We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse problem when the Lam\'{e} parameters and the density are assumed to be piecewise constant on a given domain partition.
@article{arxiv.1412.3465,
title = {Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves},
author = {Elena Beretta and Maarten V. de Hoop and Elisa Francini and Sergio Vessella and Jian Zhai},
journal= {arXiv preprint arXiv:1412.3465},
year = {2014}
}