  This paper concerns an inverse elastic scattering problem which is to
determine a rigid obstacle from time domain scattered field data for a single
incident plane wave. By using Helmholtz decomposition, we reduce the
initial-boundary value problem of the time domain Navier equation to a coupled
initial-boundary value problem of wave equations, and prove the uniqueness of
the solution for the coupled problem by employing energy method. The retarded
single layer potential is introduced to establish the coupled boundary integral
equations, and the uniqueness is discussed for the solution of the coupled
boundary integral equations. Based on the convolution quadrature method for
time discretization, the coupled boundary integral equations are reformulated
into a system of boundary integral equations in s-domain, and then a
convolution quadrature based nonlinear integral equation method is proposed for
the inverse problem. Numerical experiments are presented to show the
feasibility and effectiveness of the proposed method.

Numerical Analysis;Numerical Analysis