking between them. Both of these
   seismic observations may be compatible if the differential rotation of
   the inner core is oscillatory in nature, with no mean offset over
   geologically long timescales. In this work, we investigate the possible
   rates of rotation of an oscillating inner core and the dynamics of
   coupling within the core-mantle system from an angular momentum
   perspective. We find that gravitational coupling between the inner core
   and mantle acts to prevent differential rotation, although the period
   at which `locking' occurs differs depending on which of the inner core
   or mantle is driving the motion. We also show that for an internally
   generated torque, a long period (longer than 100 yr) oscillation of the
   inner core with a rate equal to 0.25 degrees yr-1, on the high end of
   the rates inferred from seismic observations, is possible. However, the
   mantle oscillations entrained by gravitational coupling in such a
   scenario are only marginally compatible with the observed changes in
   length of day. We show that, in order to explain the seismically
   inferred rotation rates, either the gravitational coupling must be
   lower than previous estimates, or the electromagnetic coupling at the
   core-mantle boundary must be stronger than typical estimates.}},
	address = {{COMMERCE PLACE, 350 MAIN ST, MALDEN 02148, MA USA}},
	affiliation = {{Dumberry, M (Reprint Author), Univ Alberta, Dept Phys, Edmonton, AB, Canada. {[}Dumberry, Mathieu] Univ Alberta, Dept Phys, Edmonton, AB, Canada. {[}Mound, Jon] Univ Leeds, Sch Earth \& Environm, Leeds, W Yorkshire, England.}},
	author = {Dumberry, Mathieu and Mound, Jon},
	author-email = {{dumberry@ualberta.ca}},
	date-added = {2010-05-25 17:08:38 +0200},
	date-modified = {2010-05-25 17:09:05 +0200},
	doc-delivery-number = {{583RO}},
	doi = {{10.1111/j.1365-246X.2010.04563.x}},
	funding-acknowledgement = {{NSERC/CRSNG ; WUN-Leeds }},
	funding-text = {{Mathieu Dumberry is currently supported by a NSERC/CRSNG discovery grant. Jon Mound recognizes support of the WUN-Leeds Fund for International Research Collaboration.}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	journal-iso = {{Geophys. J. Int.}},
	keywords = {{Earth rotation variations; Dynamo: theories and simulations; Core; outer core and inner core}},
	keywords-plus = {{EARTHS CORE; ANGULAR-MOMENTUM; TORSIONAL OSCILLATIONS; WESTWARD DRIFT; MAGNETIC-FIELD; LENGTH; FLOWS; HETEROGENEITY; ANISOTROPY; VISCOSITY}},
	language = {{English}},
	month = {{MAY}},
	number = {{2}},
	number-of-cited-references = {{42}},
	pages = {{806-817}},
	publisher = {{WILEY-BLACKWELL PUBLISHING, INC}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{0}},
	title = {{Inner core-mantle gravitational locking and the super-rotation of the inner core}},
	type = {{Article}},
	unique-id = {{ISI:000276697000013}},
	volume = {{181}},
	year = {{2010}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2010.04563.x%7D}}

@article{Christ2001,
	author = {Christensen, U. R. and Aubert, J. and Busse, F. H. and Cardin, P. and Dormy, E. and Gibbons, S. and Glatzmaier, G. A. and Honkura, Y. and Jones, C. A. and Kono, M. and Matsushima, M. and Sakuraba, A. and Takahashi, F. and Tilgner, A. and Wicht, J. and Zhang, K.},
	date-added = {2010-05-20 16:54:26 +0200},
	date-modified = {2010-05-20 16:54:26 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {25-34},
	title = {A numerical dynamo benchmark},
	volume = {128},
	year = {2001}}

@article{Cao2007,
	abstract = {{Constraining the topography of the inner-core boundary is important for
   studies of core-mantle coupling and the generation of the geodynamo. We
   present evidence for significant temporal variability in the amplitude
   of the inner core reflected phase PKiKP for an exceptionally
   high-quality earthquake doublet, observed postcritically at the
   short-period Yellowknife seismic array (YK), which occurred in the
   South Sandwich Islands within a 10-year interval (1993/2003). This
   observation, complemented by data from several other doublets,
   indicates the presence of topography at the innercore boundary, with a
   horizontal wavelength on the order of 10 km. Such topography could be
   sustained by small-scale convection at the top of the inner core and is
   compatible with a rate of super rotation of the inner core of
   approximate to 0.1-0.15 degrees per year. In the absence of inner-core
   rotation, decadal scale temporal changes in the innercore boundary
   topography would provide an upper bound on the viscosity at the top of
   the inner core.}},
	address = {{2101 CONSTITUTION AVE NW, WASHINGTON, DC 20418 USA}},
	affiliation = {{Romanowicz, B (Reprint Author), Univ Calif Berkeley, Berkeley Seismol Lab, Berkeley, CA 94720 USA. Univ Calif Berkeley, Berkeley Seismol Lab, Berkeley, CA 94720 USA.}},
	author = {Cao, Aimin and Masson, Yder and Romanowicz, Barbara},
	author-email = {{barbara@seismo.berkeley.edu}},
	date-added = {2010-05-20 15:56:37 +0200},
	date-modified = {2010-05-20 15:56:47 +0200},
	doc-delivery-number = {{125QF}},
	doi = {{10.1073/pnas.0609810104}},
	issn = {{0027-8424}},
	journal = {PNAS},
	journal-iso = {{Proc. Natl. Acad. Sci. U. S. A.}},
	keywords = {{PKiKP; super rotation; doublet}},
	keywords-plus = {{SEISMOLOGICAL EVIDENCE; DIFFERENTIAL ROTATION; SEISMIC ATTENUATION; MANTLE BOUNDARY; TRAVEL-TIMES; PCP DATA; CONSTRAINTS; PKIKP; TOP; VELOCITY}},
	language = {{English}},
	month = {{JAN 2}},
	number = {{1}},
	number-of-cited-references = {{27}},
	pages = {{31-35}},
	publisher = {{NATL ACAD SCIENCES}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{9}},
	title = {{Short wavelength topography on the inner-core boundary}},
	type = {{Article}},
	unique-id = {{ISI:000243456300008}},
	volume = {{104}},
	year = {{2007}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.0609810104%7D}}

@article{SongRichards1996,
	abstract = {{The travel times of seismic waves that traverse the Earth's inner core
   show a small but systematic variation over the past three decades. This
   variation is best explained by a rotation of the inner core that moves
   the symmetry axis of its known seismic anisotropy. The inferred
   rotation rate is on the order of 1 degrees per year faster than the
   daily rotation of the mantle and crust.}},
	address = {{4 LITTLE ESSEX STREET, LONDON, ENGLAND WC2R 3LF}},
	affiliation = {{Song, XD (Reprint Author), COLUMBIA UNIV,LAMONT DOHERTY GEOL OBSERV,PALISADES,NY 10964. COLUMBIA UNIV,DEPT EARTH \& ENVIRONM SCI,NEW YORK,NY 10027.}},
	author = {Song, XD and Richards, PG},
	date-added = {2010-05-20 15:48:29 +0200},
	date-modified = {2010-05-20 15:48:44 +0200},
	doc-delivery-number = {{UX790}},
	issn = {{0028-0836}},
	journal = {Nature},
	journal-iso = {{Nature}},
	keywords-plus = {{PKIKP TRAVEL-TIMES; FREE OSCILLATIONS; ANISOTROPY; VISCOSITY}},
	language = {{English}},
	month = {{JUL 18}},
	number = {{6588}},
	number-of-cited-references = {{34}},
	pages = {{221-224}},
	publisher = {{MACMILLAN MAGAZINES LTD}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{207}},
	title = {{Seismological evidence for differential rotation of the Earth's inner core}},
	type = {{Article}},
	unique-id = {{ISI:A1996UX79000039}},
	volume = {{382}},
	year = {{1996}}}

@article{Sakuraba2009,
	abstract = {{The Earth's main magnetic field is thought to be generated by motions
   in the planet's fluid outer core, which lead to an effect similar to
   that of a dynamo(1-3). Recent high-resolution numerical simulations
   produce only a non-dipolar(4) or a dipolar but comparatively weak
   magnetic field(5,6) unlike that of the Earth. Older models that did
   generate a strong, Earth-like field needed to use unrealistically high
   viscosities for the core fluid(7-10). Common to most of the models is
   the assumption of a laterally uniform core-surface temperature. Here we
   use a low-viscosity geodynamo model to evaluate the effect of a
   different and more realistic boundary condition-a uniform heat flux at
   the surface of the core-on the simulation of an Earth-like magnetic
   field. Our results show that when the surface temperature is laterally
   uniform, only a weak magnetic field is generated because
   planetary-scale fluid circulations are suppressed. In contrast, a
   laterally uniform heat flux at the core's surface leads to large-scale
   convective flows, and a comparatively strong dipole-type magnetic
   field. Contrary to previous work(11,12), we suggest that thermal
   conditions at the core surface have a strong effect on low-viscosity
   geodynamo models.}},
	address = {{75 VARICK ST, 9TH FLR, NEW YORK, NY 10013-1917 USA}},
	affiliation = {{Sakuraba, A (Reprint Author), Univ Tokyo, Sch Sci, Dept Earth \& Planetary Sci, Tokyo 1130033, Japan. {[}Sakuraba, Ataru] Univ Tokyo, Sch Sci, Dept Earth \& Planetary Sci, Tokyo 1130033, Japan. {[}Roberts, Paul H.] Univ Calif Los Angeles, Inst Geophys \& Planetary Phys, Los Angeles, CA 90095 USA.}},
	author = {Sakuraba, A. and Roberts, P. H.},
	author-email = {{sakuraba@eps.s.u-tokyo.ac.jp}},
	date-added = {2010-01-27 17:36:05 +0100},
	date-modified = {2016-11-14 13:52:44 +0000},
	doc-delivery-number = {{514IU}},
	doi = {{10.1038/NGEO643}},
	funding-acknowledgement = {{Yamada Science Foundation ; NSF }},
	funding-text = {{Numerical simulations were carried out at the Earth Simulator Center, Yokohama, Japan. A. S. was supported by a grant-in-aid from Yamada Science Foundation. P. H. R. thanks NSF for partial support.}},
	issn = {{1752-0894}},
	journal = {Nature Geosci.},
	journal-iso = {{Nat. Geosci.}},
	keywords-plus = {{CONVECTION-DRIVEN DYNAMOS; EARTHS CORE; MAGNETOHYDRODYNAMIC DYNAMO; GEOMAGNETIC-FIELD; GEODYNAMO SIMULATIONS; COMPUTER-SIMULATION; THERMAL INSTABILITY; LATERAL VARIATIONS; BOUNDARIES; REVERSALS}},
	language = {{English}},
	month = {NOV},
	number = {11},
	number-of-cited-references = {{30}},
	pages = {802-805},
	publisher = {{NATURE PUBLISHING GROUP}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{1}},
	title = {Generation of a strong magnetic field using uniform heat flux at the surface of the core},
	type = {{Article}},
	unique-id = {{ISI:000271388500027}},
	volume = {2},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/NGEO643%7D}}

@article{Takahashi2005Taylor,
	abstract = {{High-resolution, low-viscosity geodynamo simulations have been carried
   out on the Earth Simulator, one of the fastest supercomputers, in a
   dynamic regime similar to that of Earth's core, that is, in a
   quasi-Taylor state. Our dynamo models exhibit features of the geodynamo
   not only in spatial and temporal characteristics but also in dynamics.
   Polarity reversals occurred when magnetic flux patches at high
   latitudes moved poleward and disappeared; patches with reversed field
   at low and mid-latitudes then moved poleward.}},
	address = {{1200 NEW YORK AVE, NW, WASHINGTON, DC 20005 USA}},
	affiliation = {{Takahashi, F (Reprint Author), Japan Aerosp Explorat Agcy, Inst Space \& Astronaut Sci, 3-1-1 Yoshinodai, Kanagawa, Japan. Japan Aerosp Explorat Agcy, Inst Space \& Astronaut Sci, Kanagawa, Japan. Tokyo Inst Technol, Dept Earth \& Planetary Sci, Meguro Ku, Tokyo 152, Japan.}},
	author = {Takahashi, F and Matsushima, M and Honkura, Y},
	author-email = {{futoshi@stp.isas.jaxa.jp}},
	date-added = {2010-01-27 17:18:29 +0100},
	date-modified = {2010-01-27 17:20:40 +0100},
	doc-delivery-number = {{946LY}},
	doi = {{10.1126/science.1111831}},
	issn = {{0036-8075}},
	journal = {Science},
	journal-iso = {{Science}},
	keywords-plus = {{DYNAMO SIMULATIONS; INNER-CORE; MAGNETIC-FIELD; GEODYNAMO; MODEL; NUMBER; MANTLE}},
	language = {{English}},
	month = {JUL 15},
	number = {5733},
	number-of-cited-references = {{25}},
	pages = {459-461},
	publisher = {{AMER ASSOC ADVANCEMENT SCIENCE}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{29}},
	title = {Simulations of a quasi-Taylor state geomagnetic field including polarity reversals on the Earth Simulator},
	type = {{Article}},
	unique-id = {{ISI:000230574900044}},
	volume = {309},
	year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1111831%7D}}

@article{Ferraro1937,
	author = {Ferraro, V. C. A.},
	date-added = {2010-01-27 11:29:19 +0100},
	date-modified = {2010-01-27 11:29:19 +0100},
	journal = {Month. Not. Roy. Astr. Soc.},
	pages = {458},
	title = {The non-uniform rotation of the Sun and its magnetic field},
	volume = {97},
	year = {1937}}

@article{Holme1998,
	author = {Holme, R.},
	date-added = {2009-10-02 17:03:31 +0200},
	date-modified = {2009-10-02 17:04:08 +0200},
	journal = {Geophys. J. Int.},
	pages = {167-180},
	title = {Electromagnetic core-mantle coupling - I. Explaining decadal changes in the length of day},
	volume = {132},
	year = {1998}}

@article{Aubert2008,
	author = {Aubert, J. and Aurnou, J. and Wicht, J.},
	date-added = {2009-09-29 15:23:18 +0200},
	date-modified = {2011-06-07 15:13:49 +0200},
	doi = {10.1111/j.1365-246X.2007.03693.x},
	journal = {Geophys. J. Int.},
	pages = {945-956},
	title = {The magnetic structure of convection-driven numerical dynamos},
	volume = {172},
	year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2007.03693.x}}

@article{Aubert2008_2,
	abstract = {{Seismic waves sampling the top 100 km of the Earth's inner core reveal
   that the eastern hemisphere (40 degrees E-180 degrees E) is seismically
   faster(1,2), more isotropic(2,3) and more attenuating(4) than the
   western hemisphere. The origin of this hemispherical dichotomy is a
   challenging problem for our understanding of the Earth as a system of
   dynamically coupled layers. Previously, laboratory experiments have
   established that thermal control from the lower mantle can drastically
   affect fluid flow in the outer core(5), which in turn can induce
   textural heterogeneity on the inner core solidification front(6). The
   resulting texture should be consistent with other expected
   manifestations of thermal mantle control on the geodynamo, specifically
   magnetic flux concentrations(7,8) in the timeaverage palaeomagnetic
   field(9,10) over the past 5 Myr, and preferred eddy locations(11) in
   flows imaged below the core-mantle boundary by the analysis of
   historical geomagnetic secular variation(12). Here we show that a
   single model of thermochemical convection and dynamo action can account
   for all these effects by producing a large-scale, long-term outer core
   flow that couples the heterogeneity of the inner core with that of the
   lower mantle. The main feature of this thermochemical `wind' is a
   cyclonic circulation below Asia, which concentrates magnetic field on
   the core-mantle boundary at the observed location and locally agrees
   with core flow images. This wind also causes anomalously high rates of
   light element release in the eastern hemisphere of the inner core
   boundary, suggesting that lateral seismic anomalies at the top of the
   inner core result from mantle-induced variations in its freezing rate.}},
	address = {{MACMILLAN BUILDING, 4 CRINAN ST, LONDON N1 9XW, ENGLAND}},
	affiliation = {{Aubert, J (Reprint Author), Univ Paris Diderot, Inst Phys Globe, INSU, CNRS, 4 Pl Jussieu, F-75252 Paris 05, France. {[}Aubert, Julien; Amit, Hagay; Hulot, Gauthier] Univ Paris Diderot, Inst Phys Globe, INSU, CNRS, F-75252 Paris 05, France. {[}Olson, Peter] Johns Hopkins Univ, Dept Earth \& Planetary Sci, Baltimore, MD 21218 USA.}},
	author = {Aubert, Julien and Amit, Hagay and Hulot, Gauthier and Olson, Peter},
	author-email = {{aubert@ipgp.jussieu.fr}},
	date-added = {2009-09-22 14:17:52 +0200},
	date-modified = {2011-06-07 15:17:04 +0200},
	doc-delivery-number = {{334NH}},
	doi = {10.1038/nature07109},
	issn = {{0028-0836}},
	journal = {Nature},
	journal-iso = {{Nature}},
	keywords-plus = {{NUMERICAL DYNAMOS; LABORATORY MODEL; MAGNETIC-FIELD; DEEP MANTLE; GEODYNAMO; CONVECTION; ANISOTROPY; ROTATION; SOLIDIFICATION; SIMULATIONS}},
	language = {{English}},
	month = {{AUG 7}},
	number = {{7205}},
	number-of-cited-references = {{33}},
	pages = {758-761},
	publisher = {{NATURE PUBLISHING GROUP}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{3}},
	title = {{Thermochemical flows couple the Earth's inner core growth to mantle heterogeneity}},
	type = {{Article}},
	unique-id = {{ISI:000258228000043}},
	volume = {{454}},
	year = {{2008}},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature07109%7D}}

@article{Zatman1997,
	author = {Zatman, S. and Bloxham, J.},
	date-added = {2009-09-22 14:11:54 +0200},
	date-modified = {2009-09-22 14:11:54 +0200},
	journal = {Nature},
	pages = {760-763},
	title = {Torsional oscillations and the magnetic field within the {E}arth's Core},
	volume = {388},
	year = {1997}}

@article{Abarca2000,
	author = {Abarca del Rio, R. and Gambis, D. and Salstein, D.},
	date-added = {2009-09-22 13:55:45 +0200},
	date-modified = {2009-09-22 13:56:47 +0200},
	journal = {Ann. Geophys.},
	pages = {347-364},
	title = {Interannual signals in length of day and atmospheric angular momentum},
	volume = {18},
	year = {2000}}

