Inverse Boundary Value and Inverse Scattering Problems

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

PI: James Ralston/Gregory Eskin DMS-0139192 Abstract Inverse scattering problems arise when one wishes to recover physical properties of an object from data obtained by remote observations or from measurements made on its surface without penetrating the interior. Interpreted broadly they include methods of nondestructive testing and medical imaging. The problems proposed here include showing that it is possible, in principle, to determine the properties of an inhomogeneous elastic body from its response to pressures on its surface, and to determine both the acoustic properties of a medium surrounding a solid obstacle and the obstacle itself from reflected sound waves. More specifically, the problems we propose include: 1) showing that it is possible to uniquely determine the Lame' parameters of an inhomogeneous elastic body from its response to infinitesimal boundary deformations. 2) For an obstacle in an inhomogeneous medium we propose to show that both the obstacle and the sound speed in the medium can be recovered from the scattering amplitude at a fixed frequency. 3) Do problem 2) in the more technically difficult case of two space dimensions, where it becomes a "determined" inverse problem.