  We consider an isotropic elastic medium occupying a bounded domain D whose
density and Lam\'e parameters are piecewise smooth. In the elastic wave initial
value inverse problem, we are given the solution operator for the elastic wave
equation, but only outside the domain D and only for initial data supported
outside D, and we study the recovery of the density and Lam\'e parameters. For
known density, results have recently been obtained using the scattering control
method to recover wave speeds. Here, we extend this result to include the
recovery of the density in addition to the Lam\'e parameters under certain
geometric conditions using techniques from microlocal analysis and a connection
to local tensor tomography.