@article{Buffett1999,
	abstract = {{Seismological observations suggest the inner core has been rotating
   faster than the mantle during the past 30-50 years. Differential
   rotation can produce large gravitational torques on the mantle which,
   if not balanced by other torques, would be detectable as changes in the
   rotation;rate of the mantle (Length of Day or LOD). We compare
   seismological estimates of inner core rotation with estimates derived
   by inverting LOD observations using models of gravitational coupling.
   Model predictions depend on several parameters, but for the expected
   range of parameter values, the seismological estimates of relative
   rotation are at least an order of magnitude larger than those predicted
   by the LOD data. Furthermore, the LOD data predict oscillation in the
   angular alignment of the inner core and mantle during the past 30-50
   years, while the seismological data seem to require a component of
   steady rotation. We show that steady rotation of the inner core implies
   a steady torque on the mantle. This torque is not accelerating the
   rotation rate of the mantle, so it must be opposed by another torque.
   The required torque is consistent with a frictional electromagnetic
   stress on the base of the mantle due to a westward flow at the top of
   the core.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Buffett, BA (Reprint Author), Univ British Columbia, Dept Earth \& Ocean Sci, Vancouver, BC V6T 1Z4, Canada. Univ British Columbia, Dept Earth \& Ocean Sci, Vancouver, BC V6T 1Z4, Canada. Univ Washington, Geophys Program, Seattle, WA 98195 USA.}},
	author = {Buffett, BA and Creager, KC},
	date-added = {2009-09-22 13:45:31 +0200},
	date-modified = {2009-09-22 13:46:48 +0200},
	doc-delivery-number = {{197PR}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	journal-iso = {{Geophys. Res. Lett.}},
	keywords-plus = {{DIFFERENTIAL ROTATION; TRAVEL-TIMES; EARTH; ANISOTROPY; SURFACE; LENGTH; MANTLE; FLOW}},
	language = {{English}},
	month = {{MAY 15}},
	number = {{10}},
	number-of-cited-references = {{22}},
	pages = {1509-1512},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{14}},
	title = {{A comparison of geodetic and seismic estimates of inner-core rotation}},
	type = {{Article}},
	unique-id = {{ISI:000080374500042}},
	volume = {{26}},
	year = {{1999}}}

@article{Hulot2002,
	author = {Hulot, G. and Eymin, C. and Langlais, B. and Mandea, M. and Olsen, N.},
	date-added = {2009-09-22 12:06:46 +0200},
	date-modified = {2009-09-22 12:06:46 +0200},
	journal = {Nature},
	pages = {620-623},
	title = {Small-scale structure of the geodynamo inferred from {O}ersted and {M}agsat satellite data},
	volume = {416},
	year = {2002}}

@article{deWijs1998,
	abstract = {{It is thought that the Earth's outer core consists mainly of liquid
   iron and that the convection of this metallic liquid gives rise to the
   Earth's magnetic field. A full understanding of this convection is
   hampered, however, by uncertainty regarding the viscosity of the outer
   core. Viscosity estimates from various sources span no less than 12
   orders of magnitude(1,2), and it seems unlikely that this uncertainty
   will be substantially reduced by experimental measurements in the near
   future. Here we present dynamical first-principles simulations of
   liquid iron which indicate that the viscosity of iron at core
   temperatures and pressures is at the low end of the range of previous
   estimates - roughly 10 times that of typical liquid metals at ambient
   pressure. This estimate supports the promotion commonly made in
   magnetohydrodynamic models that the outer core is an inviscid
   fluid(3-5) undergoing small-scale circulation and turbulent
   convection(6), rather than large-scale global circulation.}},
	address = {{PORTERS SOUTH, 4 CRINAN ST, LONDON, ENGLAND N1 9XW}},
	affiliation = {{Gillan, MJ (Reprint Author), Univ Keele, Dept Phys, Keele ST5 5BG, Staffs, England. Univ Keele, Dept Phys, Keele ST5 5BG, Staffs, England. Vienna Univ Technol, Inst Theoret Phys, A-1040 Vienna, Austria. Univ London Birkbeck Coll, Res Sch Geol \& Geophys Sci, London WC1E 6BT, England. UCL, London WC1E 6BT, England.}},
	author = {de Wijs, GA and Kresse, G and Vocadlo, L and Dobson, D and Alfe, D and Gillan, MJ and Price, GD},
	author-email = {{pha71@keele.ac.uk}},
	date-added = {2009-09-22 11:14:22 +0200},
	date-modified = {2009-09-22 11:17:18 +0200},
	doc-delivery-number = {{ZJ679}},
	issn = {{0028-0836}},
	journal = {Nature},
	journal-iso = {{Nature}},
	keywords-plus = {{GENERALIZED-GRADIENT APPROXIMATION; INITIO MOLECULAR-DYNAMICS; SIMULATION; PSEUDOPOTENTIALS; TRANSITION; FORMALISM; METALS; FIELD; GPA}},
	language = {{English}},
	month = {{APR 23}},
	number = {{6678}},
	number-of-cited-references = {{30}},
	pages = {805-807},
	publisher = {{MACMILLAN MAGAZINES LTD}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{79}},
	title = {{The viscosity of liquid iron at the physical conditions of the Earth's core}},
	type = {{Article}},
	unique-id = {{ISI:000073241200050}},
	volume = {{392}},
	year = {{1998}}}

@article{Buffett1997,
	abstract = {{Recent seismological studies(1,2) have suggested that the inner core is
   rotating relative to the bulk of the Earth, a situation which
   (according to numerical simulations(3)) may be sustained by convective
   flow in the liquid outer core. On the other hand, large gravitational
   forces due to the heterogeneous distribution of mass in the Earth's
   mantle should be sufficient to keep the inner core aligned with the
   mantle(4). Here I show that the differential rotation of the inner core
   can be reconciled with these strong gravitational forces by allowing
   the shape of the inner core to adjust as it rotates, so permitting an
   estimate of the effective viscosity of this innermost region of the
   Earth. The inferred rotation rate constrains the viscosity of the inner
   core to be less than 10(16) Pa s or greater than 10(20) Pa s, as two
   different dynamical regimes are possible. The viscosity estimates for
   these two regimes have very different implications for the origin of
   seismic anisotropy in the inner core.}},
	address = {{PORTERS SOUTH, 4 CRINAN ST, LONDON, ENGLAND N1 9XW}},
	affiliation = {{Buffett, BA (Reprint Author), UNIV BRITISH COLUMBIA,DEPT EARTH \& OCEAN SCI,VANCOUVER,BC V6T 1Z4,CANADA.}},
	author = {Buffett, BA},
	date-added = {2009-09-18 14:50:19 +0200},
	date-modified = {2009-09-18 14:50:39 +0200},
	doc-delivery-number = {{XP722}},
	issn = {{0028-0836}},
	journal = {Nature},
	journal-iso = {{Nature}},
	keywords-plus = {{ANISOTROPY}},
	language = {{English}},
	month = {{AUG 7}},
	number = {{6642}},
	number-of-cited-references = {{21}},
	pages = {571-573},
	publisher = {{MACMILLAN MAGAZINES LTD}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{71}},
	title = {{Geodynamic estimates of the viscosity of the Earth's inner core}},
	type = {{Article}},
	unique-id = {{ISI:A1997XP72200045}},
	volume = {{388}},
	year = {{1997}}}

@article{Aurnou1998,
	abstract = {{We use numerical calculations of magnetic induction by axisymmetric
   motions in a spherical Shell of conducting fluid to investigate the
   relationship between the Earth's toroidal magnetic field and the
   time-dependent anomalous rotation of the solid inner core. We compute
   the induced toroidal magnetic field and inner core rotation maintained
   by the interaction of time-independent, axisymmetric outer core fluid
   flow with models of the poloidal magnetic field. Three possible models
   of-the azimuthal flow in the outer core are investigated: two thermal
   wind flows inside the tangent cylinder (predicted by some numerical
   models of the geodynamo) and a columnar flow outside the inner core
   tangent cylinder inferred from the geomagnetic westward drift. Results
   indicate that electromagnetic torques tightly couple the inner core
   rotation to the fluid motion. Electromagnetic spin-up of the inner core
   occurs through damped torsional oscillations with periodicity near 4
   years depending on the strength of the poloidal magnetic field. In
   steady state the thermal winds inside the tangent cylinder generate a
   peak toroidal field of 25 mT accompanying a prograde inner core
   rotation rate of 1 degrees/yr. In contrast, the columnar westward drift
   model generates toroidal field with peak intensity near 4 mT and a
   small, retrograde anomalous inner core rotation of -0.013 degrees/yr.
   The weak retrograde motion of the inner core produced by
   electromagnetic coupling to the westward drift cannot explain the
   seismically inferred prograde anomalous rotation.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}},
	affiliation = {{Aurnou, J (Reprint Author), Johns Hopkins Univ, Dept Earth \& Planetary Sci, Olin Hall,3400 N Charles St, Baltimore, MD 21218 USA. Johns Hopkins Univ, Dept Earth \& Planetary Sci, Baltimore, MD 21218 USA.}},
	author = {Aurnou, J and Brito, D and Olson, P},
	date-added = {2009-09-17 15:50:10 +0200},
	date-modified = {2009-09-17 15:50:43 +0200},
	doc-delivery-number = {{ZM406}},
	journal = {{J. Geophys. Res.}},
	journal-iso = {{J. Geophys. Res.-Solid Earth}},
	keywords-plus = {{MANTLE; EARTH}},
	language = {{English}},
	month = {{MAY 10}},
	number = {{B5}},
	number-of-cited-references = {{27}},
	pages = {9721-9738},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{17}},
	title = {{Anomalous rotation of the inner core and the toroidal magnetic field}},
	type = {{Article}},
	unique-id = {{ISI:000073536500010}},
	volume = {{103}},
	year = {{1998}}}

@article{Aurnou1999,
	abstract = {{Numerical dynamo models have been successful in explaining the origin
   of the Earth's magnetic field and its secular variation by convection
   in the electrically conducting fluid outer core(1-7). An important
   component of the convection in the numerical dynamos are polar vortices
   beneath the core-mantle boundary in each hemisphere. These polar
   vortices in the outer core have been proposed as sources for both the
   anomalous rotation of the inner core and the toroidal part of the
   geomagnetic field(2,8). Here we use the observed structure of the
   Earth's magnetic field and its variation since 1870 to infer the
   existence of an anticyclonic polar vortex with a polar upwelling in the
   northern hemisphere of the core, consistent with the polar vortices
   found in numerical dynamos.}},
	address = {{PORTERS SOUTH, 4 CRINAN ST, LONDON N1 9XW, ENGLAND}},
	affiliation = {{Olson, P (Reprint Author), Johns Hopkins Univ, Dept Earth \& Planetary Sci, Baltimore, MD 21218 USA. Johns Hopkins Univ, Dept Earth \& Planetary Sci, Baltimore, MD 21218 USA.}},
	author = {Olson, P and Aurnou, J},
	date-added = {2009-09-17 14:36:10 +0200},
	date-modified = {2009-09-17 14:36:31 +0200},
	doc-delivery-number = {{256FZ}},
	issn = {{0028-0836}},
	journal = {Nature},
	journal-iso = {{Nature}},
	keywords-plus = {{INNER-CORE; GEOMAGNETIC-FIELD; ROTATION; MOTIONS}},
	language = {{English}},
	month = {{NOV 11}},
	number = {{6758}},
	number-of-cited-references = {{28}},
	pages = {170-173},
	publisher = {{MACMILLAN MAGAZINES LTD}},
	subject-category = {{Multidisciplinary Sciences}},
	times-cited = {{45}},
	title = {{A polar vortex in the Earth's core}},
	type = {{Article}},
	unique-id = {{ISI:000083716400046}},
	volume = {{402}},
	year = {{1999}}}

@article{Hollerbach1998,
	abstract = {{The discovery that the Earth's inner core is rotating relative to the
   mantle has prompted a number of authors to reinvestigate the dynamics
   of inner core rotation. These models include a highly idealized
   analytical one by Aurnou, Brito \& Olson (1996), as well as a fully 3-D
   numerical one by Glatzmaier \& Roberts (1996). In this work I present a
   model intermediate between these two extremes. In particular, I retain
   the simplicity of the model of Aurnou et nl. by kinematically
   prescribing a thermal wind and poloidal magnetic field. By doing so it
   is possible to vary the strengths of these quantities at will, and
   thereby explore the dependence of the inner core's rotation rate on
   them more thoroughly than in the model of Glatzmaier \& Roberts, where
   these quantities emerge as part of the solution, and one therefore has
   far less control over their strengths. However, as in the model of
   Glatzmaier \& Roberts, the full back-reaction of the magnetic field on
   the fluid flow in the outer core is included. It is found that if one
   includes this effect, the relationship between the;;inner core's
   rotation rate and the strength of the thermal wind is more complicated
   than that found by Aurnou et nl., who did not include it. As a result,
   while the observed rotation of the inner core certainly gives a
   rigorous lower bound on the maximum difference in angular velocity
   throughout the outer core, that maximum difference could be as much as
   an order of magnitude greater. Finally, it is also pointed out that,
   because of the particular nature of the torque balance that determines
   the inner core's rotation rate, it is difficult, if not impossible, to
   use that observed rate to obtain precise bounds on the magnetic field
   strength deep within the core.}},
	address = {{P O BOX 88, OSNEY MEAD, OXFORD OX2 0NE, OXON, ENGLAND}},
	affiliation = {{Hollerbach, R (Reprint Author), Univ Glasgow, Dept Math, Univ Gardens, Glasgow G12 8QW, Lanark, Scotland. Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland.}},
	author = {Hollerbach, R},
	date-added = {2009-09-17 14:03:25 +0200},
	date-modified = {2009-09-17 14:03:56 +0200},
	doc-delivery-number = {{137DK}},
	issn = {{0956-540X}},
	journal = {Geophys. J. Int.},
	journal-iso = {{Geophys. J. Int.}},
	keywords = {{Earth's core; Earth's magnetic field}},
	keywords-plus = {{MAGNETIC-FIELD; GEODYNAMO MODEL; FLUCTUATIONS; MANTLE; LAYERS; FLOW}},
	language = {{English}},
	month = {{NOV}},
	number = {{2}},
	number-of-cited-references = {{30}},
	pages = {564-572},
	publisher = {{BLACKWELL SCIENCE LTD}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{8}},
	title = {{What can the observed rotation of the Earth's inner core reveal about the state of the outer core?}},
	type = {{Article}},
	unique-id = {{ISI:000076899400019}},
	volume = {{135}},
	year = {{1998}}}

@article{Stacey2001,
	abstract = {{Extrapolation to core conditions of laboratory observations of
   electrical resistivities of iron and its alloys has been hampered by
   lack of understanding of interactions between the effects of
   temperature, pressure and impurities. We present a new theory that
   offers a simple resolution of the combined temperature and pressure
   effects: for a pure metal they can be represented by constant
   resistivity on the melting curve. On this basis the resistivity of pure
   iron under conditions in the outermost part of the core would be 1.22
   mu Omega m. This reduces the estimation of core resistivity to an
   assessment of the impurity effect. Measurements by P.W. Bridgman on a
   range of iron alloys up to 10 Cpa show that, for dilute alloys,
   impurity resistivity is proportional to total impurity content but
   relatively insensitive to which elements are present. Therefore, we use
   measurements by G. Matassov on Fe-Si alloys shock-compressed to 140 GPa
   to estimate the impurity contribution to core resistivity. Comparison
   with similar data for Fe and Fe-Ni alloy shows that under these
   conditions the effect of Si is only twice that of Ni on an atomic
   percent basis (and precisely the same on a weight percent basis). We
   estimate the total core resistivity to be about 2.1 mu Omega m with
   little variation in the outer core and 1.6 mu Omega m in the inner
   core. Allowing for a lattice thermal conductivity of 3 W m(-1) K-1 the
   corresponding thermal conductivities are 46 W m(-1) K-1 at the CMB, 63
   W m(-1) K-1 just above the ICB and 79 W m(-1) K-1 in the inner core.
   (C) 2001 Elsevier Science B.V. All rights reserved.}},
	address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}},
	affiliation = {{Stacey, FD (Reprint Author), CSIRO, Explorat \& Min, POB 883, Kenmore, Qld 4069, Australia. CSIRO, Explorat \& Min, Kenmore, Qld 4069, Australia. Univ Calif Los Angeles, Dept Earth \& Space Sci, Los Angeles, CA 90095 USA. Univ Calif Los Angeles, Inst Geophys \& Planetary Phys, Los Angeles, CA 90095 USA.}},
	author = {Stacey, FD and Anderson, OL},
	date-added = {2009-09-16 15:32:53 +0200},
	date-modified = {2009-09-16 15:33:11 +0200},
	doc-delivery-number = {{453GQ}},
	issn = {{0031-9201}},
	journal = {Phys. Earth Planet. Int.},
	journal-iso = {{Phys. Earth Planet. Inter.}},
	keywords = {{core alloy; electrical conductivity; thermal conductivity}},
	keywords-plus = {{OUTER CORE; GRUNEISEN-PARAMETER; EARTHS}},
	language = {{English}},
	month = {{AUG}},
	number = {{3-4}},
	number-of-cited-references = {{23}},
	pages = {153-162},
	publisher = {{ELSEVIER SCIENCE BV}},
	subject-category = {{Geochemistry \& Geophysics}},
	times-cited = {{21}},
	title = {{Electrical and thermal conductivities of Fe-Ni-Si alloy under core conditions}},
	type = {{Article}},
	unique-id = {{ISI:000169908500002}},
	volume = {{124}},
	year = {{2001}}}

@article{Buffett1996b,
	abstract = {{Gravitational interactions between mass anomalies in the core and the
   mantle cause rotational oscillations of the Earth that can be detected
   as fluctuations in the length of day. A simple theoretical expression
   for the frequency of these oscillations is derived using a Lagrangian
   formulation. The value of the frequency depends on the aspherical
   distribution of mass, providing a useful constraint on the structure of
   the Earth. Numerical estimates are obtained using two different models
   of density, both of which are based on seismically inferred density
   anomalies. The predicted period of the gravitational oscillation is 2
   to 3 years, depending on the choice of density model. Longer period
   modes of oscillation can also arise from the smaller convective
   fluctuations in the core about the hydrostatic state. Qualitative
   estimates for these low frequency oscillations depend on the size of
   the density fluctuations, but typical values yield a period of several
   hundred years.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009}},
	affiliation = {{UNIV BRITISH COLUMBIA,DEPT GEOPHYS \& ASTRON,VANCOUVER,BC V6T 1Z4,CANADA.}},
	author = {Buffett, BA},
	date-added = {2009-09-15 15:55:11 +0200},
	date-modified = {2009-09-15 15:55:38 +0200},
	doc-delivery-number = {{VD376}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	journal-iso = {{Geophys. Res. Lett.}},
	keywords-plus = {{MANTLE HETEROGENEITY; DYNAMIC EARTH; CORE SURFACE; MODELS; FLOW; MOTION}},
	language = {{English}},
	month = {{AUG 15}},
	number = {{17}},
	number-of-cited-references = {{21}},
	pages = {2279-2282},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{47}},
	title = {{Gravitational oscillations in the length of day}},
	type = {{Article}},
	unique-id = {{ISI:A1996VD37600020}},
	volume = {{23}},
	year = {{1996}}}

