A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only

The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements some displacement fields inside medium, we show that stable reconstruction elastic parameters possible, even discontinuous without boundary information. We provide general approach based on weak definition stiffness-toforce operator which conduces see problem as system. prove in case shear modulus reconstruction, have an L 2-stability with only one measurement under minimal smoothness assumptions. This stability result obtained though proof invert has closed range. then describe discretization provides reconstructions both isotropic anisotropic stiffness tensors.