Dr. Thi-Phong Nguyen, University of Minnesota (hosted by Loc Nguyen)
Title: Sampling methods for inverse elastic scattering problems in finite solid bodies.
Abstract: I will present and discuss in this talk sampling methods to reconstruct partially-closed fractures in rock from surface seismic measurements. For the mathematical viewpoint, the fracture is characterized by a second order tensor synthesizing its special stiffness – relation the jump in seismic field cross the fracture to the contact traction. This method relies on a careful analysis of so-called Generalized Linear Sampling Method to build an indicator function for detecting the fracture. The first challenging of this problem is tensorial quantity intrinsically dependent on the fractures’ aperture and the surface roughness, which makes it partially heterogeneous and difficult to solve. The second one is to deal with the near-filed measurement (which has very little reference) and to numerically approximate the gradient of Green tensor in finite space, which can not be expressed by an analytic formula. Some related numerical results will be presented at the end.