Dislocations in a layered elastic medium with applications to fault detection

We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting mixed-boundary-value-transmission problem, assuming only bounded elastic moduli. We establish uniqueness in the inverse problem of determin-ing the fault surface and the slip from a unique measurement of the displacement on an open patch at the surface, assuming in addition that the Earth's crust is an isotropic, layered medium with Lame coefficients piecewise Lipschitz on a known partition and that the fault surface satisfies certain geo-metric conditions. These results substantially extend those of the authors in [Arch. Ration. Mech. Anal. 236, 71-111 (2020)].