The inverse scattering problem in three-dimensional elasticity

In this paper the inverse rigid scatterer problem in, linear elasticity is considered. A uniquely solvable integral equation which describes the scattering process is used to compute the elastic scattering amplitudes. A classical regularization procedure is proposed in order to reduce the integral equation to a Fredholm type equation with compact integral operators. A continuity dependence of the far-field amplitudes upon the shape of the scatterer is proved to stabilize the inverse problem and an optimization scheme is proposed to derive quasi solutions incorporating a priori data about the shape of the scatterer.