Identification of obstacles using only the scattered P-waves or the scattered S-waves

Abstract

In this work, we are concerned with the inverse scattering by obstacles for the linearized, homogeneous and isotropic elastic model.We study the uniqueness issue of detecting smooth obstaclesfrom the knowledge of elastic far field patterns. We prove that the'pressure' parts of the far field patterns over all directions of measurementscorresponding to all 'pressure' (or all 'shear') incident plane waves areenough to guarantee uniqueness. We also establish that the shear parts ofthe far field patterns corresponding to all the 'shear' (or all 'pressure') incidentwaves are also enough. This shows that any of the two different types ofwaves is enough to detect obstacles at a fixed frequency. The proof is reconstructive and it can be used to set up an algorithmto detect the obstacle from the mentioned data.