An inverse problem in fault detection

Abstract: I will discuss a model for dislocations in an elastic medium, modeling faults in the Earth’s crust. The direct problem consists in solving a non-standard boundary value/interface problem for isotropic linear elasticity with piecewise Lipschitz Lame’ parameters. The inverse problem consists in determining the fault surface and slip vector from displacement measurements made at the surface. We prove uniqueness under some geometric conditions, using unique continuation results. The results extend to certain anisotropic media in 2 dimensions. We also establish shape derivative formulas under infinitesimal movements of the fault and changes in the slip. . This is joint work with Andrea Aspri (Milan University), Elena Beretta (NYU-Abu Dhabi), and Maarten de Hoop (Rice University).

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine