A combined Reduced Order-Bayesian scheme to drastically accelerate stochastic inversions

One of the main challenges in modern geophysics is the understanding and characterization of the present-day physical state of the thermal and compositional structure of the Earth’s lithospheric and sub-lithospheric mantle. In doing so, high resolution inverse problems need to be solved (with thousands of parameters to determine).
One of the most abundant and better constrained data used for the inversion is the Earth’s topography. Despite its quality, the topography models included in inversion schemes are usually very simplistic, based on density contrasts and neglecting dynamic components. The reason for this is simply computational efficiency; 3D dynamical models are too expensive to be embedded within inversion schemes.
In this context we propose the use of a greedy reduced basis strategy within a probabilistic Bayesian inversion scheme (MCMC) that makes feasible accounting for the fully dynamic topography model within the inversion.

We tested the proposed approach in a synthetic experiment aiming to recover the base of the African plate. It is well-agreed within the geophysical community that the dynamic component in the region is of first order importance. Our scheme is able to successfully recover the expected shape of the plate while reducing the computational time to less than 1% when compared to a full Finite Element approach.