  We consider the inverse boundary value problem for the system of equations
describing elastic waves in isotropic media on a bounded domain in
$\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical
Dirichlet-to-Neumann map. More precisely, using the full symbol of the
transformed Dirichlet-to-Neumann map viewed as a semiclassical
pseudodifferential operator, we give an explicit reconstruction of both
Lam\'{e} parameters and the density, as well as their derivatives, at the
boundary. We also show how this boundary reconstruction leads to a
decomposition of incoming and outgoing waves.
