We consider the question: what can be determined about the stiffness distribution in biological tissue from indirect measurements? This leads us to consider an inverse problem for the identification of coefficients in the secondorder hyperbolic system that models the propagation of elastic waves. The measured data for our inverse problem are the time-dependent interior vector displacements. In the isotropic case, we establish sufficient conditions for the unique identifiability of wave speeds

more »

... d the simultaneous identifiability of both density and the Lamé parameters. In the anisotropic case, counterexamples are presented to exhibit the nonuniqueness and to show the structure of the set of shear tensors corresponding to the same given data.