@article{Buffett1996a,
	abstract = {{Strong gravitational coupling between the solid inner core and the
   mantle provides a means of exchanging angular momentum between the
   fluid outer core and the mantle. The proposed mechanism involves
   oscillations in the fluid core which exert a large electromagnetic
   torque on the inner core by virtue of its high electrical conductivity.
   The inner core does not freely respond to this torque because it is
   constrained by gravitational forces to remain nearly aligned with the
   mantle. Angular momentum is transferred to the mantle by the
   gravitational torques that result from small misalignments with the
   inner core. A calculation of the normal modes of this coupled system
   predicts observable fluctuations of the mantle with periods of several
   decades. Damping of the oscillations due to ohmic losses produces a
   quality factor Q of about 20. An excitation mechanism to sustain the
   oscillations is proposed on the basis of recent dynamo calculations.}},
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009}},
	affiliation = {{Buffet, BA (Reprint Author), UNIV BRITISH COLUMBIA,DEPT EARTH \& OCEAN SCI,VANCOUVER,BC V6T 1Z4,CANADA.}},
	author = {Buffet, BA},
	date-added = {2009-09-15 15:48:52 +0200},
	date-modified = {2009-09-15 15:49:24 +0200},
	doc-delivery-number = {{VY929}},
	issn = {{0094-8276}},
	journal = {Geophys. Res. Lett.},
	journal-iso = {{Geophys. Res. Lett.}},
	keywords-plus = {{EARTHS ROTATION; CORE; MANTLE; SURFACE; FLOW}},
	language = {{English}},
	month = {{DEC 15}},
	number = {{25}},
	number-of-cited-references = {{20}},
	pages = {3803-3806},
	publisher = {{AMER GEOPHYSICAL UNION}},
	subject-category = {{Geosciences, Multidisciplinary}},
	times-cited = {{54}},
	title = {{A mechanism for decade fluctuations in the length of day}},
	type = {{Article}},
	unique-id = {{ISI:A1996VY92900033}},
	volume = {{23}},
	year = {{1996}}}

@article{Gubbins1981,
	address = {{2000 FLORIDA AVE NW, WASHINGTON, DC 20009}},
	affiliation = {{GUBBINS, D (Reprint Author), BULLARD LABS,MADINGLEY RISE,CAMBRIDGE CB3 0EZ,ENGLAND.}},
	author = {Gubbins, D},
	date-added = {2009-09-15 15:20:39 +0200},
	date-modified = {2010-03-05 12:22:40 +0100},
	doc-delivery-number = {{MU367}},
	issn = {{0148-0227}},
	journal = {{J. Geophys. Res.}},
	language = {{English}},
	number = {{NB12}},
	number-of-cited-references = {{22}},
	pages = {1695-1699},
	title = {{Rotation of the inner core}},
	volume = {{86}},
	year = {{1981}}}

@article{McNamara2005,
	abstract = {Large low-velocity seismic anomalies have been detected in the Earth's lower mantle beneath Africa and the Pacific Ocean that are not easily explained by temperature variations alone(1-11). The African anomaly has been interpreted to be a northwest southeast-trending structure(3-5,7) with a sharp-edged linear, ridgelike morphology(9,10). The Pacific anomaly, on the other hand, appears to be more rounded in shape(1-4,6,7,11). Mantle models with heterogeneous composition have related these structures to dense thermochemical piles or superplumes(12-19). It has not been shown, however, that such models can lead to thermochemical structures that satisfy the geometrical constraints, as inferred from seismological observations. Here we present numerical models of thermochemical convection in a three-dimensional spherical geometry using plate velocities inferred for the past 119 million years(20). We show that Earth's subduction history can lead to thermochemical structures similar in shape to the observed large, lower-mantle velocity anomalies. We find that subduction history tends to focus dense material into a ridge-like pile beneath Africa and a relatively more-rounded pile under the Pacific Ocean, consistent with seismic observations.},
	address = {LONDON},
	author = {McNamara, A. K. and Zhong, S. J.},
	author-address = {Univ Colorado, Dept Phys, Boulder, CO 80309 USA.},
	cited-reference-count = {25},
	date = {OCT 20},
	date-added = {2008-02-07 18:29:49 +0100},
	date-modified = {2008-02-07 18:30:58 +0100},
	document-type = {Article},
	e-mail-address = {allen.mcnamara@asu.edu},
	isi = {ISI:000232660500040},
	isi-document-delivery-number = {975KD},
	iso-source-abbreviation = {Nature},
	issn = {0028-0836},
	journal = {Nature},
	keywords = {MANTLE CONVECTION; BOUNDARY-LAYER; DEEP MANTLE; MODELS; SHEAR; HETEROGENEITY; INVERSION; VELOCITY; SUPERPLUME; VISCOSITY},
	language = {English},
	month = {Oct},
	number = {7062},
	page-count = {4},
	pages = {1136--1139},
	publication-type = {J},
	publisher = {NATURE PUBLISHING GROUP},
	publisher-address = {MACMILLAN BUILDING, 4 CRINAN ST, LONDON N1 9XW, ENGLAND},
	reprint-address = {McNamara, AK, Arizona State Univ, Dept Geol Sci, Tempe, AZ 85287 USA.},
	source = {NATURE},
	subject-category = {Multidisciplinary Sciences},
	times-cited = {23},
	title = {Thermochemical structures beneath Africa and the Pacific Ocean},
	volume = {437},
	year = {2005}}

@article{Aurnou2000,
	author = {Aurnou, J. and Olson, P.},
	date = {JAN},
	date-added = {2008-01-30 18:43:49 +0100},
	date-modified = {2008-01-30 18:44:00 +0100},
	isi = {ISI:000084326400010},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	month = {Jan},
	number = {1-4},
	pages = {111--121},
	publication-type = {J},
	title = {Control of inner core rotation by electromagnetic, gravitational and mechanical torques},
	volume = {117},
	year = {2000}}

@article{Mound2006,
	author = {Mound, J. E. and Buffett, B. A.},
	date = {MAR 30},
	date-added = {2008-01-30 18:02:08 +0100},
	date-modified = {2008-01-30 18:02:23 +0100},
	isi = {ISI:000236600600007},
	issn = {0012-821X},
	journal = {Earth Planet. Sci. Lett.},
	month = {Mar},
	number = {3-4},
	pages = {383--389},
	publication-type = {J},
	title = {Detection of a gravitational oscillation in length-of-day},
	volume = {243},
	year = {2006}}

@article{Glatzmaier1996,
	abstract = {We have extended our geodynamo simulation 40000 years using a more realistic representation of the thermodynamics and convection. The anelastic approximation replaces the Boussinesq approximation; and compositional buoyancy, in addition to thermal buoyancy, drives convection in the fluid outer core. Boundary conditions at the inner core boundary model the freezing of the heavy constituent onto the solid inner core and the release of the light constituent into the fluid outer core. The resulting simulated magnetic field has a strongly dipole dominated structure outside the core, similar to the Earth's field, so far displaying no tendency to reverse its dipole polarity. The non-dipolar structure of the field at the core-mantle boundary is also quite similar to the Earth's, including the rate of its general westward drift. As in our original simulation, the solid inner core typically rotates about 1 degrees/yr faster than the mantle, in agreement with recent seismic studies of the Earth. This three-dimensional self-consistent solution seems to be simulating the stable regime of the geodynamo between reversals.},
	author = {Glatzmaier, G. A. and Roberts, P. H.},
	date = {OCT 1},
	date-added = {2008-01-18 16:26:32 +0100},
	date-modified = {2008-01-18 16:26:38 +0100},
	isi = {ISI:A1996VK36600006},
	issn = {0167-2789},
	journal = {PHYSICA D},
	month = {Oct},
	number = {1-3},
	pages = {81--94},
	publication-type = {J},
	title = {An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection},
	volume = {97},
	year = {1996}}

@article{Buffett2002,
	abstract = {[1] Regeneration of the magnetic field by convection in the core places demands on heat flow into the base of the mantle. If the heat flow is too low, thermal convection is shut off and the rate of generation of compositional buoyancy by the solidification of the core becomes too low to sustain the geodynamo. Conversely, a large heat flow causes rapid growth of the inner core, so that convection prior to the appearance of the inner core must be sustained by thermal buoyancy alone. The attendant requirements on primordial heat become more severe as the age of the inner core decreases. We show that estimates of the present-day heat flow satisfy the power requirements for the geodynamo. However, the resulting thermal history is incompatible with estimates of mantle temperatures prior to 3 Ga. This discrepancy can be resolved by accumulating radioactive isotopes in D" or adding heat sources to the core.},
	author = {Buffett, B. A.},
	date = {JUN 15},
	date-added = {2008-01-18 16:11:52 +0100},
	date-modified = {2008-01-18 16:12:03 +0100},
	di = {ARTN 1566},
	isi = {ISI:000178964100057},
	issn = {0094-8276},
	journal = {Geophys. Res. Lett.},
	month = {Jun},
	number = {12},
	pages = {1566},
	publication-type = {J},
	title = {Estimates of heat flow in the deep mantle based on the power requirements for the geodynamo},
	volume = {29},
	year = {2002}}

@article{Labrosse2007,
	abstract = {The distribution of geochemical species in the Earth's interior is largely controlled by fractional melting and crystallization processes that are intimately linked to the thermal state and evolution of the mantle. The existence of patches of dense partial melt at the base of the Earth's mantle(1), together with estimates of melting temperatures for deep mantle phases(2) and the amount of cooling of the underlying core required to maintain a geodynamo throughout much of the Earth's history(3), suggest that more extensive deep melting occurred in the past. Here we show that a stable layer of dense melt formed at the base of the mantle early in the Earth's history would have undergone slow fractional crystallization, and would be an ideal candidate for an unsampled geochemical reservoir hosting a variety of incompatible species ( most notably the missing budget of heat-producing elements) for an initial basal magma ocean thickness of about 1,000 km. Differences in Nd-142/Nd-144 ratios between chondrites and terrestrial rocks(4) can be explained by fractional crystallization with a decay timescale of the order of 1 Gyr. These combined constraints yield thermal evolution models in which radiogenic heat production and latent heat exchange prevent early cooling of the core and possibly delay the onset of the geodynamo to 3.4-4 Gyr ago(5).},
	af = {Labrosse, S. Hernlund, J. W. Coltice, N.},
	author = {Labrosse, S. and Hernlund, J. W. and Coltice, N.},
	date = {DEC 6},
	date-added = {2008-01-18 16:10:04 +0100},
	date-modified = {2008-01-18 16:10:39 +0100},
	isi = {ISI:000251394900053},
	issn = {0028-0836},
	journal = {Nature},
	month = {Dec},
	number = {7171},
	pages = {866--869},
	publication-type = {J},
	title = {A crystallizing dense magma ocean at the base of the Earth's mantle},
	volume = {450},
	year = {2007}}

@article{Buffett1996,
	abstract = {The Earth's magnetic field is sustained by dynamo action in the fluid outer core. The energy sources available to the geodynamo are well established, but their relative importance remains uncertain. We focus on the issue of thermal versus compositional convection, which is inextricably coupled to the evolution of the core as the Earth cools. To investigate the effect of the various physical processes on this evolution, we develop models based on conservation of energy and the assumption that the core is well mixed by vigorous convection. We depart from previous numerical studies by developing an analytical model. The simple algebraic form of the solution affords insight into both the evolution of the core and the energy budget of the geodynamo. We also present a numerical model to compare with the quantitative predictions of our analytical model and find that the differences between the two are negligible. An important conclusion of this study is that thermal convection can contribute significantly to the geodynamo. In fact, a modest heat flux in excess of that conducted down the adiabatic gradient is sufficient to power the geodynamo, even in the absence of compositional convection and latent-heat release. The relative contributions of thermal and compositional convection to the dynamo are largely determined by the magnitude of the heat flux from the core and the inner-core radius. For a plausible current-day heat flux df Q = 3.0 x 10(12) W and the current inner-core radius, we find that compositional convection is responsible for approximately two thirds of the ohmic dissipation in the core and thermal convection for the remaining one third. The proportion of ohmic dissipation produced by thermal convection increases to 45% with an increase in Q to 6.0 x 10(12) W. In the early Earth, when the inner core was smaller and the heat flux probably greater than the present values, thermal convection would have been the dominant energy source for the dynamo. We also calculate the history of inner-core growth as a function of the heat flux. For example, the inner core would have grown to its present size in 2.8 x 10(9) years if the average heat flux was Q = 4.0 x 10(12) W. The model does not require the heat flux to be constant.},
	author = {Buffett, B. A. and Huppert, H. E. and Lister, J. R. and Woods, A. W.},
	date = {APR 10},
	date-added = {2008-01-18 16:10:04 +0100},
	date-modified = {2008-01-18 16:10:19 +0100},
	isi = {ISI:A1996UF00500001},
	issn = {0148-0227},
	journal = {J. Geophys. Res.},
	month = {Apr},
	number = {B4},
	pages = {7989--8006},
	publication-type = {J},
	title = {On the thermal evolution of the Earth's core},
	volume = {101},
	year = {1996}}

@article{Song2007,
	abstract = {The last decade has witnessed an animated debate on whether the inner core rotation is a fact or an artifact. Here we examine the temporal change of inner core waves using a technique that compares differential travel times at the same station but between two events. The method does not require precise knowledge of earthquake locations and earth models. The pairing of the events creates a large data set for the application of statistical tools. Using measurements from 87 events in the South Sandwich Islands recorded at College, Alaska station, we conclude the temporal change is robust. The estimates of the temporal change range from about 0.07 to 0.10 s/decade over the past 50 yr. If we used only pairs with small inter-event distances, which reduce the influence of mantle heterogeneity, the rates range from 0.084 to 0.098 s/decade, nearly identical to the rate inferred by Zhang et al. [Zhang, J., Song, X.D., Li, Y.C., Richards, P.G., Sun, X.L., Waldhauser, F., Inner core differential motion confirmed by earthquake waveform doublets, Science 309 (5739) (2005) 1357-1360.] from waveform doublets. The rate of the DF change seems to change with time, which may be explained by lateral variation of the inner core structure or the change in rotation rate on decadal time scale. (C) 2007 Elsevier BN. All rights reserved.},
	af = {Song, Xiaodong Poupinet, Georges},
	author = {Song, X. D. and Poupinet, G.},
	date = {SEP 15},
	date-added = {2008-01-17 15:24:55 +0100},
	date-modified = {2008-01-17 15:25:11 +0100},
	isi = {ISI:000250042500020},
	issn = {0012-821X},
	journal = {Earth Plan. Sci. Let.},
	month = {Sep},
	number = {1-2},
	pages = {259--266},
	publication-type = {J},
	title = {Inner core rotation from event-pair analysis},
	volume = {261},
	year = {2007}}

@article{Christensen2004,
	author = {Christensen, U. and Tilgner, A.},
	date-added = {2007-10-25 18:20:11 +0200},
	date-modified = {2011-10-05 15:52:58 +0200},
	journal = {Nature},
	note = {doi: 10.1038/nature02508},
	pages = {169-171},
	title = {Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos},
	volume = {429},
	year = {2004}}

@article{DumberryGJI2007,
	af = {Dumberry, Mathieu},
	author = {Dumberry, M.},
	date = {AUG},
	date-added = {2007-10-23 14:08:19 +0200},
	date-modified = {2007-10-23 14:08:35 +0200},
	isi = {ISI:000248846600033},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {Aug},
	number = {2},
	pages = {886--895},
	publication-type = {J},
	title = {Geodynamic constraints on the steady and time-dependent inner core axial rotation},
	volume = {170},
	year = {2007}}

@article{Lay2006,
	af = {Lay, Thorne Hernlund, John Garnero, Edward J. Thorne, Michael S.},
	author = {Lay, T. and Hernlund, J. and Garnero, E. J. and Thorne, M. S.},
	date = {NOV 24},
	date-added = {2007-10-22 17:57:29 +0200},
	date-modified = {2007-10-22 17:58:07 +0200},
	isi = {ISI:000242215800035},
	issn = {0036-8075},
	journal = {Science},
	month = {Nov},
	number = {5803},
	pages = {1272--1276},
	publication-type = {J},
	title = {A post-perovskite lens and {D''} heat flux beneath the central Pacific},
	volume = {314},
	year = {2006}}

@article{VanDerHilst2007,
	author = {van der Hilst, R. and De Hoop, M. V. and Wang, P. and Shim, S.-H. and Ma, P. and Tenorio, L.},
	date-added = {2007-10-22 15:41:46 +0200},
	date-modified = {2007-10-22 16:33:38 +0200},
	journal = {Science},
	pages = {1813-1817},
	title = {Seismostratigraphy and Thermal Structure of {E}arth's Core-Mantle Boundary Region},
	volume = {315},
	year = {2007}}

@article{VanDerHilst1997,
	author = {van der Hilst, R. and Widiyantoro, S. and Engdahl, E. R.},
	date-added = {2007-10-10 16:30:36 +0200},
	date-modified = {2007-10-10 16:32:15 +0200},
	journal = {Nature},
	pages = {578-584},
	title = {Evidence for deep mantle circulation from global tomography},
	volume = {386},
	year = {1997}}

@article{Gubbins2007,
	abstract = {Variations in the Earth's lower mantle appear to influence the geodynamo operating in the liquid core. We present a solution to the full dynamo equations with lateral variations in heat flux on the outer boundary defined by the shear wave velocity of the lowermost mantle. The magnetic field is almost stationary and locked to the boundary, with 4 symmetrical concentrations of flux sited beneath cold mantle. This allows for the first time a direct comparison between a dynamo solution and the main features of the present geomagnetic field. Of the four main equatorially symmetric flux lobes, two (the "Siberian" pair) are centered within 5 degrees of the corresponding Earth's pair; the other two (the "Canadian" pair) are not quite so close but are more mobile, as the corresponding Earth's pair have been in the last 300 years. Our study strongly suggests that geomagnetic field morphology is dominated not only by geometry related to the inner core but also by structure in the bottom few hundred kilometres of the mantle, notably the seismically fast ring beneath the Pacific rim and large fast anomalies beneath Siberia and Canada. Tighter locking of one of the pairs of flux lobes suggests the seismic anomaly beneath the Siberian side of the ring is in some way stronger than the one on the Canadian side. These locked solutions only occur for a limited parameter range with the large Ekman numbers available to numerical experiments, which explains why none have been found earlier. This solution provides an important starting point for further searches for dynamos with realistic geomagnetic fields. (C) 2007 Elsevier B.V. All rights reserved.},
	af = {Gubbins, David Willis, Ashley P. Sreenivasan, Binod},
	author = {Gubbins, D. and Willis, A. P. and Sreenivasan, B.},
	date = {JUL 16},
	date-added = {2007-10-10 14:40:50 +0200},
	date-modified = {2007-10-10 14:41:18 +0200},
	isi = {ISI:000248437800008},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	month = {Jul},
	number = {3-4},
	pages = {256--260},
	publication-type = {J},
	title = {Correlation of Earth's magnetic field with lower mantle thermal and seismic structure},
	volume = {162},
	year = {2007}}

