Uniqueness and Lipschitz stability of an inverse boundary value problem   for time-harmonic elastic waves
  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. 
Elena Beretta, Maarten V. de Hoop, Elisa Francini, Sergio Vessella,   Jian Zhai
math.AP