We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in R3 via a finite-time Laplace transform. The data are 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 Lamé 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.