Inverse scattering problem for a rigid scatterer or a cavity in elastodynamics

We consider the inverse scattering problem for the shape determination of a rigid scatterer or a cavity in a homogeneous and isotropic elastic medium. Both problems are formulated in R-2 for time-harmonic fields and longitudinal or transversal incident plane waves. Representation of the scattered field as a single- or a double-layer potential, equivalently, leads to a system of two nonlinear integral equations for the density and the parametrization of the boundary. A detailed numerical implementation is presented for computing the corresponding solutions of both systems and numerical reconstructions are given to show the effectiveness of the method. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim