A uniqueness theorem in inverse scattering of elastic waves

The scattering of plane elastic waves in an isotropic inhomogeneous medium is considered. The existence and uniqueness of the direct problem is stated, and a reciprocity principle for the far fields of the scattered waves formulated. Finally, it is proved that the knowledge of the far-field patterns for a bounded sequence of different frequencies and certain sets of incoming plane waves uniquely determines the density of the medium. 1