  Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose
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 $\Omega$ and only for initial data supported outside
$\Omega$. Using the recently introduced scattering control series in the
acoustic case, we prove that piecewise smooth Lam\'e parameters are uniquely
determined by this map under certain geometric conditions. We also show the
extent that multiple scattering in the interior may be suppressed and
eliminated with access to only this partial solution map, which is akin to the
dynamic Dirichlet-to-Neumann map.
