Direct and inverse elastic scattering from anisotropic media

Assume that a time-harmonic elastic wave is incident onto a penetrable anisotropic elastic body embedded in a homogeneous isotropic background medium. The scattering problem is reduced to a truncated domain. Uniqueness and existence of weak solutions are proved by applying the Fredholm alternative and using properties of the Dirichlet-to-Neumann map in both two and three dimensions. The Frechet derivative of the near-field solution operator with respect to the boundary of the scatterer is derived. As an application, a descent algorithm is designed for recovering the interface from the near-field data of one or several incident directions and frequencies. Numerical examples in 2D are presented to show the validity and accuracy of the algorithm. (C) 2018 Elsevier Masson SAS. All rights reserved.