A linear sampling method for the inverse transmission problem in near-field elastodynamics

Elastic-wave shape reconstruction of buried penetrable scatterers from near-field surface measurements is examined within the framework of the linear sampling method. The proposed inversion scheme is based on a linear integral equation of the first kind whose solution becomes unbounded as the (trial) source point of the reference Green's function approaches the boundary of an elastic scatterer from its interior. We provide a comprehensive theoretical setting to establish (i) the necessary transmission problems for near-field elastodynamics and (ii) solvability properties of the postulated linear equation in the context of penetrable obstacles. A set of numerical results with simply and multiply connected elastic scatterers is included to illustrate the performance of the reconstruction technique.