Linear sampling methods for 2D inverse elastic wave scattering

The problem of determining the shape of a rigid body from the knowledge of the far-field patterns of incident plane compressional and shear waves in two-dimensional elasticity is considered. We discuss the application of the original linear sampling method and of the related (F * F) (1/4)-method to tackle this problem. It is established that the far-field operator is compact and normal. A theoretical basis for both reconstruction methods is developed and numerical results are shown, illustrating the excellent quality of reconstructions attainable.