https://sites.google.com/view/andrea-aspri/home?authuser=0
Thu, April 24, 2025, 9:00-10:00 am PDT via Zoom
Title: Direct and Inverse Problems for Elastic Dislocations.
Abstract: I will present a mathematical model for dislocations in an elastic medium, aimed at describing faults in the Earth’s crust. The forward problem involves solving a non-standard boundary/interface value problem for inhomogeneous, potentially anisotropic linear elasticity. The associated nonlinear inverse problem is to recover both the fault surface and the slip vector from surface displacement data, typically obtained via GPS arrays and satellite interferometry.
We establish uniqueness results for the inverse problem under certain geometric assumptions, relying on unique continuation properties for elasticity systems. Furthermore, I will present a shape derivative formula that forms the basis of an iterative reconstruction algorithm, along with numerical results in the two-dimensional setting.
The results I will present stem from a body of work developed through a series of collaborative research papers with Elena Beretta (NYU Abu Dhabi), Maarten de Hoop (Rice University), Arum Lee (Penn State University), and Anna L. Mazzucato (Penn State University).