@book{Stacey1992,
	author = {Stacey, F. D.},
	date-added = {2007-10-09 17:27:31 +0200},
	date-modified = {2007-10-09 17:27:31 +0200},
	publisher = {Brookfield Press},
	title = {Physics of the Earth},
	year = {1992}}

@article{Trampert2004,
	author = {Trampert, J. and Deschamps, F. and Resovsky, J. and Yuen, D.},
	date-added = {2007-10-09 15:22:06 +0200},
	date-modified = {2007-10-09 15:22:06 +0200},
	journal = {Science},
	pages = {853-856},
	title = {Probabilistic Tomography Maps Chemical Heterogeneities Throughout the Lower Mantle},
	volume = {306},
	year = {2004}}

@article{Wicht2002,
	author = {Wicht, J.},
	date-added = {2007-09-18 15:21:29 +0200},
	date-modified = {2007-09-18 15:21:29 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {281-302},
	title = {Inner-Core Conductivity in Numerical Dynamo Simulations},
	volume = {132},
	year = {2002}}

@article{Eymin2005,
	author = {Eymin, C. and Hulot, G.},
	date-added = {2007-09-14 14:27:57 +0200},
	date-modified = {2007-09-14 14:27:57 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {200-220},
	title = {On core surface flows inferred from satellite magnetic data},
	volume = {152},
	year = {2005}}

@article{Kutzner2004,
	author = {Kutzner, C. and Christensen, U. R.},
	date = {JUN},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000222667100011},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {Jun},
	number = {3},
	pages = {1105--1118},
	publication-type = {J},
	title = {Simulated geomagnetic reversals and preferred virtual geomagnetic pole paths},
	volume = {157},
	year = {2004}}

@article{Labrosse2001,
	author = {Labrosse, S. and Poirier, J. P. and Le Mouel, J. L.},
	date = {AUG 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000170543800002},
	issn = {0012-821X},
	journal = {Earth Planet. Sci. Let.},
	month = {Aug},
	number = {3-4},
	pages = {111--123},
	publication-type = {J},
	title = {The age of the inner core},
	volume = {190},
	year = {2001}}

@article{Braginsky1995,
	author = {Braginsky, S. I. and Roberts, P. H.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2011-10-05 15:47:12 +0200},
	isi = {ISI:A1995RX08800001},
	issn = {0309-1929},
	journal = {Geophys. Astrophys. Fluid Dyn.},
	number = {1-4},
	pages = {1--97},
	publication-type = {J},
	title = {Equations governing convection in {e}arth's core and the geodynamo},
	volume = {79},
	year = {1995}}

@article{Secco1989,
	author = {Secco, R. A. and Shloessin, H. H.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {J. Geophys. Res.},
	pages = {5887-5894},
	title = {The electrical resistivity of solid and liquid {Fe} at pressures up to 7 {GPa}},
	volume = {94},
	year = {1989}}

@article{Olson1999,
	author = {Olson, P. and Christensen, U. and Glatzmaier, G. A.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {J. Geophys. Res.},
	number = {B5},
	pages = {10383-10404},
	title = {Numerical modelling of the geodynamo: mechanisms of field generation and equilibration},
	volume = {104},
	year = {1999}}

@article{Glatzmaier1999,
	abstract = {A series of computer simulations of the Earth's dynamo illustrates how the thermal structure of the lowermost mantle might affect convection and magnetic-field generation in the fluid core. Eight different patterns of heat flux from the core to the mantle are imposed over the core-mantle boundary. Spontaneous magnetic dipole reversals and excursions occur in seven of these cases, although sometimes the field only reverses in the outer part of the core, and then quickly reverses back. The results suggest correlations among the frequency of reversals, the duration over which the reversals occur, the magnetic-field intensity and the secular variation. The case with uniform heat flux at the core-mantle boundary appears most 'Earth-like'. This result suggests that variations in heat flux at the care-mantle boundary of the Earth are smaller than previously thought, possibly because seismic velocity anomalies in the lowermost mantle might have more of a compositional rather than thermal origin, or because of enhanced heat flux in the mantle's zones of ultra-low seismic velocity,},
	author = {Glatzmaier, G. A. and Coe, R. S. and Hongre, L. and Roberts, P. H.},
	date = {OCT 28},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000083464700049},
	issn = {0028-0836},
	journal = {Nature},
	month = {Oct},
	number = {6756},
	pages = {885--890},
	publication-type = {J},
	title = {The role of the {E}arth's mantle in controlling the frequency of geomagnetic reversals},
	volume = {401},
	year = {1999}}

@article{Bloxham1987,
	author = {Bloxham, J. and Gubbins, D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Nature},
	pages = {511-513},
	title = {Thermal core-mantle interactions},
	volume = {325},
	year = {1987}}

@article{Hide1970,
	author = {Hide, R.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Q. J. R. Meterol. Soc.},
	pages = {579-590},
	title = {On the {E}arth's core-mantle interface},
	volume = {96},
	year = {1970}}

@article{Buffett2000science,
	abstract = {Earth's magnetic field is generated by fluid motion in the liquid iron core. Details of how this occurs are now emerging from numerical simulations that achieve a serf-sustaining magnetic field. Early results predict a dominant dipole field outside the core, and some models even reproduce magnetic reversals. The simulations also show how different patterns of flow can produce similar external fields. Efforts to distinguish between the various possibilities appeal to observations of the time-dependent behavior of the field. important constraints will come from geological records of the magnetic field in the past.},
	author = {Buffett, B. A.},
	date = {JUN 16},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000087687000040},
	issn = {0036-8075},
	journal = {Science},
	month = {Jun},
	number = {5473},
	pages = {2007--2012},
	publication-type = {J},
	title = {Earth's core and the geodynamo},
	volume = {288},
	year = {2000}}

@article{Kelly1997,
	abstract = {The modern geomagnetic held is usually expressed as a spherical harmonic expansion. Although the palaeomagnetic record is very incomplete in both space and time, sufficient data are available from a span of ages to generate time-averaged spherical harmonic field models with many degrees of freedom. Here three data sets are considered: directional measurements from lavas, inclination measurements from ocean sediments, and intensity measurements from lavas. Individual data are analysed, as well as site-averages, using the same methods that have been developed for the modern held, to give models for the past 5 Myr. The normal-polarity held model has an axial-dipole intensity similar to that of the modern-day held, whilst the equatorial-dipole component is very much smaller. The held is not axisymmetric, but shows flux concentrations at the core's surface under Canada and Siberia similar to those observed in the held over historical timescales. Tests on synthetic data show that it is unlikely that these similarities result from the overprinting of the palaeomagnetic held due to inadequate cleaning of the samples. The reverse-polarity held model does not show such obvious features, but this may be due to the sparsity of the data. The patterns observed in the normal-polarity held, with persistent features in the northern hemisphere and a smooth southern hemisphere, could be explained if the present pattern of secular variation is typical of the past several million years. This would reveal itself as large variations over time in the direction of the magnetic vector in regions of high secular variation, with relatively little change over quieter regions. However, we have been unable to find any evidence for a geographical pattern of secular variation in the data.},
	author = {Kelly, P. and Gubbins, D.},
	date = {FEB},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1997WG09600005},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {Feb},
	number = {2},
	pages = {315--330},
	publication-type = {J},
	title = {The geomagnetic field over the past 5 million years},
	volume = {128},
	year = {1997}}

@article{Johnson1995,
	abstract = {A recently compiled lava flow data base spanning the last 5 million years is used to investigate properties of the time-averaged geomagnetic field. More than 90 per cent of the power in the palaeofield can be accounted for by a geocentric axial dipole; however, there are significant second-order structures in the held. Declination and inclination anomalies for the new data base indicate that the main second-order signal is the 'far-sided' effect, and there is also evidence for non-zonal structure. VGP (virtual geomagnetic pole) latitude distributions indicate that, over the last 5 million years, normal and reverse polarity morphologies are different, and that any changes in the normal polarity field morphology are undetectable, given the present data distribution. Regularized non-linear inversions of the palaeomagnetic directions support all these observations. We test the hypothesis that zonal models for the time-averaged field are adequate to describe the data and find that they are not. Non-zonal models are needed to fit the data to within the required tolerance level. Normal and reverse polarity held models obtained are significantly different. Field models obtained for the Brunhes epoch data alone are much smoother than those obtained from combining an the normal polarity data; simulations indicate that these differences can be explained by the less extensive data distribution for the Brunhes epoch. The field model for all of the normal polarity data (LN1) contains features observed in the historical field maps, although the details differ. LN1 suggests that, although the two northern hemisphere flux lobes observed in the historical field are stationary to a first-order approximation, they do show changes in position and amplitude. A. third, less pronounced flux lobe is observed in LN1 over central Europe. The lack of structure ih the southern hemisphere is due in part to the paucity of data. Jackknife estimates of the field models for different subsets of the data suggest that a few sites contribute significant structure to the final field models. More conservative estimates of the time-averaged field morphology are obtained by removing these sites.},
	author = {Johnson, C. L. and Constable, C. G.},
	date = {AUG},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1995RP23000010},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	month = {Aug},
	number = {2},
	pages = {489--519},
	publication-type = {J},
	title = {The time averaged geomagnetic field as recorded by lava flows over the past 5 {M}yr},
	volume = {122},
	year = {1995}}

@article{Karato2001,
	abstract = {Strong constraints can be placed on the origin of heterogeneity of seismic wave velocities and density if the observed ratios of various parameters are compared with mineral physics predictions. They include the shear to compressional wave velocity heterogeneity ratio, R-s/p = delta log V-s/delta logV(p), the bulk sound to shear wave velocity heterogeneity ratio, R-phi /s = delta log V-phi / delta log V-s, and the density to velocity heterogeneity ratio, R-p/s = delta log rho / delta log V-s,V-p. Using mineral physics considerations, we calculate these ratios in the lower mantle corresponding to the thermal and chemical origin of velocity and density heterogeneity. Both anharmonic and. anelastic effects are considered for thermal origin. Anharmonic effects are estimated from the theoretical calculations as well as from laboratory measurements which show a marked increase in R-s/p, with pressure from similar to1.5 to similar to2.1 in the lower mantle. Such a trend is marginally consistent with seismological observations showing an increase in R-s/p with depth (from similar to1.7 to similar to3.2 in the lower mantle). However, anharmonic effect alone cannot explain inferred low R-rho /s (<0.2-0.4), and the values of R,l, predicted from anharmonic effects are systematically smaller than seismological observations. Anelastic; effects must be included to account for these geophysical observations. A new formulation of anelastic effect is developed in which the role of nonlinear temperature dependence of anelasticity is included. When anharmonic and anelastic effects are combined, thermal effects on velocity and density can account for most of the geophysical observations in Earth's lower mantle. Effects other than temperature variations (such as chemical heterogeneity) are required only in the very deep portions of the mantle (deeper than similar to 2000-2300 km). A puzzling observation is very large values of R-s/p (>2.7) and corresponding negative values of R-phi /s (and R-rho /s) in the deep lower mantle which cannot be accounted for by thermal or simple chemical heterogeneity such as the heterogeneity in the Fe/(Fe+Mg) and/or Mg/(Mg+Si) ratios. Possible causes of anomalies in this region are discussed, including the role of anisotropy and a combined effect of heterogeneity in Fe and Ca content.},
	author = {Karato, S. and Karki, B. B.},
	date = {OCT 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000171420800004},
	issn = {0148-0227},
	journal = {J. Geophys. Res.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Karato2001.pdf},
	month = {Oct},
	number = {B10},
	pages = {21771--21783},
	publication-type = {J},
	title = {Origin of lateral variation of seismic wave velocities and density in the deep mantle},
	volume = {106},
	year = {2001},
	Bdsk-File-1 = {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}}

@article{Karato1999,
	abstract = {Seismological observations indicate that the inner core of the Earth is elastically anisotropic(1). Anisotropic structures are likely to be formed by dynamic processes and therefore such observations have the potential to provide constraints on flow in the inner core and on the geodynamo itself. But in addition to the difficulties in estimating the relevant physical properties of iron under inner-core conditions(2-4), even the macroscopic processes responsible for generating seismic anisotropy in this region have yet to be determined(5-9). As a result, the geodynamic significance of seismic anisotropy in the inner core has remained unknown. Here I propose-based on geodynamic and mineral physics considerations-that flow induced by the stress due to the magnetic field, the Maxwell stress, near the inner-core boundary produces an axisymmetric fabric responsible for the observed seismic anisotropy. The resultant seismic anisotropy reflects the geometry of the magnetic field near the inner-core boundary and therefore seismological observations might provide constraints ori the geodynamo. This flow also causes non-uniform release of energy at the inner-core boundary, associated with solidification and melting which may affect the pattern of convection in the outer core.},
	author = {Karato, S.},
	date = {DEC 23},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000084482000031},
	issn = {0028-0836},
	journal = {NATURE},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Karato1999.pdf},
	month = {Dec},
	number = {6764},
	pages = {871--873},
	publication-type = {J},
	title = {Seismic anisotropy of the Earth's inner core resulting from flow induced by Maxwell stresses},
	volume = {402},
	year = {1999},
	Bdsk-File-1 = {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}}

@article{Deguen2007,
	author = {Deguen, R. and Alboussi{\`e}re, T. and Brito, D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	doi = {doi:10.1016/j.pepi.2007.05.003},
	journal = {Phys. Earth Planet. Int.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Deguen2007.pdf},
	title = {On the existence and structure of a mush at the inner core boundary of the Earth},
	year = {2007},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.pepi.2007.05.003}}

@article{ChristensenAubert2006,
	author = {Christensen, Ulrich R. and Aubert, J.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2013-09-06 09:13:55 +0000},
	doi = {10.1111/j.1365-246X.2006.03009.x},
	journal = {Geophys. J. Int.},
	local-url = {file://localhost/Users/aubert/Desktop/Scaling/scaling.pdf},
	pages = {97-114},
	title = {Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields},
	volume = {166},
	year = {2006},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2006.03009.x}}

@article{Kuang1999,
	abstract = {Kuang and Bloxham [Kuang, W., Bloxham, J., 1997a. An Earth-like numerical dynamo model. Nature 389, 371-374] found that numerical strong-field dynamo solutions in the earth's core depend strongly on viscous couplings introduced in simulation. In this paper, we discuss in detail how the force balances, the convective patterns and the magnetic field inside the core vary with the viscous couplings on the boundaries. We find that dynamo action region depends on the viscous couplings on the boundaries. When strong viscous couplings are retained in simulation, dynamo action is confined in the region near the inner core boundary (ICB) and within the tangent cylinder (the co-axial cylindrical surface across the core tangent to the inner core at the equator). Dynamo action occurs in the bulk of the fluid core when viscous couplings are neglected. The convective flow inside the tangent cylinder is very sensitive to the viscous couplings on the ICE, while the flow patterns outside the tangent cylinder do not vary qualitatively with the viscous couplings. We also find that when the viscous couplings are eliminated, the axial Lorentz torques acting on the co-axial cylindrical surfaces balance almost the fluid inertia, resulting in strong zonal flow (differential rotation) outside the tangent cylinder. However, they are strongly damped when the viscous couplings are retained. The thermal wind and the magnetic wind inside the tangent cylinder vary significantly with the viscous couplings on the ICE. With strong viscous couplings on the ICE, the magnetic wind is small compared with the thermal wind. Both winds are unidirectional, resulting in a zonal flow increasing with the depth and a super-rotating inner core. Without viscous coupling, both winds are comparable, Their directions vary with depth and with time, resulting in a zonal flow varying non-monotonically with the depth and an oscillating inner core. (C) 1999 Elsevier Science B.V. All rights reserved.},
	author = {Kuang, W. J.},
	date = {DEC},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000084072600006},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	month = {Dec},
	number = {1-4},
	pages = {65--79},
	publication-type = {J},
	title = {Force balances and convective state in the {E}arth's core},
	volume = {116},
	year = {1999}}

@incollection{Souriau2007,
	author = {Souriau, A.},
	booktitle = {Treatise on Geophysics. 1- Seismology and Structure of the Earth},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2008-01-17 15:23:11 +0100},
	doi = {doi:10.1016/B978-044452748-6.00023-7},
	editor = {Dziewonski, A. and Romanowicz, B.},
	number = {1},
	pages = {655-693},
	publisher = {Elsevier},
	title = {The {E}arth's Cores},
	volume = {11},
	year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/B978-044452748-6.00023-7}}

@article{Song2000,
	abstract = {Observational evidence for differential rotation of the inner core has recently been reported from time-dependent travel times of the seismic inner core phase, PKP(DF). These analyses are hindered by potential biases from the mantle heterogeneity and systematic earthquake location errors, which have raised doubts about the reality of the inferred differential rotation. Here we report time-dependent PKP(DF)-PKP(BC) differential travel times of a total of 611 measurements obtained from 92 earthquakes in the South Sandwich Islands (SSI) over the past nearly half a century recorded at the College, Alaska station (COL) and Alaska Seismic Network (ASN). The events are relocated using the joint hypercenter determination (JHD) technique [Dewey, 1971]. Travel time residuals at COL from SSI earthquakes over a period of 45 years and at three additional stations from SSI earthquakes over periods of about 22 years show steady increases with time; the temporal trends are demonstrated to be statistically very significant. With dense samples of the pathway at different time periods, we use a joint inversion technique that allows us to separate the time-dependent inner core structure from the time-independent mantle biases. Surprisingly, the inner core rotation seems resolvable even from digital data observed at ASN in the 1990s (spanning over 8 years) alone in such a joint inversion. The results provide strong support for a differential inner core rotation. The inferred rotation rate ranges from 0.3 degrees to 1.1 degrees per year faster than the mantle when we take into account the uncertainty in the tilt of the anisotropy axis of the patch, of the inner core that was sampled. A westward inner core rotation can be ruled out.},
	author = {Song, X. D.},
	date = {APR 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000086437500009},
	issn = {0148-0227},
	journal = {J. Geophys. Res.},
	month = {Apr},
	number = {B4},
	pages = {7931--7943},
	publication-type = {J},
	title = {Joint inversion for inner core rotation, inner core anisotropy, and mantle heterogeneity},
	volume = {105},
	year = {2000}}

