  Classically, anisotropic surface wave tomography is treated as an
optimisation problem where it proceeds through a linearised two-step approach.
It involves the construction of 2D group or phase velocity maps for each
considered period, followed by the inversion of local dispersion curves
inferred from these maps for 1D depth-functions of the elastic parameters.
Here, we cast the second step into a fully Bayesian probability framework.
Solutions to the inverse problem are thus an ensemble of model parameters
(\textit{i.e.} 1D elastic structures) distributed according to a posterior
probability density function and their corresponding uncertainty limits. The
method is applied to azimuthally-varying synthetic surface wave dispersion
curves generated by a 3D-deforming upper mantle. We show that such a procedure
captures essential features of the upper mantle structure. The robustness of
these features however strongly depend on the wavelength of the wavefield
considered and the choice of the model parameterisation. Additional information
should therefore be incorporated to regularise the problem such as the
imposition of petrological constraints to match the geodynamic predictions.
