THE INVERSE SCATTERING PROBLEM IN LINEAR ELASTICITY VIA A PAIR OF NONLINEAR INTEGRAL EQUATIONS

We consider the inverse problem of determining the shape of a rigid scatterer inside a homogeneous and isotropic elastic medium. The problem is stated in R-2 and the wave field is assumed to be time-harmonic. The inverse boundary value problem consists of solving a pair of nonlinear and ill-posed integral equations for the unknown boundary derived from a single layer representation of the scattered field. A linearization of the equations is performed using Frechet derivatives of the integral operators. The ill-posedness of the system leads to regularization via Tikhonov method. Numerical examples are given which illustrate the applicability of the method.