@article{Aubert2005,
	annote = {In press},
	author = {Aubert, J.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {J. Fluid. Mech.},
	pages = {53-67},
	title = {Steady zonal flows in spherical shell dynamos},
	volume = {542},
	year = {2005}}

@article{Olson1999PC,
	author = {Olson, P. and Aurnou, J.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Nature},
	pages = {170-173},
	title = {A polar vortex in the {E}arth's core},
	volume = {402},
	year = {1999}}

@article{Pais2000,
	author = {Pais, A. and Hulot, G.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Int.},
	optpages = {291-316},
	optvolume = {118},
	pages = {291-316},
	title = {Length of day decade variations, torsional oscillations and inner core superrotation: evidence from recovered core surface zonal flows},
	volume = {118},
	year = {2000}}

@article{Sumita2000,
	author = {Sumita, I. and Olson, P.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Int.},
	number = {2},
	pages = {153-170},
	title = {Laboratory experiments on high {R}ayleigh number thermal convection in a rapidly rotating hemispherical shell},
	volume = {117},
	year = {2000}}

@article{Takahashi2005,
	abstract = {We investigate convection-driven dynamos in a rotating spherical shell with the Rayleigh number Ra up to about 53 times the critical value Ra-C, emphasizing Rayleigh number dependence of the thermal convection and the magnetic field generated by dynamo action. The Rayleigh numbers used in calculations are chosen so as to be in a range which allows us to study the sequence of bifurcation. In the low-Ra-dynamo regime, the flow structure is characterized by columnar convection cells, which mainly generate the magnetic field that is predominantly dipolar. Force balance is essentially in a geostrophic state. Both the magnetic energy and the kinetic energy increase with increase in Ra. In the moderate-Ra-dynamo regime, convective motions appear inside the tangent cylinder (TC), where the azimuthal magnetic field is generated through the so-called omega effect. However, the magnetic energy shows saturation due to relatively inefficient magnetic field generation. In the high-Ra-dynamo regime, dominance of convection inside the TC is remarkable. The advection processes play important roles both in force balance and in magnetic field generation. The magnetic field is generated very inefficiently, leading to the reduced magnetic energy in spite of higher kinetic energy. These three dynamo regimes exhibit distinctive differences in the process of generating magnetic field and characteristic dissipation scales. (c) 2005 American Institute of Physics.},
	author = {Takahashi, F. and Matsushima, M.},
	date = {JUL},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN 076601},
	isi = {ISI:000230633700042},
	issn = {1070-6631},
	journal = {Phys. Fluids},
	month = {Jul},
	number = {7},
	pages = {076601},
	publication-type = {J},
	title = {Dynamo action in a rotating spherical shell at high Rayleigh numbers},
	volume = {17},
	year = {2005}}

@article{Yu2005,
	abstract = {[1] We constrain seismic velocity structure in the Earth's outer core by analyzing differential travel times, waveforms, and amplitude ratios of several pairs of core phases. We use differential travel times and waveforms of PKPbc-PKIKP at 144degrees- 148degrees, PKiKP-PKIKP at 120degrees - 141degrees, PKiKP-PKPBdiff at the PKP caustics distance range (141degrees - 145degrees), and differential travel times and amplitude ratios of PKPab-PKPbc at 146degrees - 159degrees. To avoid the influence of the inner core anisotropy in velocity, we only use the PKiKP-PKIKP and the PKPbc-PKIKP observations whose PKIKP phases sample the inner core along the equatorial paths (paths with their ray angles being larger than 35degrees from the Earth's rotation axis). These observations show the following characteristics: (1) both the observed PKPbc-PKIKP and PKiKP-PKIKP differential travel times show a distinct "east-west'' hemispheric pattern. PKIKP phases arrive about 0.7 s earlier for those sampling the "eastern'' hemisphere (40degreesE - 180degreesE) than those sampling the "western'' hemisphere (180degreesW - 40degreesE); (2) the observed differential PKiKP-PKPBdiff travel time residuals also exhibit a hemispheric difference. PKiKP-PKPBdiff differential travel times are about 0.9 s larger for those sampling the western hemisphere than those sampling the eastern hemisphere; and (3) both the observed PKPab-PKPbc differential travel times and PKPbc/PKPab amplitude ratios show scatter. Overall, these observations can be best explained by two one-dimensional P velocity models, one for each hemisphere, at the bottom of the outer core. The seismic data sampling the eastern hemisphere can be explained by PREM at the bottom of the outer core, while those sampling the western hemisphere can be explained by a lower velocity gradient at the bottom of the outer core, which has reduced velocities relative to PREM linearly increasing from 0% at 200 km above the inner core boundary (ICB) to -0.35% at the ICB. Different velocity gradients at the bottom of the outer core indicate that there may exist a compositional difference and/or a large-scale temperature difference there and that inner core formation processes may be different between the two hemispheres. Different inner core formation processes may produce different geometric inclusions of melt in the top of the inner core, and thus may provide an explanation to the hemispheric variation of seismic velocity and attenuation in the top of the inner core. The seismic data also suggest that the variation of seismic velocity in the tangential cylinder of the outer core, if it exists, is less than 0.1%. We use a compressional wave tomographic model to study the travel time delays caused by the seismic heterogeneities in the mantle. The tomographic model is unable to explain the scatter of the travel time data, suggesting the existence of unknown strong small-scale seismic heterogeneities in the mantle.},
	author = {Yu, W. C. and Wen, L. X. and Niu, F. L.},
	date = {FEB 24},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN B02302},
	isi = {ISI:000227527600002},
	issn = {0148-0227},
	journal = {J. Geophys. Res.},
	month = {Feb},
	number = {B2},
	pages = {B02302},
	publication-type = {J},
	title = {Seismic velocity structure in the {E}arth's outer core},
	volume = {110},
	year = {2005}}

@article{Dumberry2006,
	author = {Dumberry, M. and Bloxham, J.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. J. Int.},
	pages = {32--46},
	title = {Azimuthal flows in the Earth's core and changes in length of day at millennial time scales},
	volume = {165},
	year = {2006}}

@inproceedings{Laske2003,
	address = {Washington D.C.},
	author = {Laske, G. and Masters, G.},
	booktitle = {\textit{Earth's Core: Dynamics, Structure, Rotation}},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	editor = {Dehant, V. and Creager, K. and Zatman, S. and Karato, S.I.},
	publisher = {AGU monograph},
	title = {The {E}arth's free oscillations and differential rotation of the inner core},
	volume = {31},
	year = {2003}}

@article{Cormier2007,
	author = {Cormier, V.F.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2008-01-17 15:37:36 +0100},
	journal = {Earth Planet. Sci. Lett.},
	pages = {442-453},
	publication-type = {J},
	title = {Texture of the uppermost inner core from forward and back scattered seismic waves},
	volume = {258},
	year = {2007}}

@article{Amit2006,
	author = {Amit, H. and Olson, P.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {120-139, doi: 10.1016/J.pepi.2005.10.006},
	title = {Time average and time dependent parts of core flow},
	volume = {155},
	year = {2006}}

@article{Kutzner2002,
	author = {Kutzner, C. and Christensen, U.R.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {29-45},
	title = {From stable dipolar to reversing numerical dynamos},
	volume = {131},
	year = {2002}}

@article{Jackson2000,
	author = {Jackson, A. and Jonkers, A. R. T. and Walker, M. R.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2013-05-23 13:39:51 +0000},
	journal = {Phil. Trans. Roy. Soc. A},
	pages = {957-990},
	title = {Four centuries of geomagnetic secular variation from historical records},
	volume = {358},
	year = {2000}}

@article{Lister1995,
	abstract = {The evolution of the Earth's outer core is calculated theoretically by assuming that the fluctuations about a vigorously convecting, well-mixed, isentropic and hydrostatic mean state are small. The global energy equation describes the evolution of the mean state, but contains no information about the division between convective and diffusive transport of heat or composition within the core itself. As the diffusive transport of either heat or composition makes no contribution to the dynamo, estimates of the dynamo power must be derived by explicit consideration oft he correlation of small density fluctuations with the large convective velocities. By such consideration, the dynamo power is shown to be equal to the integrated thermal and compositional buoyancy flux, which is calculated from the requirement that the mean state remain isentropic and well mixed. The resulting new and simple expression for the dynamo efficiency has an easily understood physical interpretation in terms of Carnot-style redistribution of heat and mass in the core, though it takes full account of both thermal and compositional effects and the evolution of the mean state. Once the equation of state and thermodynamic parameters are given, the dynamo power can be evaluated readily and explicitly. Analytic solutions based on a simple example equation of state show that the relative importance of thermal and compositional convection depends on the size of the inner core and the amount by which the heat flux across the core-mantle boundary (CMB) exceeds that which can be conducted up the core adiabat. Thermal convection was dominant in the early Earth when the inner core was small and the Earth was probably cooling rapidly. Estimates of the present-day heat loss across the CMB suggest that thermal convection now contributes about 20% of the dynamo power and compositional convection about 80%. As a result of the release of latent heat at the inner-core boundary, thermal convection can make a net positive contribution to the dynamo power even if the heat flux at the CMB is subadiabatic.},
	author = {Lister, J. R. and Buffett, B. A.},
	date = {SEP},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1995RU59600003},
	issn = {0031-9201},
	journal = {Phys. Earth Planet. Int.},
	month = {Sep},
	number = {1-3},
	pages = {17--30},
	publication-type = {J},
	title = {THE STRENGTH AND EFFICIENCY OF THERMAL AND COMPOSITIONAL CONVECTION IN THE GEODYNAMO},
	volume = {91},
	year = {1995}}

@article{Christensen2006,
	abstract = {Mercury has a global magnetic field of internal origin and it is thought that a dynamo operating in the fluid part of Mercury's large iron core is the most probable cause. However, the low intensity of Mercury's magnetic field-about 1% the strength of the Earth's field-cannot be reconciled with an Earth-like dynamo. With the common assumption that Coriolis and Lorentz forces balance in planetary dynamos(1), a field thirty times stronger is expected. Here I present a numerical model of a dynamo driven by thermo-compositional convection associated with inner core solidification. The thermal gradient at the core mantle boundary is subadiabatic(2,3), and hence the outer region of the liquid core is stably stratified with the dynamo operating only at depth, where a strong field is generated. Because of the planet's slow rotation the resulting magnetic field is dominated by small-scale components that fluctuate rapidly with time. The dynamo field diffuses through the stable conducting region, where rapidly varying parts are strongly attenuated by the skin effect, while the slowly varying dipole and quadrupole components pass to some degree. The model explains the observed structure and strength of Mercury's surface magnetic field and makes predictions that are testable with space missions both presently flying and planned.},
	af = {Christensen, Ulrich R.},
	author = {Christensen, U. R.},
	date = {DEC 21},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000242971100052},
	issn = {0028-0836},
	journal = {Nature},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Christensen2006.pdf},
	month = {Dec},
	number = {7122},
	pages = {1056--1058},
	publication-type = {J},
	title = {A deep dynamo generating {M}ercury's magnetic field},
	volume = {444},
	year = {2006},
	Bdsk-File-1 = {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}}

@article{Gibbons2000,
	author = {Gibbons, S. and Gubbins, D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. J. Int.},
	pages = {631-642},
	title = {Convection in the {E}arth's core driven by lateral variation in the core-mantle boundary heat flux},
	volume = {142},
	year = {2000}}

@article{ZhangGubbins1992,
	author = {Zhang, K. and Gubbins, D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. J. Int.},
	pages = {247-255},
	title = {On convection in the {E}arth's core driven by lateral temperature variations in the lower mantle},
	volume = {108},
	year = {1992}}

@article{Morelli1986,
	abstract = {Travel-time residuals of the PKIKP phase observed between 170$\,^{\circ}$ and 180$\,^{\circ}$ show an axisymmetric pattern of degree 2 with an amplitude of about 2 seconds. The effect at shorter distances is much less pronounced and the entire data set cannot be explained by a physically realistic radial distribution of (isotropic) heterogeneity. We propose that, in addition to the general (isotropic) heterogeneity, the inner core is anisotropic with cylindrical symmetry aligned with the earth's rotation axis. Average P-velocity along this axis is about 1 percent faster than the equatorial plane.},
	adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System},
	adsurl = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986GeoRL..13.1545M&db_key=PHY},
	author = {{Morelli}, A. and {Dziewonski}, A.~M. and {Woodhouse}, J.~H.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. Res. Let.},
	pages = {1545-1548},
	title = {Anisotropy of the inner core inferred from {PKIKP} travel times},
	volume = {13},
	year = {1986}}

@article{Olson2002,
	author = {Olson, P. and Christensen, U.R.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. J. Int.},
	pages = {809-823},
	title = {The time averaged magnetic field in numerical dynamos with non-uniform boundary heat flow},
	volume = {151},
	year = {2002}}

@article{AmitAubert2007,
	author = {Amit, H. and Aubert, J. and Hulot, G. and Olson, P.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Earth Plan. Sci. Let.},
	title = {Thermal wind at the top of the Core, submitted},
	year = {2007}}

@article{Aubert2007,
	author = {Aubert, J. and Amit, H. and Hulot, G.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2008-02-22 17:06:38 +0100},
	doi = {10.1016/S0012-821X(04)00102-5},
	journal = {Phys. Earth Planet. Int.},
	pages = {143-156},
	title = {Detecting thermal boundary control in surface flows from numerical dynamos},
	volume = {160},
	year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0012-821X(04)00102-5}}

@article{Aurnou2003,
	author = {Aurnou, J. and Andreadis, S. and Zhu, L. and Olson, P.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Earth Plan. Sci. Let.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Aurnou2003.pdf},
	pages = {119-134},
	title = {Experiments on convection in {E}arth's core tangent cylinder},
	volume = {212},
	year = {2003},
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@book{Davies1999,
	address = {Cambridge UK},
	author = {Davies, G.F.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	publisher = {Cambridge University Press},
	title = {Dynamic Earth},
	year = {1999}}

@incollection{Masters2000,
	address = {Washington D.C.},
	author = {Masters, G. and Laske, G. and Bolton, H. and Dziewonski, A.},
	booktitle = {Earth's Deep Interior},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	editor = {Karato, S. and Forte, A.M. and Liebermann, R. C. and Masters G. and Stixrude, L.},
	publisher = {AGU Monograph},
	title = {The Relative Behavior of Shear Velocity, Bulk Sound Speed, and Compressional Velocity in the Mantle: Implications for Chemical and Thermal Structure},
	volume = {117},
	year = {2000}}

@article{Tanaka1997,
	abstract = {We have investigated the relationship between heterogeneity and anisotropy in the inner core. Heterogeneity was examined using PKP(DF) and PKP(BC) phases traveling in the east-west direction (E-W paths). The geographical pattern of the PKP differential travel time (BC-DF) residuals was found to be a manifestation of degree one heterogeneity in the outermost 100 to 500 km of the inner core. Spherical harmonics analysis showed that the P velocities in the inner core are fast in the region from 43 degrees E to 177 degrees E (the quasi-eastern hemisphere) with a peak value of +0.29+/-0.15% and slow in the region from 183 degrees W to 43 degrees E (the quasi-western hemisphere) with a peak value of -0.66+/-0.20%. Regional variation of anisotropy in the inner core was examined using PKP phases traveling nearly parallel to the Earth's spin axis (polar paths). The averages of BC-DF time residuals were 2.4+/-0.8 s in the quasi-western hemisphere and 0.5+/-0.4 s in the quasi-eastern hemisphere. We found that the inner core anisotropy predominates only in the quasi-western hemisphere in which the 0.66% slow P velocity is observed fdr the E-W paths. Geophysical implications of the degree one pattern in the inner core were briefly discussed. We propose that the hemispherical structure of the inner core reflects ancient core dynamics immediately after core formation.},
	author = {Tanaka, S. and Hamaguchi, H.},
	date = {FEB 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1997WH69400017},
	journal = {J. Geophys. Res.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Tanaka1997.pdf},
	month = {Feb},
	number = {B2},
	pages = {2925--2938},
	publication-type = {J},
	title = {Degree one heterogeneity and hemispherical variation of anisotropy in the inner core from {PKP(BC)-PKP(DF)} times},
	volume = {102},
	year = {1997},
	Bdsk-File-1 = {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}}

@article{Wen2002,
	abstract = {We collect a global data set of PKIKP and PKiKP phases recorded by the Global Seismic Network and many regional seismic arrays to study seismic structure in the top of the Earth's inner core. The PKIKP and PKiKP observations show different characteristics between those sampling the 'eastern' hemisphere (40degreesE-180degreesE) of the inner core and those sampling the 'western' hemisphere (180degreesW-40degreesE). PKIKP phases (1) arrive about 0.4 s earlier than the theoretical arrivals based on Preliminary Reference Earth Model (PREM) for those sampling the eastern hemisphere of the inner core and about 0.3 s later for those sampling the western hemisphere (131degrees-141degrees); (2) bifurcate at smaller epicentral distances for those sampling the eastern hemisphere, compared to those sampling the western hemisphere; and (3) have smaller amplitudes for those sampling the eastern hemisphere. Waveform modeling of these observations suggests two different types of models for the two 'hemispheres' of the top of the inner core, with a model in the eastern hemisphere having a P velocity increase of 0.765 km/s across the inner core boundary, a small radial velocity gradient of 0.000055 (km/s)/ km, and an average Q value of 250, and a model in the western hemisphere with a P velocity increase of 0.633 km/s across the inner core boundary, a radial velocity gradient of 0.000533 (km/s)/ km and an average Q value of 600. The hemispherical difference of seismic structures may be explained by different geometric inclusions of melt and/or different alignments of iron crystals with anisotropic properties in both velocity and attenuation. We speculate that this large-scale pattern of seismic heterogeneities may be caused by a large-scale heat flow anomaly at the bottom of the outer core and/or different vigorousness of convection in the top of the inner core between the two hemispheres.},
	af = {Wen, Lianxing},
	author = {Wen, L. X. and Niu, F.L.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {J. Geophys. Res.},
	pages = {2273},
	publication-type = {J},
	title = {Seismic velocity and attenuation structures in the top of the Earth's inner core},
	volume = {107},
	year = {2002}}

@article{Song1996,
	author = {Song, X. D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {J. Geophys. Res.},
	pages = {16089--16097},
	publication-type = {J},
	title = {Anisotropy in central part of inner core},
	volume = {101},
	year = {1996}}

@article{McSweeney1997,
	author = {McSweeney, T. and Creager, K.C. and Merrill, R.T.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Inter.},
	pages = {131--156},
	publication-type = {J},
	title = {Depth extent of inner-core seismic anisotropy and implications for geomagnetism},
	volume = {101},
	year = {1997}}

