Faults in elastic half space: direct and inverse problem

This paper starts from a model in geophysics for the quasi static evolution of displacement fields occurring during the destabilization of a fault subject to excessive stress. A boundary value problem in elastic half space with specified jump and continuity conditions across the fault is formulated, and the adequate Green's tensor for this problem is introduced. We prove that the fault inverse problem can be in some approximate sense solved solely from surface displacements. Finally, we discuss progress on recent work regarding a related eigenvalue problem of Steklov kind across faults.