A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only
Abstract
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic parameters is possible, even for discontinuous parameters and without boundary information. We provide a general approach based on the weak definition of the stiffness-to-force operator which conduces to see the problem as a linear system. We prove that in the case of shear modulus reconstruction, we have an -stability with only one measurement under minimal smoothness assumptions. This stability result is obtained though the proof that the linear operator to invert has closed range. We then describe a direct discretization which provides stable reconstructions of both isotropic and anisotropic stiffness tensors.
Keywords
Cite
@article{arxiv.1806.03147,
title = {A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only},
author = {Habib Ammari and Elie Bretin and Pierre Millien and Laurent Seppecher},
journal= {arXiv preprint arXiv:1806.03147},
year = {2018}
}