Georgia Institute of Technology College of Sciences

We discuss the inverse problem of determining elastic parameters in the interior of an anisotropic elastic media from dynamic measurements made at the surface. This problem has applications in medical imaging and seismology. The boundary data is modeled by the Dirichlet-to-Neumann map, which gives the correspondence between surface displacements and surface tractions. We first show that, without a priori information on the anisotropy type, uniqueness can hold only up to change of coordinates fixing the boundary. In particular, we study orbits of elasticity tensors under diffeomorphisms. Then, we obtain partial uniqueness for special classes of transversely isotropic media. This is joint work with L. Rachele (RPI).