Layer Stripping for a Transversely Isotropic Elastic Medium

Abstract

In this paper we develop a layer stripping algorithm for transversely isotropic elastic materials in three-dimensional space. We first prove that by making displacement and traction measurements at the boundary of these elastic materials one can determine the elastic tensor and all its derivatives at the boundary. The elastic measurements made at the boundary are encoded in the Dirichlet to Neumann (DN) map. Then we use the Riccati equation developed in [G. Nakamura and G. Uhlmann, A layer stripping algorithm in elastic impedance tomography, in Inverse Problems in Wave Propagation, IMA Vol. Math. 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.