Thermoacoustic Tomography in Elastic Media

Abstract

We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 is some bounded domain containing the support of f . For the acoustic wave equation, this problem is known as thermoacoustic tomography (TAT), and has been well-studied; for the elastic wave equation, the situation is somewhat more subtle, and we give sufficient conditions on the Lame parameters to ensure that recovery is possible. Following this, we investigate the numerical simulation of this problem.