@article{Vinnik1994,
	author = {Vinnik, L. and Romanowiz, B. and Berger, L.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Geophys. Res. Lett.},
	pages = {1671--1674},
	title = {Anisotropy in the center of the inner core},
	volume = {21},
	year = {1994}}

@article{POUPINET1983,
	abstract = {The core of the Earth is usually described by spherically-symmetrical velocity models. The core is made of two main spherical layers: the fluid outer core with a radius close to 3,480 km and a P-velocity increasing with depth from 8 km s-1 to 10.3 km s-1, and the solid inner core with a radius of 1,220 km and a P-velocity close to 11 km s-1 (refs 1, 2). Station residuals of the seismic core phase PKIKP have been computed for 400 seismological observatories worldwide using 5 yr of the International Seismological Centre (ISC) Bulletins. PKIKP travel times can be corrected for upper mantle propagation by subtracting P delays; thus PKIKP-P residuals are a measurement of the average vertical travel times in the lower mantle and in the core of the Earth beneath seismic stations. A spherical harmonic development of PKIKP-P delays up to degree 4 explains 58% of the variance in the data. PKIKP-P exhibit a latitudinal dependence: polar stations tend to be faster than equatorial stations. We show here that this pattern may reflect a departure from spherical symmetry in the P-velocity distribution in the vicinity of the inner core boundary of the Earth.},
	author = {Poupinet, G. and Pillet, R. and Souriau, A.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1983RG37100033},
	issn = {0028-0836},
	journal = {Nature},
	number = {5931},
	pages = {204--206},
	publication-type = {J},
	title = {POSSIBLE HETEROGENEITY OF THE EARTHS CORE DEDUCED FROM PKIKP TRAVEL-TIMES},
	volume = {305},
	year = {1983}}

@article{Garnero2000,
	author = {Garnero, E.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Annu. Rev. Earth Planet. Sci.},
	pages = {509--537},
	publication-type = {J},
	title = {Heterogeneity of the lowermost mantle},
	volume = {28},
	year = {2000}}

@article{Dzie1981,
	author = {Dziewonski, A. and Anderson, D.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	journal = {Phys. Earth Planet. Int.},
	pages = {297-356},
	title = {Preliminary Reference {E}arth Model {PREM}},
	volume = {25},
	year = {1981}}

@article{Torsvik2006,
	abstract = {There is a clear correlation between downward projected large igneous province (LIP) eruption sites of the past 200 Myr and the margins of the large low-velocity provinces (LLVPs) at the base of the mantle. We established this correlation by using palaeomagnetic as well as fixed and moving hotspot reference frames. Our finding indicates that the majority of the LIPs have been generated by plumes that rose from the D' zone at the edges of the LLVPs. Most LIP eruption sites project radially downwards to the core-mantle boundary (CMB) within +/- 10 degrees of the 1 per cent slow shear wave velocity contour in the SMEAN tomographic model. Steep shear wave velocity gradients have been mapped near the CMB along much of the lengths of the LLVP margins close to that contour which marks a faster/slower boundary (FSB) within the D' zone. The observation that eruption sites of LIPs as old as 200 Myr can be linked to this prominent present day seismic structure shows that the FSBs of the two LLVPs have occupied their current positions for at least as long and that the process that leads to the generation of deep-seated plumes has been localized on the FSBs at the margins of the African and Pacific LLVPs for the same interval. The persistence of the LLVPs over 200 Myr is consistent with independent evidence that they are compositionally distinct and are not just simply hotter than the material making up the rest of the D' zone.},
	af = {Torsvik, Trond H. Smethurst, Mark A. Burke, Kevin Steinberger, Bernhard},
	author = {Torsvik, T. H. and Smethurst, M. A. and Burke, K. and Steinberger, B.},
	date = {DEC},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000242661600032},
	issn = {0956-540X},
	journal = {Geophys. J. Int.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Torsvik2006.pdf},
	month = {Dec},
	number = {3},
	pages = {1447--1460},
	publication-type = {J},
	title = {Large igneous provinces generated from the margins of the large low-velocity provinces in the deep mantle},
	volume = {167},
	year = {2006},
	Bdsk-File-1 = {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}}

@article{Glatzmaier:1996bs,
	abstract = {Three-dimensional numerical simulations of the geodynamo suggest that a super-rotation of Earth's solid inner core relative to the mantle is maintained by magnetic coupling between the inner core and an eastward thermal wind in the fluid outer core. This mechanism, which is analogous to a synchronous motor, also plays a fundamental role in the generation oi Earth's magnetic field.},
	author = {Glatzmaier, G. A. and Roberts, P. H.},
	date = {DEC 13},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2009-09-15 15:26:06 +0200},
	isi = {ISI:A1996VY20000037},
	journal = {Science},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Glatzmaier1996.pdf},
	month = {Dec},
	number = {5294},
	pages = {1887--1891},
	publication-type = {J},
	title = {Rotation and magnetism of earth's inner core},
	volume = {274},
	year = {1996},
	Bdsk-File-1 = {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}}

@article{Dumberry2007,
	abstract = {We analyse the secular variation captured by the archaeomagnetic field model CALS7K.2 in an effort to determine episodes of
eastward and westward motions of Earth's magnetic field at the core--mantle boundary (CMB) over the past 3000 yr. The direction,
amplitude and geographical distribution of these motions are described. We find that the clearest azimuthal motions are observed at
mid- to high latitudes in the Northern hemisphere, where both eastward and westward motions occur. These azimuthal motions
correspond to displacements and distortions of the two main, quasi-stationary, high-latitude magnetic flux patches. Similar motions
are not observed in the Southern hemisphere, although this may be a consequence of the poorer data coverage there. The globally
averaged drift for the past 1000 yr has been westward since 1400 AD, but eastward between 1000 AD and 1400 AD. In the broad
region of the CMB under Europe, the times of transition in the direction of the mean azimuthal motion coincide with the times at
which ``archaeomagnetic jerks'' have been reported. Our results suggest that these are caused by a relatively rapid (<100 yr) change
in the direction of the underlying azimuthal flow near the core surface. We find indications that equatorial westward motions of
field features at the CMB, similar to those observed during historical times, may have been present for much of the past 3000 yr.
When observed, these low-latitude motions are most prominent in the Atlantic hemisphere, which we interpret as a signature of
core--mantle thermal coupling.},
	author = {Dumberry, M. and Finlay, C.},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	doi = {10.1016/j.epsl.2006.11.026},
	journal = {Earth Plan. Sci. Let.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Dumberry2007.pdf},
	pages = {146-157},
	title = {Eastward and westward drift of the Earth's magnetic field for the last three millennia},
	volume = {254},
	year = {2007},
	Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxAsLi4vLi4vLi4vRHJvcGJveC9wcy1lcHMtcGRmL0R1bWJlcnJ5MjAwNy5wZGZPEQFyAAAAAAFyAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAAAAAAAAQkQAAf////8QRHVtYmVycnkyMDA3LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA/////wAAAABQREYgQ0FSTwADAAMAAAogY3UAAAAAAAAAAAAAAAAACnBzLWVwcy1wZGYAAgA6LzpVc2VyczphdWJlcnQ6RGVza3RvcDpEcm9wYm94OnBzLWVwcy1wZGY6RHVtYmVycnkyMDA3LnBkZgAOACIAEABEAHUAbQBiAGUAcgByAHkAMgAwADAANwAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAOFVzZXJzL2F1YmVydC9EZXNrdG9wL0Ryb3Bib3gvcHMtZXBzLXBkZi9EdW1iZXJyeTIwMDcucGRmABMAAS8AABUAAgAN//8AAAAIAA0AGgAkAFMAAAAAAAACAQAAAAAAAAAFAAAAAAAAAAAAAAAAAAAByQ==},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.epsl.2006.11.026}}

@article{Aurnou:1996th,
	abstract = {A mechanism is proposed to explain the seismologically-inferred prograde rotation of the Earth's solid inner core in terms of the structure of convection in the fluid outer core. Numerical calculations of convection and dynamo action in the outer core exhibit excess temperatures inside the tangent cylinder surrounding the inner core. We show that this temperature difference generates a prograde thermal wind and a strong azimuthal magnetic field inside the tangent cylinder. Electromagnetic torques on the inner core derived from induced azimuthal magnetic fields and the ambient poloidal field equilibrate when the inner core angular velocity lags the nearby tangent cylinder fluid angular velocity by approximately 14%. The inferred prograde rotation of the inner core (1.1-3 degrees/year relative to the mantle) can be produced by a very small (similar or equal to 0.001 K) temperature anomaly within the tangent cylinder and indicates strong toroidal magnetic fields with peak intensities of 24- 66 mT in that region of the core.},
	author = {Aurnou, J. M. and Brito, D. and Olson, P. L.},
	date = {NOV 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2010-05-31 15:11:48 +0200},
	isi = {ISI:A1996VU34600030},
	journal = {Geophys. Res. Lett.},
	month = {Nov},
	number = {23},
	pages = {3401--3404},
	publication-type = {J},
	title = {Mechanics of inner core super-rotation},
	volume = {23},
	year = {1996}}

@article{Brito:2002ij,
	abstract = {We present ultrasonic measurements of elastic anisotropy in gallium undergoing directional solidification in the presence of imposed thermal gradients, rotation, convection, turbulence, and magnetic fields. Simultaneous in situ measurements of temperature and compressional wave speed are used to track the crystallization front during solidification. We find that individual solidified gallium samples are always polycrystalline and elastically anisotropic, with grains elongated in the solidification direction. The measured compressional wave anisotropy in individual solid samples ranges from 20 to 80% of the single crystal values, depending on experimental conditions. We also find the amount of elastic anisotropy varies with position in an individual sample. Based on ensemble averages from multiple experiments made under similar environmental conditions, we find the direction of elastic anisotropy in the solid is sensitive to the thermal: gradient direction, while the amount of anisotropy is most sensitive to the presence or absence of initial nucleation in the melt. Experiments that show average anisotropy have the ultrasonically fast axis aligned with gravity and the thermal gradient. Strongly anisotropic solids result when nucleation grains are present in the initial melt, whereas smaller or zero average anisotropy results when nucleation grains are initially absent. Other externally imposed factors we have examined, such as turbulence and magnetic fields, have either no measurable influence or tend to reduce the amount of anisotropy of the solid. Our results suggest that during crystallization of Earth's inner core, the orientation of average anisotropy in the newly formed solid is controlled primarily by radial solidification, while the amount of anisotropy may be influenced by pre-existing inner core texture. (C) 2002 Elsevier Science B.V All rights reserved.},
	author = {Brito, D. and Elbert, D. and Olson, P.},
	date = {FEB 25},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000174302700008},
	journal = {PHYSICS OF THE EARTH AND PLANETARY INTERIORS},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Brito2002.pdf},
	month = {Feb},
	number = {3-4},
	pages = {325--346},
	publication-type = {J},
	title = {Experimental crystallization of gallium: ultrasonic measurements of elastic anisotropy and implications for the inner core},
	volume = {129},
	year = {2002},
	Bdsk-File-1 = {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}}

@article{Aurnou:2000sp,
	abstract = {We compute the polar rotation of the Earth's inner core in response to the combined effects of electromagnetic, gravitational and mechanical torques. We obtain electromagnetic torques between 10(18) and 10(20) Nm, compared to gravitational torques between 10(19) and 10(21) Nm estimated by Xu et al. [Xu, S., Crossley D., Szeto, A.M.K., 1999. Variations in length of day and inner core differential rotation from gravitational coupling. Phys. Earth Planet. Inter., 116, 95-110] and Buffett [Buffett, B.A., 1996b. A mechanism for decade fluctuations in the length of day. Geophys. Res. Lett., 23, 3803-3806.], respectively. We obtain mechanical torques on the order of 10(15) Nm. Gravitationally dominated cases produce inner core oscillations with periods between 1 and 10 years. In electromagnetically dominated cases, the inner core rotates close to the imposed rotation rate of the outer core fluid. Modulations in the rotation rate are produced as the inner core passes through successive gravitational wells. These modulations occur over roughly 90 year timescales for outer core flow rates of 1 degrees/year. When the electromagnetic torques are only marginally stronger than the gravitational torques, the inner core slowly rotates prograde by 90 degrees relative to the mantle, escaping a gravitational well in roughly 100 years, then falls into the next gravitational well, rotating through 90 degrees in just 4 years. Finite inner core viscosity is modeled using a relaxation time for the inner core topography. With relaxation, the gravitational torque reduces but does not eliminate the anomalous inner core rotation. Because of the short timescales of many of the irregularities in inner core rotation, it may be possible to observe them in presently-available seismic data. (C) 2000 Elsevier Science B.V. All rights reserved.},
	author = {Aurnou, J. and Olson, P.},
	date = {JAN},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000084326400010},
	journal = {PHYSICS OF THE EARTH AND PLANETARY INTERIORS},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Aurnou2000.pdf},
	month = {Jan},
	number = {1-4},
	pages = {111--121},
	publication-type = {J},
	title = {Control of inner core rotation by electromagnetic, gravitational and mechanical torques},
	volume = {117},
	year = {2000},
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@article{Aurnou:1998hc,
	abstract = {We use numerical calculations of magnetic induction by axisymmetric motions in a spherical Shell of conducting fluid to investigate the relationship between the Earth's toroidal magnetic field and the time-dependent anomalous rotation of the solid inner core. We compute the induced toroidal magnetic field and inner core rotation maintained by the interaction of time-independent, axisymmetric outer core fluid flow with models of the poloidal magnetic field. Three possible models of-the azimuthal flow in the outer core are investigated: two thermal wind flows inside the tangent cylinder (predicted by some numerical models of the geodynamo) and a columnar flow outside the inner core tangent cylinder inferred from the geomagnetic westward drift. Results indicate that electromagnetic torques tightly couple the inner core rotation to the fluid motion. Electromagnetic spin-up of the inner core occurs through damped torsional oscillations with periodicity near 4 years depending on the strength of the poloidal magnetic field. In steady state the thermal winds inside the tangent cylinder generate a peak toroidal field of 25 mT accompanying a prograde inner core rotation rate of 1 degrees/yr. In contrast, the columnar westward drift model generates toroidal field with peak intensity near 4 mT and a small, retrograde anomalous inner core rotation of -0.013 degrees/yr. The weak retrograde motion of the inner core produced by electromagnetic coupling to the westward drift cannot explain the seismically inferred prograde anomalous rotation.},
	author = {Aurnou, J. and Brito, D. and Olson, P.},
	date = {MAY 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000073536500010},
	journal = {JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Aurnou1998.pdf},
	month = {May},
	number = {B5},
	pages = {9721--9738},
	publication-type = {J},
	title = {Anomalous rotation of the inner core and the toroidal magnetic field},
	volume = {103},
	year = {1998},
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@article{Buffett2000,
	abstract = {The effects of gravitational coupling between the inner core and the mantle are incorporated into numerical simulations of the geodynamo. Differential rotation between the inner core and the mantle is permitted by allowing the inner core to viscously deform. Calculations with a deformation time scale of 1 yr, corresponding to an average viscosity of 5 x 10(16) Pa s, predict eastward rotation of the inner core with a mean rate of 0.02 deg/yr relative to the mantle. Fluctuations about this mean rate of rotation occur with a typical period of 75 yr and have sufficient amplitude to explain observed changes in length of day at decadal periods. When gravitational coupling is removed, or viscous coupling is added by imposing no-slip boundary conditions, the mean inner core rotation rate is almost an order of magnitude greater.},
	author = {Buffett, B. A. and Glatzmaier, G. A.},
	date = {OCT 1},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000089711900025},
	journal = {Geophys. Res. Let.},
	month = {Oct},
	number = {19},
	pages = {3125--3128},
	publication-type = {J},
	title = {Gravitational braking of inner-core rotation in geodynamo simulations},
	volume = {27},
	year = {2000}}

@article{Creager:1999kl,
	abstract = {I analyze nearly 2000 handpicked differential times of core-penetrating compressional waves to image lateral variations in the anisotropic structure of the solid inner core. The inner core is strongly anisotropic (2-4% on average) throughout most of the western hemisphere from near the surface to its center and into the lowermost several hundred kilometers of the eastern hemisphere. In contrast, the outer half of the eastern hemisphere from 40 degrees to 160 degrees E (the quasi-eastern hemisphere) exhibits very weak anisotropy with an average amplitude of only 0.5%. The symmetry direction is the fast direction and lies on or near the spin axis. Voigt's isotropic average of compressional wavespeeds is the same in the eastern and western hemispheres, suggesting that there are no large-scale lateral variations in the chemistry or temperature in the inner core. Instead, I suggest that the variations seen in anisotropy represent lateral variations in the degree of crystal alignment. The inner core appears to be organized in a very simple way with 60-90% of its volume containingwell-aligned crystals and the remaining part (uppermost 400-700 km of the quasi-eastern hemisphere) containing less well aligned crystals. A mechanism consistent with axi-symmetry and large-scale variability of anisotropy is discussed. It incorporates the inference that the inner core is rotating faster than the mantle and that gravitational coupling to the mantle forces large-scale inner core deformation, inducing flow with strain rates as high as 10(-14) s(-1). A positive feedback mechanism, related to anisotropic viscosity, may reinforce lateral variations in the strength of anisotropy.},
	author = {Creager, K. C.},
	date = {OCT 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000083019100018},
	journal = {JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH},
	month = {Oct},
	number = {B10},
	pages = {23127--23139},
	publication-type = {J},
	title = {Large-scale variations in inner core anisotropy},
	volume = {104},
	year = {1999}}

@article{Creager1992,
	abstract = {The difference between the travel times of compressional waves that turn in the Earth's liquid outer core (PKP-BC) and those that run in the solid inner core (PKIKP-DF) is primarily sensitive to structure near the inner-core boundary. Such differential travel times measured from short-period waveforms are consistent with small-amplitude deviations from radial symmetry except when ray paths are nearly parallel to the Earth's spin axis. These near-axial paths consistently produce large travel-time anomalies, providing compelling evidence for large-amplitude, axisymmetric anisotropy in the outermost portions of the inner core.},
	author = {Creager, K. C.},
	date = {MAR 26},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1992HK79400053},
	journal = {Nature},
	month = {Mar},
	number = {6367},
	pages = {309--314},
	publication-type = {J},
	title = {ANISOTROPY OF THE INNER CORE FROM DIFFERENTIAL TRAVEL-TIMES OF THE PHASES {PKP} AND {PKIKP}},
	volume = {356},
	year = {1992}}

