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 jumps only along 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 establish shape derivative formulas under infinitesimal movements of the fault and changes in the slip. The application of the inverse problem is in fault monitoring and microseismicity. This is joint work with Andrea Aspri (Pavia University), Elena Beretta (Politechnico, Milan & NYU-Abu Dhabi), and Maarten de Hoop (Rice).

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

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