Estimating basal properties of glaciers from surface measurements: A non-linear Bayesian inversion approach applied to synthetic data

We introduce a non-linear Bayesian inference approach to estimate the basal properties of a glacier, i.e. bedrock topography and basal slipperiness from observations of surface topography and surface velocities. The inverse procedure is based on an iterative Newtonian optimization of a cost function involving a forward step solved with a numerical finite-element model. The first order forward model derivatives needed for inversion are approximated by analytical linear transfer functions (Gudmundsson, 2003). Using synthetic surface data generated with a forward finite-element model, we show that the inversion procedure resolves accurately the perturbations and converges quickly to the correct solution. The number of iterations needed for convergence increases with the amplitude of the basal perturbations.