@article{Song:1998oq,
	abstract = {Seismic waves that traverse Earth's inner core along north-south paths produce unusually broad pulse shapes at long periods (compared with waves along east-west paths) and reflections from below;the inner core boundary at short periods. The observations provide compelling evidence for a seismic velocity discontinuity along north-south paths about 200 kilometers below the inner core boundary separating an isotropic upper inner core from an anisotropic Lower inner core. The triplication associated with such a structure might be responsible for reported waveform complexity of short-period inner core arrivals along north-south paths and, if the depth of the boundary is laterally variable, their Large travel-time variation.},
	author = {Song, X. D. and Helmberger, D. V.},
	date = {OCT 30},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000076727300043},
	journal = {SCIENCE},
	month = {Oct},
	number = {5390},
	pages = {924--927},
	publication-type = {J},
	title = {Seismic evidence for an inner core transition zone},
	volume = {282},
	year = {1998}}

@article{Bergman2002,
	abstract = {[1] Directional solidification of salt water results in a preferred crystallographic orientation, with ice platelets growing with their short dimension (the c axis of the hexagonal close packed (hcp) ice crystal) transverse to the growth direction. In the absence of a mean saltwater flow parallel to the solidification interface, the ice platelets, and hence the c axes, are arbitrarily oriented in the plane transverse to growth. Here we report on laboratory experiments on salt water solidifying horizontally from a vertical chill plate. This geometry yields a convectively driven, organized fluid flow parallel to the solidification interface, which we found causes the platelets to trend parallel to the flow direction. This contrasts with previous field and laboratory observations of ice solidifying vertically from salt water in the presence of an externally forced flow, such as an ocean current, where the c axes lie parallel to the flow direction. The results support the hypothesis that transverse textures result from a hydrodynamic interaction with hcp dendritic platelets but highlight the difference between flow driven internally versus externally to the dendritic mushy layer. They also suggest that convective fluid flow may be the cause for the fabric observed in resolidified cracks in sea ice sheets and perhaps that fluid motion in the Earth's outer core may play a role in the seismic anisotropy of the hcp iron inner core.},
	author = {Bergman, M. I. and Cole, D. M. and Jones, J. R.},
	date = {SEP},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN 2201},
	isi = {ISI:000180366100025},
	journal = {J. Geophys. Res.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Bergman2002.pdf},
	month = {Sep},
	number = {B9},
	pages = {2201},
	publication-type = {J},
	title = {Preferred crystal orientations due to melt convection during directional solidification},
	volume = {107},
	year = {2002},
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@article{Bergman2003,
	abstract = {Previous studies on directionally soilidified h-exagonal close-packed (hcp) sea ice have found that the c-axis orient parallel to a shear fluid flow that is driven external to the solute boundary layer, and perpendicular to a flow that is driven from within the mushy zone as a result of the solidification itself. The origin of these transverse solidification textures is-thought to arise from the interaction of these flows with the platelet-like dendrites. However, transverse textures have not been previously studied in hcp phase-rich metallic alloys, which also exhibit platelets. Unlike in a control on a Zn-3wt% Sn alloy solidified vertically at 0.3degreesC/min and in an experiment on the same alloy solidified horizontally at the same rate, we found that a Zn-19wt% Sn alloy solidified horizontally at 0.1degreesC/min exhibits some preferred orientation W the c-axis in the direction perpendicular to the flow, presumably due to the efficacy of convection over diffusion in removing solute from within the mushy zone. This suggests that transverse texturing is a general phenomenon of directionally solidified hcp alloys in the presence of fluid flow, as a result of the. platelet nature of hcp dendrites. (C) 2003 Elsevier Science B.V. All rights reserved.},
	author = {Bergman, M. I. and Agrawal, S. and Carter, M. and Macleod-Silberstein, M.},
	date = {JUL},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000183767000024},
	journal = {J. Crystal Growth},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Bergman2003.pdf},
	month = {Jul},
	number = {1-2},
	pages = {204--211},
	publication-type = {J},
	title = {Transverse solidification textures in hexagonal close-packed alloys},
	volume = {255},
	year = {2003},
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@article{Yu2006,
	abstract = {We investigate the attenuation structure of the Earth's inner core and its relationship to the velocity structure globally and along various sampling directions, by studying the amplitude ratios and the differential travel times of the PKiKP-PKIKP and PKPbc-PKIKP phases. Our observations reveal that the amplitude ratios of these core phases, like the differential travel times, vary in both sampling direction and geographic location, and the correlation is ubiquitous between small (large) PKIKP/PKiKP or PKIKP/PKPbc amplitude ratios and large (small) differential PKiKP-PKIKP or PKPbc-PKIKP travel times. These observations indicate that the Earth's inner core is anisotropic in attenuation, and the direction of high (low) attenuation corresponds to that of high (low) velocity. Such anisotropic behaviors can be explained by different alignments of the hexagonal close-packed (hcp) iron crystals under the hypothesis that the hcp iron crystals are anisotropic in attenuation with their axis of high (low) attenuation corresponding to that of high (low) velocity. (c) 2006 Elsevier B.V. All rights reserved.},
	author = {Yu, W. C. and Wen, L. X.},
	date = {MAY 30},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000238672500008},
	journal = {Earth Plan. Sci. Let.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Yu2006.pdf},
	month = {May},
	number = {3-4},
	pages = {581--594},
	publication-type = {J},
	title = {Inner core attenuation anisotropy},
	volume = {245},
	year = {2006},
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@article{Yu:2006cr,
	abstract = {[ 1] We study seismic velocity and attenuation structures in the top 400 km of the Earth's inner core based on modeling of differential traveltimes, amplitude ratios, and waveforms of the PKiKP-PKIKP phases observed at the epicentral distance range of 120 degrees - 141 degrees and the PKPbc-PKIKP phases observed at the distance range of 146 degrees - 160 degrees along equatorial paths. Our data are selected from the seismograms recorded in the Global Seismographic Network from 1990 to 2001 and many regional seismic networks. The observed PKiKP-PKIKP and PKPbc-PKIKP phases exhibit distinctive "east-west'' hemispheric patterns: ( 1) At the distance ranges of 131 degrees - 141 degrees and 146 degrees - 151 degrees, PKIKP phases arrive about 0.3 s earlier than the theoretical arrivals based on the Preliminary Reference Earth Model (PREM) for the PKIKP phases sampling the "eastern hemisphere'' (40 degrees E - 180 degrees E) of the inner core and about 0.4 s later for those sampling the "western hemisphere'' (180 degrees W - 40 degrees E). At the distance range of 151 degrees - 160 degrees, PKIKP phases arrive about 0.7 s earlier than the predicted arrivals based on PREM for those sampling the eastern hemisphere and about 0.1 s later for those sampling the western hemisphere. ( 2) Amplitude ratios of the PKIKP/PKiKP phases at the distance range of 131 degrees - 141 degrees and of the PKIKP/PKPbc phases at the distance range of 146 degrees - 151 degrees are, in general, smaller for the PKIKP phases sampling the eastern hemisphere than for those sampling the western hemisphere. At distances greater than 151 degrees, the PKIKP/PKPbc amplitude ratios become indistinguishable for the two hemispheres. These observations can be best explained by two different types of seismic velocity and attenuation models along equatorial paths, one for each hemisphere, in the top 400 km of the inner core. For the eastern hemisphere, the velocity structure has a velocity increase of 0.748 km/s across the inner core boundary (ICB), a small velocity gradient of 0.0042 (km/s)/ 100 km in the top 235 km, followed by a steeper velocity gradient of 0.1 (km/s)/ 100 km extending from 235 km to 375 km, and a velocity gradient of 0.01 (km/s)/ 100 km in the deeper portion of the inner core; the attenuation structure has an average Q value of 300 in the top 300 km and an average Q value of 600 in the deeper portion of the inner core. For the western hemisphere, the velocity structure has a velocity increase of 0.645 km/s across the ICB and a velocity gradient of 0.049 (km/s)/ 100 km in the top 375 km; the attenuation structure has an average Q value of 600 in the top 375 km of the inner core. Our results suggest that the inner core hemispheric variations in velocity extend deeper than 375 km below the ICB and the top 235 km of the inner core in the eastern hemisphere is anomalous compared to the rest of the inner core in having a small velocity gradient, high velocity, and high attenuation.},
	af = {Yu, Wen-che Wen, Lianxing},
	author = {Yu, W. C. and Wen, L. X.},
	date = {JUL 27},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN B07308},
	isi = {ISI:000239491200002},
	journal = {JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH},
	month = {Jul},
	number = {B7},
	pages = {B07308},
	publication-type = {J},
	title = {Seismic velocity and attenuation structures in the top 400 km of the Earth's inner core along equatorial paths},
	volume = {111},
	year = {2006}}

@article{Luo2002,
	abstract = {[1] Variations in regional differential times between PKiKP ( i) and PKIKP (I) have been attributed to hemispheric P-velocity variations of about 1% in the upper 100 km of the inner core (referred to as HIC). The top of the inner core appears relatively fast beneath Asia where D is also fast. An alternative interpretation could be the lateral variation in P velocity at the lowermost outer core (HOC) producing the same differential times. To resolve this issue, we introduce the diffracted PKP phase near the B caustic (B-diff) in the range of 139-145degrees epicenter distances, and the corresponding differential times between B-diff and PKiKP and PKIKP as observed on broadband arrays. Due to the long-wavelength nature of B-diff, we scaled the S-wave tomography model with k values (k = dlnV(s) / dlnV(p)) to obtain large-scale P-wave velocity structure in the lower mantle as proposed by earlier studies. Waveform synthetics of B-diff constructed with small k's predict complex waveforms not commonly observed, confirming the validity of large scaling factor k. With P-velocity in lower mantle constrained at large scale, the extra travel-time constraint imposed by B-diff helps to resolve the HOC-HIC issue. Our preliminary results suggest k > 2 for the lowermost mantle and support HIC hypothesis. An important implication is that there appears to be a relationship of D velocity structures with the structures near the inner core boundary via core dynamics.},
	author = {Luo, S. N. and Ni, S. D. and Helmberger, D.},
	date = {JUN 1},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN 1527},
	isi = {ISI:000178964000033},
	journal = {Geophys. Res. Let.},
	month = {Jun},
	number = {11},
	pages = {1527},
	publication-type = {J},
	title = {Relationship of D '' structure with the velocity variations near the inner-core boundary},
	volume = {29},
	year = {2002}}

@article{Sun:2006dq,
	abstract = {[1] One of the most robust observations for the inner core rotation is that the differential PKP BC-DF traveltimes from South Sandwich Islands (SSI) earthquakes to College, Alaska ( and some other stations in Alaska), have increased systematically over the past 50 years. The time shift in the differential time residuals is some 0.3 s over 30 years. This temporal change is thought to result from a shift of the inner core structure from a superrotation of the inner core. However, the observation has been hotly debated and has been suggested to be an artifact of systematic earthquake mislocation. Here we examine this issue using three mutually independent approaches, with a goal to quantify the amount of the systematic mislocation, if any. All three approaches involve differencing data between north stations at a similar azimuth as the SSI-Alaska azimuth and south stations at nearly the opposite azimuth. Mislocation along this azimuth has greatest impact on the PKP differential times. In approach 1, we examine how the double difference of P traveltimes between a north station and a south station changes with time. Because the differential apparent slowness between the P traveltimes of the pairs is 8 to 16 times that of the differential BC-DF times, mislocation would cause a time shift in the double difference an order of magnitude larger than that of BC-DF times. In approach 2, we compare directly difference in P arrival times between two SSI events that are close by and between a north and a south stations, which avoids using earthquake locations and Earth models entirely. In approach 3, we compare PKP traveltime residuals between a group of north and south stations. Because PKP traveltimes are generally not used for location in earthquake bulletins, they provide an independent data set to check earthquake location errors. The results from approaches 1 and 2, both of which use P data, are generally consistent. The mislocation is up to 3.6 +/- 4.2 km ( one standard deviation), explaining less than 10% of the observed COL temporal change. The results from approach 3 using PKP data show a larger mislocation but with a larger error (14.4 +/- 10.8 km over 30 years). It can explain about 30% +/- 22% of the observed COL temporal change. Therefore inner-core superrotation is still the best explanation for the observed temporal change in the differential traveltimes.},
	af = {Sun, Xinlei Poupinet, Georges Song, Xiaodong},
	author = {Sun, X. L. and Poupinet, G. and Song, X. D.},
	date = {NOV 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN B11305},
	isi = {ISI:000242178100001},
	journal = {JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Sun2006.pdf},
	month = {Nov},
	number = {B11},
	pages = {B11305},
	publication-type = {J},
	title = {Examination of systematic mislocation of South Sandwich Islands earthquakes using station pairs: Implications for inner core rotation},
	volume = {111},
	year = {2006},
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@article{Koper:2005lq,
	abstract = {A recent study of PKiKP / PcP amplitude ratios found surprisingly low values for the change in density (Delta rho (ICB) = 0.3 g/cm(3)) and shear velocity (Delta S-ICB = 2.0 km/s) across the inner core boundary (ICB). However, because the data set was limited to small source-receiver distances (< 50 degrees) there was a significant trade-off between the two parameters, with higher values in one parameter nearly compensated by higher values in the other. In this study we augment the existing PKiKP/PcP data set with new observations of PKiKP/P amplitude ratios at larger distances (50-90 degrees), and jointly model the two data sets. Considering assumptions in the modeling and observational errors we estimate Delta rho(ICB) = 0.52 +/- 0.24 g/cm(3) and Delta S-ICB = 2.82 +/- 0.32 km/s. These values can be reconciled with the slightly higher values obtained from normal mode analysis if the outermost inner core is either structurally or chemically distinct from the bulk of the inner core. The new PKiKP/P amplitude ratios show dramatic variation but are geographically coherent; this suggests that significant lateral heterogeneity is present at, or just below, the ICB. (c) 2005 Elsevier B.V. All rights reserved.},
	author = {Koper, K. D. and Dombrovskaya, M.},
	date = {SEP 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000232155200026},
	journal = {EARTH AND PLANETARY SCIENCE LETTERS},
	month = {Sep},
	number = {3-4},
	pages = {680--694},
	publication-type = {J},
	title = {Seismic properties of the inner core boundary from PKiKP/P amplitude ratios},
	volume = {237},
	year = {2005}}

@article{Garcia2002,
	abstract = {The determination of the inner-core boundary structure is key to understanding the mechanisms of inner-core growth, iron solidification and anisotropy formation in the inner core. A waveform inversion of a worldwide data set of PKIKP and PKiKP core phases is performed to investigate the velocity and the attenuation structure of this region. The data set is chosen to sample the top 50 km of the inner core. Two inversion methods combining time and frequency domain observations are presented. Synthetic tests are performed in order to evaluate the resolution and the confidence intervals of the model parameters. The attenuation of P waves in the uppermost inner core is poorly resolved but appears to be high (Q < 100). The uppermost inner-core interface is divided into two regions: a region extending from 180 W to 60 E and characterized by negative P-wave velocity perturbations (dV/V < 0 per cent), and a region extending from 60 E to 180 E and characterized by positive P-wave velocity perturbations (dV/V similar to 1 per cent). The results of the inversion do not favour the presence of transverse isotropy aligned along the spin axis of the Earth in the uppermost inner core for these two regions. However, these regions are correlated with those where large-scale variations of the inner-core anisotropy have been determined previously in the deeper inner core, 100 km beneath the inner-core boundary.},
	author = {Garcia, R.},
	date = {SEP},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000177790300005},
	journal = {Geophys. J. Int.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Garcia2002.pdf},
	month = {Sep},
	number = {3},
	pages = {651--664},
	publication-type = {J},
	title = {Constraints on upper inner-core structure from waveform inversion of core phases},
	volume = {150},
	year = {2002},
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@article{Sumita:2002,
	abstract = {[1] We report the results of thermal convection experiments in a rapidly rotating hemispherical shell with a heterogeneous heat flux at the outer boundary to model the effect of a thermally heterogeneous core-mantle boundary on the convection in the Earth's outer core. A parameter study is made by varying the heat flux, size, and location of an anomalously heated patch for a range of Rayleigh numbers at similar to10(8) and a fixed Ekman number 4.7 x 10(-6). Experiments show that fully developed, boundary-driven convection occurs when the radial convective heat transfer from the heater exceeds that of the surrounding boundary region. The flow consists of a large-scale cyclonic circulation originating from the heater and includes a radially extending spiralling front with a jet. The front is stationary when the sectorial high heat flux region is imposed at low latitudes but becomes unstable when it is imposed at high latitudes. The ratio of applied heat which is partitioned to radial and lateral heat transfer becomes fixed in this regime. Measurements also indicate that there is a close correlation between the flow direction and the statistics of temperature fluctuations. Applied to the Earth, the experiments suggest that there are two scales of flows in the core: fine-scaled jets and slower, large-scale flows. The large-scale hemispherical structure of the core can be interpreted in terms of the boundary-driven flow driven by the high heat flow region beneath east Asia.},
	author = {Sumita, I. and Olson, P.},
	date = {AUG 23},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN 2169},
	isi = {ISI:000179638200002},
	journal = {JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH},
	month = {Aug},
	number = {B8},
	pages = {2169},
	publication-type = {J},
	title = {Rotating thermal convection experiments in a hemispherical shell with heterogeneous boundary heat flux: Implications for the Earth's core},
	volume = {107},
	year = {2002}}

@article{Sumita1999,
	abstract = {Thermal convection experiments in a rapidly rotating hemispherical shell suggest a model in which the convection in Earth's liquid outer core is controlled by a thermally heterogeneous mantle. Experiments show that heterogeneous boundary heating induces an eastward flow in the core, which, at a sufficiently Large magnitude, develops into a Large-scale spiral with a sharp front. The front separates the warm and cold regions in the core and includes a narrow jet flowing from the core-mantle boundary to the inner-core boundary. The existence of this front in the core may explain the Pacific quiet zone in the secular variation of the geomagnetic field and the Longitudinally heterogeneous structure of the solid inner core.},
	author = {Sumita, I. and Olson, P.},
	date = {NOV 19},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000083768300054},
	journal = {Science},
	month = {Nov},
	number = {5444},
	pages = {1547--1549},
	publication-type = {J},
	title = {A laboratory model for convection in Earth's core driven by a thermally heterogeneous mantle},
	volume = {286},
	year = {1999}}

