Layer stripping for a transversely isotropic elastic medium

In this paper we develop a layer stripping algorithm for transversely isotr opic elastic materials in three-dimensional space. We first prove that by m aking displacement and traction measurements at the boundary of these elast ic materials one can determine the elastic tensor and all its derivatives a t the boundary. The elastic measurements made at the boundary are encoded i n the Dirichlet to Neumann (DN) map. Then we use the Riccati equation devel oped in [G. Nakamura and G. Uhlmann, A layer stripping algorithm in elastic impedance tomography, in Inverse Problems in Wave Propagation, IMA Vol. Ma th. Appl. 90, Springer-Verlag, New York, 1997, pp. 375-384] for the DN map in any anisotropic elastic medium to approximate the elastic tensor in the interior.