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Texas A&M University

Events for 09/01/2020 from all calendars

Nonlinear Partial Differential Equations

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Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Anna Mazzucato, Penn State University

Title: Direct and inverse problems for a model of dislocations in geophysics

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, in-homogeneous linear elasticity with piecewise Lipschitz Lame' parameters, for which we prove well-posedness and a double-layer potential representation for the solution if the coefficients do not jump except at the fault. The non-linear 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 for systems. We also established a distributed shape derivative under infinitesimal movements of the fault for an iterative reconstruction algorithm. The application of the inverse problem is in fault monitoring in the interseimic period. This is joint work with Andrea Aspri (RICAM, Linz), Elena Beretta (NYU-Abu Dhabi), and Maarten de Hoop (Rice).