A novel method to solve large scale 3D inverse problems with application to continental collision

Simulating geodynamic processes such as mountain building has become possible in recent years. Since rock rheology and initial parameters are usually poorly constrained, determining them from the observations is an inverse problem. There are broadly two classes of inversion techniques adopted in geodynamics: (i) The adjoint method, which is a gradient-based algorithm combined with the adjoint evaluation of the misfit function gradient, and (ii) the Neighborhood Algorithm (NA), which falls into the class of adaptive direct-search algorithms. Both methods have advantages and pitfalls. Adjoint methods are computationally efficient, but sensitive to the local minima. The NA, on the other hand, is able to identify the global minimum, but becomes very computationally expensive if the high-dimensional parameter space is considered.

In this project, we propose a synergetic approach between the two techniques. The new method, which we call MISO (Multivariate Inversion by Surrogate Optimization) relies on building of a misfit function interpolant, similar to NA, but enhances it with the gradients from the adjoint method. Preliminary tests show that MISO is indeed capable of solving the typical inverse problems, while requiring significantly less number of forward problem evaluations compared to NA. In this project we will further develop the new method and apply it to the challenging India-Asia continental collision problem in 3D.