@article{Cao2004,
	abstract = {In contrast to the liquid Outer core, the earth's inner core is mostly solid. and its composition is more pure iron. Based on dynamic arguments related to the freezing process of the inner core. and the observation of much lower P-wave quality factor in the inner core (Q(alpha)<450) than in the outer core (Q(alpha)>10,000), it has been suggested that a mushy layer with liquid inclusions may exist at the top of the inner core. On the other hand, seismic measurements indicate that Q(alpha) increases towards the center of the inner core. We here present estimates of Q(alpha) in the depth range 32-110 km beneath the Inner Core Boundary (ICB), based on the measurement of PKIKP/PKiKP amplitude ratios after a narrow band-pass filtering (0.7-2.0 Hz). Our measurements indicate that there are pronounced hemispherical differences in the values of Q(alpha) (similar to335 and similar to160 in the western (180degreesC to 40degreesE) and eastern (40degreesE to 180degreesE) hemispheres, respectively), and in the depth of transition front decreasing to increasing Q(alpha)(<32 km beneath the ICB in the eastern hemisphere and similar to85 km in the western hemisphere). Below 85 km, the hemispherical pattern disappears. We also confirm the existence of a correlated hemispherical pattern in P velocity down to 85 km. The P velocity and Q(alpha) variations are compatible with an interpretation in terms of small hemispherical variations of temperature at the top of the inner core and their influence on the morphology of porosity and connectivity of liquid inclusions in the mushy zone. The disappearance of the differences in Q(alpha) beneath 85 km provide constraints on the likely depth extent of the mushy zone. (C) 2004 Elsevier BY All rights reserved.},
	author = {Cao, A. and Romanowicz, B.},
	date = {DEC 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000225936100003},
	journal = {Earth Plan. Sci. Let.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Cao2004.pdf},
	month = {Dec},
	number = {3-4},
	pages = {243--253},
	publication-type = {J},
	title = {Hemispherical transition of seismic attenuation at the top of the {E}arth's inner core},
	volume = {228},
	year = {2004},
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@article{Koper2004,
	abstract = {Recent seismic observations have provided evidence that the inner core contains strong heterogeneity at a scale-length of tens of kilometers. The corresponding lateral variations in elastic properties could be caused by pockets of partial melt, alignment of iron crystals, or variations in chemistry. However, the relevant seismic observations (precritical PKiKP coda waves) were subtle and were made using historic seismic data. Furthermore, it has been suggested that the seismic data might be explainable by scatterers in the lower mantle or by a complex inner core boundary. To address these issues. we investigate a preexisting global database of precritical PKiKP waveforms at distances of 10degrees-50degrees, and a second, newly generated global data base of PKiKP waveforms at distances of 50degrees-90degrees. We analyze the data using standard array processing techniques and identify PKiKP coda waves based on travel time, ray parameter, amplitude, and coherence. Although it remains unclear whether the scattered energy is being created within the inner core or along its boundary, we find three lines of evidence which support the idea that it is in fact related to the inner core: at smaller distances the decay rate of PKiKP coda is significantly lower than the decay rates of the corresponding PcP and ScP codas; at larger distances. we find examples of emergent, spindle-shaped PKiKP coda waves that exist without the parent PKiKP phase;, and at larger distances. we infer a PKiKP coda decay rate to that determined from the data at the smaller distances. It is likely that many more PKiKP coda observations can be made with existing data sets, and hence seismologists possess a new, extraordinarily fine probe for inferring inner core structure. (C) 2004 Elsevier B.V. All rights reserved.},
	author = {Koper, K. D. and Franks, J. M. and Dombrovskaya, M.},
	date = {DEC 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000225936100002},
	journal = {EARTH AND PLANETARY SCIENCE LETTERS},
	month = {Dec},
	number = {3-4},
	pages = {227--241},
	publication-type = {J},
	title = {Evidence for small-scale heterogeneity in Earth's inner core from a global study of PKiKP coda waves},
	volume = {228},
	year = {2004}}

@article{Niu2001,
	abstract = {Knowledge of the seismic velocity structure at the top of the Earth's inner core is important for deciphering the physical processes responsible for inner-core growth(1-3). Previous global seismic studies(4-9) have focused on structures found 100 km or deeper within the inner core, with results for the uppermost 100 km available for only isolated regions(10-12). Here we present constraints on seismic velocity variations just beneath the inner-core boundary, determined from the difference in travel time between waves reflected at the inner-core boundary and those transmitted through the inner core. We found that these traveltime residuals-observed on both global seismograph stations and several regional seismic networks-are systematically larger, by about 0.8 s, for waves that sample the 'eastern hemisphere' of the inner core (40 degrees E to 180 degrees E) compared to those that sample the 'western hemisphere' (180 degrees W to 40 degrees E). These residuals show no correlation with the angle at which the waves traverse the inner core; this indicates that seismic anisotropy is not strong in this region and that the isotropic seismic velocity of the eastern hemisphere is about 0.8% higher than that of the western hemisphere.},
	author = {Niu, F. L. and Wen, L. X.},
	date = {APR 26},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000168285500044},
	journal = {Nature},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Niu2001.pdf},
	month = {Apr},
	number = {6832},
	pages = {1081--1084},
	publication-type = {J},
	title = {Hemispherical variations in seismic velocity at the top of the {E}arth's inner core},
	volume = {410},
	year = {2001},
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@article{Vidale:2000zr,
	abstract = {The seismological properties of the Earth's inner core have become of particular interest as we understand more about its composition and thermal state(1,2). Observations of anisotropy and velocity heterogeneity in the inner core are beginning to reveal how it has grown and whether it convects(3,4). The attenuation of seismic waves in the inner core is strong, and studies of seismic body waves(5,6) have found that this high attenuation is consistent with either scattering or intrinsic attenuations, The outermost portion of the inner core has been inferred to possess layering and to be less anisotropic than at greater depths(7-10). Here we present observations of seismic waves scattered in the inner core which follow the expected arrival time of the body-wave reflection from the inner-core boundary. The amplitude of these scattered waves can be explained by stiffness variations of 1.2% with a scale length of 2 kilometres across the outermost 300 km of the inner core. These variations might be caused by variations in composition, by pods of partial melt in a mostly solid matrix or by variations in the orientation or strength of seismic anisotropy.},
	author = {Vidale, J. E. and Earle, P. S.},
	date = {MAR 16},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000086022200045},
	journal = {NATURE},
	month = {Mar},
	number = {6775},
	pages = {273--275},
	publication-type = {J},
	title = {Fine-scale heterogeneity in the Earth's inner core},
	volume = {404},
	year = {2000}}

@article{Vidale:2005ys,
	abstract = {Inner-core-grazing PKP waves from seven French nuclear tests on Mururoa Island recorded at NORSAR appear to change over a decade. We compared filtered and stacked signals from the explosions, which took place from 1977 to 1987 and were separated by less than 10 km. The PKP energy 3 to 10 s after the first arrivals differs greatly between the NORSAR subarrays, and evolves over time. The small time shifts of coda arrivals, a few tenths of a second, are qualitatively consistent with shifts predicted for point scatterers in an inner core that rotates in the range 0.05degrees to 0.10degrees per year. There are also visible changes in the envelope of the PKP energy. Although the alternative of systematic shifts in source location cannot be ruled out, the apparent time evolution of PKP supports claims of slow inner core rotation [ Song and Richards, 1996; Creager, 1997; Laske and Masters, 1999; Vidale et al., 2000] and offers a powerful new tool for its assessment.},
	author = {Vidale, J. E. and Earle, P. S.},
	date = {JAN 15},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN L01309},
	isi = {ISI:000226547400003},
	journal = {GEOPHYSICAL RESEARCH LETTERS},
	month = {Jan},
	number = {1},
	pages = {L01309},
	publication-type = {J},
	title = {XEvidence for inner-core rotation from possible changes with time in PKP coda},
	volume = {32},
	year = {2005}}

@article{Zhang:2005rt,
	abstract = {We analyzed 18 high-quality waveform doublets with time separations of up to 35 years in the South Sandwich Islands region, for which the seismic signals have traversed the inner core as PKP(DF). The doublets show a consistent temporal change of travel times at up to 58 stations in and near Alaska, and they show a dissimilarity of PKP(DF) coda. Using waveform doublets avoids artifacts of earthquake mislocations and contamination from small-scale heterogeneities. Our results confirm that Earth's inner core is rotating faster than the mantle and crust at about 0.3 degrees to 0.5 degrees per year.},
	author = {Zhang, J. and Song, X. D. and Li, Y. C. and Richards, P. G. and Sun, X. L. and Waldhauser, F.},
	date = {AUG 26},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000231543300039},
	journal = {SCIENCE},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Zhang2005.pdf},
	month = {Aug},
	number = {5739},
	pages = {1357--1360},
	publication-type = {J},
	title = {Inner core differential motion confirmed by earthquake waveform doublets},
	volume = {309},
	year = {2005},
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@article{Vidale:2000vn,
	abstract = {The finding that the Earth's inner core might be rotating faster than the mantle(1) has important implications for our understanding of core processes, including the generation of the Earth's magnetic field(2,3). But the reported signal is subtle-a change of about 0.01 s per year in the separation of two seismic waves with differing paths through the core. Subsequent studies of such data have generally supported the conclusion that differential rotation exists(4-6), but the difficulty of accurately locating historic earthquakes(7) and possible biases induced by strong lateral variations in structure near the core-mantle boundary(8) have raised doubt regarding the proposed inner-core motion(9). Also, a study of free oscillations(10) constrained the motion to be relatively small compared to previous estimates and it has been proposed that the interaction of inner-core boundary topography and mantle heterogeneity might lock the inner core to the mantle(11). The recent detection of seismic waves scattered in the inner core(12) suggests a simple test of inner-core motion. Here we compare scattered waves recorded in Montana, USA, from two closely located nuclear tests at Novaya Zemlya, USSR, in 1971 and 1974. The data show small but coherent changes in scattering which point toward an inner-core differential rotation rate of 0.15 degrees per year-consistent with constraints imposed by the free-oscillation data(10).},
	author = {Vidale, J. E. and Dodge, D. A. and Earle, P. S.},
	date = {MAY 25},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000087212000045},
	journal = {NATURE},
	month = {May},
	number = {6785},
	pages = {445--448},
	publication-type = {J},
	title = {Slow differential rotation of the Earth's inner core indicated by temporal changes in scattering},
	volume = {405},
	year = {2000}}

@article{Creager:1997,
	abstract = {The time it takes seismic waves to propagate from South Atlantic earthquakes through the inner core to station COL in Alaska has decreased systematically over the past 30 years. Travel times from three earthquakes in 1991 io an array of 37 seismometers in Alaska suggest thai lateral gradients in seismic wavespeeds are steep in this part of the inner core. This combination of observations can be explained by postulating that the inner core is rotating 0.2 degrees lo 0.3 degrees per year faster than the mantle.},
	author = {Creager, K. C.},
	date = {NOV 14},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1997YG04300043},
	journal = {SCIENCE},
	month = {Nov},
	number = {5341},
	pages = {1284--1288},
	publication-type = {J},
	title = {Inner core rotation rate from small-scale heterogeneity and time-varying travel times},
	volume = {278},
	year = {1997}}

@article{Stroujkova2004,
	abstract = {The structure of the uppermost 100 km of the inner core was examined from PKIKP and PKiKP waveforms in the distance range of 118degrees-140degrees. We found evidence of a low-velocity layer in the uppermost inner core in the equatorial region predominantly located between longitude 20degreesW to 140degreesE. In the latitudinal direction the anomaly is detectable from 35degreesS beneath the Indian Ocean to 60degreesN underneath Asia. The maximum thickness of the low-velocity layer inferred from waveform modeling is 40 km with velocity jump of about 3%. We speculate that this layer may represent newly solidified core in the area where vigorous compositional convection in the outer core coincides with new crystal growth in the inner core.},
	author = {Stroujkova, A. and Cormier, V. F.},
	date = {OCT 16},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	di = {ARTN B10307},
	isi = {ISI:000224581100004},
	journal = {J. Geophys. Res.},
	month = {Oct},
	number = {B10},
	pages = {B10307},
	publication-type = {J},
	title = {Regional variations in the uppermost 100 km of the Earth's inner core},
	volume = {109},
	year = {2004}}

@article{Bergman2005,
	abstract = {To better understand the influence of rotating convection in the outer core on the solidification of the inner core we have constructed a laboratory model for solidification of Earth's core. The model consists of a 15 cm radius hemispherical acrylic tank concentric with a 5 cm radius hemispherical aluminum heat exchanger that serves as the incipient inner core onto which we freeze ice from salt water. Long exposure photographs of neutrally buoyant particles in illuminated planes suggest reduction of flow parallel to the rotation axis. Thermistors in the tank near the heat exchanger show that in experiments with rotation the temperature near the pole is lower than near the equator, unlike for control experiments without rotation or with a polymer that increases the fluid viscosity. The photographs and thermistors suggest that our observation that ice grows faster near the pole than near the equator for experiments with rotation is a result of colder water not readily convecting away from the pole. Because of the reversal of the thermal gradient, we expect faster equatorial solidification in the Earth's core. Such anisotropy in solidification has been suggested as a cause of inner core elastic (and attenuation) anisotropy, though the plausibility of this suggestion will depend on the core Nusselt number and the slope of the liquidus, and the effects of post-solidification deformation. Previous experiments on hexagonal close-packed alloys such as sea ice and zinc-tin have shown that fluid flow in the melt can result in a solidification texture transverse to the solidification direction, with the texture depending on the nature of the flow. A comparison of the visualized flow and the texture of columnar ice crystals in thin sections from these experiments confirms flow-induced transverse textures. This suggests that the convective pattern at the base of the outer core is recorded in the texture of the inner core, and that outer core convection might contribute to the complexity in the seismically inferred pattern of anisotropy in the Earth's inner core. (c) 2005 Elsevier B.V. All rights reserved.},
	author = {Bergman, M. I. and Macleod-Silberstein, M. and Haskel, M. and Chandler, B. and Akpan, N.},
	date = {NOV 30},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:000233837100014},
	journal = {Phys. Earth Planet. Int.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Bergman2005.pdf},
	month = {Nov},
	number = {1-3},
	pages = {150--164},
	publication-type = {J},
	special-issue = {Sp. Iss. SI},
	title = {A laboratory model for solidification of {E}arth's core},
	volume = {153},
	year = {2005},
	Bdsk-File-1 = {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}}

@article{Wen2006,
	abstract = {Compressional waves of an earthquake doublet ( two events occurring in the South Sandwich Islands on 1 December 1993 and 6 September 2003), recorded at three seismic stations in Russia and Kyrgyzstan and reflected off Earth's inner core boundary, arrived at least from 39 to 70 milliseconds earlier in the 2003 event than in the 1993 event. Such changes indicate that Earth's inner core radius enlarged locally beneath middle Africa by 0.98 to 1.75 kilometers between the times of these two events. Changes of the inner core radius may be explained by either a differential motion of the inner core, assuming that irregularities are present at the inner core boundary and fixed to the inner core, or a rapid growth of the inner core by this amount.},
	af = {Wen, Lianxing},
	author = {Wen, L. X.},
	date = {NOV 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2010-05-20 15:54:01 +0200},
	isi = {ISI:000241896000045},
	journal = {Science},
	month = {Nov},
	number = {5801},
	pages = {967--970},
	publication-type = {J},
	title = {Localized temporal change of the earth's inner core boundary},
	volume = {314},
	year = {2006}}

@article{Yoshida1996,
	abstract = {We present a growth tectonic model of Earth's inner core and the resulting model of the seismic anisotropy. The inner core grows anisotropically if the convection in the outer core is of Taylor column type. The anisotropic growth produces a how held of the poloidal zonal order 2 type as a result of the isostatic adjustment of the viscous inner core. Crystals in the inner core align themselves under the stress field produced by the flow. We model the anisotropic structure of the inner core, using the theory of Kamb [1959] and elastic constants of Stixrude and Cohen [1995b]. We consider models for both hcp iron and fee iron, which are the probable crystal structures for the inner core iron according to Stixrude and Cohen [1995a]. We have found that the c axis for hcp iron and [111] direction for fee iron align in the polar direction. The alignment is consistent with seismic observations, which have revealed that the P wave velocity is faster in the polar direction. Our model predicts that the degree of the alignment decreases near the inner core boundary in accord with recent body wave observations. The radial dependence of the alignment would result from the following three effects: (1) crystals near the surface have not undergone stressed state long enough to acquire anisotropy after precipitation, (2) stress near the surface is different from that in the interior of the inner core due to shear stress free boundary condition, and (3) partially molten structure results in transversely isotropic stress condition near the inner core surface due to compaction. Thus the application of Kamb's theory successfully explains the seismic anisotropy in the inner core provided that the crystals have been subjected under the same stress condition for the timescale of the order of 10(9) years.},
	author = {Yoshida, S. and Sumita, I. and Kumazawa, M.},
	date = {DEC 10},
	date-added = {2007-09-14 14:27:54 +0200},
	date-modified = {2007-09-14 14:27:54 +0200},
	isi = {ISI:A1996VX66300027},
	journal = {J. Geophys. Res.},
	local-url = {file://localhost/Users/aubert/Desktop/ps-eps-pdf/Yoshida1996.pdf},
	month = {Dec},
	number = {B12},
	pages = {28085--28103},
	publication-type = {J},
	title = {Growth model of the inner core coupled with the outer core dynamics and the resulting elastic anisotropy},
	volume = {101},
	year = {1996},
	Bdsk-File-1 = {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}}

@article{braginsky70,
	author = {Braginsky, S. I.},
	journal = {Geomag. Aeron.},
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	title = {Torsional magnetohydrodynamic vibrations in the {E}arth's core and variations in day length},
	volume = 10,
	year = 1970}

@article{jault88,
	author = {Jault, D. and Gire, C. and Le Mou\"el, J.-L.},
	journal = {Nature},
	pages = {353--356},
	title = {Westward drift, core motions and exchanges of angular momentum between core and mantle},
	volume = 333,
	year = 1988}

@incollection{jackson93,
	address = {Washington, DC},
	author = {Jackson, A. and Bloxham, J. and Gubbins, D.},
	booktitle = {Dynamics of the {E}arth's deep interior and {E}arth rotation},
	editor = {Le Mou\"el, J.-L. and Smylie, D. E. and Herring, T.},
	pages = {97--107},
	publisher = {{AGU} {G}eophysical {M}onograph},
	title = {Time-dependent flow at the core surface and conservation of angular momentum in the coupled core-mantle system},
	volume = 72,
	year = 1993}

@article{simmons06,
	author = {Simmons, N. A. and Forte, A. M. and Grand, S. P.},
	journal = {Earth Planet. Sci. Lett.},
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	title = {Constraining mantle flow with seismic and geodynamic data: {A} joint approach},
	volume = 246,
	year = 2006}

@article{forte91,
	author = {Forte, A. M. and Peltier, R.},
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	pages = {20131--20159},
	title = {Viscous flow models of global geophysical observables 1. forward problems},
	volume = 96,
	year = 1991}

@article{defraigne96,
	author = {Defraigne, P. and Dehant, V. and Wahr, J. M.},
	journal = {Geoph. J. Int.},
	pages = {173--192},
	title = {Internal loading of an inhomogeneous compressible {E}arth with phase boundaries},
	volume = 125,
	year = 1996}

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