  The inverse problem which consists of determining the flow at the Earth's
Core Mantle Boundary according to an outer core magnetic field and secular
variation model, has been investigated through a Bayesian formalism. To
circumvent the issue arising from the truncated nature of the available fields,
we combined two modelization methods. In the first step, we applied a filter on
the magnetic field to isolate its large scales by reducing the energy contained
in its small scales, we then derived the dynamical equation, referred as
filtered frozen flux equation, describing the spatio-temporal evolution of the
filtered part of the field. In the second step, we proposed a statistical
parametrization of the filtered magnetic field in order to account for both its
remaining unresolved scales and its large scale uncertainties. These two
modelization techniques were then included in the Bayesian formulation of the
inverse problem. To explore the complex posterior distribution of the velocity
field resulting from this development, we numerically implemented an algorithm
based on Markov Chain Monte Carlo methods. After evaluating our approach on
synthetic data and comparing it to previously introduced methods, we applied it
on real data for the single epoch 2005.0.
