  This paper is concerned with the inverse scattering problem involving the
time-domain elastic wave equations in a bounded $d$-dimensional domain. First,
an explicit reconstruction formula for the density is established by means of
the Dirichlet-to-Neumann operator. The reconstruction is mainly based on the
modified boundary control method and complex geometric optics solutions for the
elastic wave. Next, the stable observability is obtained by a Carleman
estimate. Finally, the stability for the density is presented by the connect
operator.

Analysis of PDEs