Simone Puel , Thorsten W. Becker , Umberto Villa , Omar Ghattas, Dunyu Liu 

Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson's ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding non-linear inversion is implemented using adjoint-based optimization that efficiently reduces the cost functional that includes the misfit between the calculated and observed displacements and a penalty term.
We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth's structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, e.g. geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.