UNIQUENESS THEOREMS IN INVERSE OBSTACLE SCATTERING OF ELASTIC-WAVES

We consider the scattering of plane elastic waves in an isotropic homogeneous medium at an obstacle assuming boundary conditions of the first kind. We state existence and uniqueness of the direct problem. Then we prove that the far field patterns for a bounded sequence of different frequencies and an incoming plane wave with fixed incident direction and fixed polarization uniquely determine the obstacle. Finally, we prove the same result for a fixed frequency but for all incident directions and a certain set of polarizations.