I will discuss a model of elastic dislocations applicable to buried faults in the Earth’s crust between seismic events. The forward problem amounts to solving a non-standard transmission problem for a system of linear PDES in elastostatics, knowing the fault and how much the rock has slipped at the fault. The inverse problem consists in determining the geometry of the fault and the slip at the fault from surface measurements, which can be obtained from  GPS and satellite data. While the direct problem is well posed, the inverse problem is generally ill-posed unless assumptions are made on the fault.
I will present a uniqueness result for the inverse problem and an iterative reconstruction algorithm based on a distributed shape derivative, which measures the change in the rock displacement under infinitesimal movements of the fault and the slip. I will close with some simple numerical  tests from synthetic data.
This is joint work with Andrea Aspri (University of Milan), Elena Beretta (NYU-Abu Dhabi), and Maarten de Hoop (Rice University).

Refreshments will be served preceding the talk, starting at 2:45.