  We develop a stable finite difference method for the elastic wave equation in
bounded media, where the material properties can be discontinuous at curved
interfaces. The governing equation is discretized in second order form by a
fourth or sixth order accurate summation-by-parts operator. The mesh size is
determined by the velocity structure of the material, resulting in
nonconforming grid interfaces with hanging nodes. We use order-preserving
interpolation and the ghost point technique to couple adjacent mesh blocks in
an energy-conserving manner, which is supported by a fully discrete stability
analysis. In our previous work for the wave equation, two pairs of
order-preserving interpolation operators are needed when imposing the interface
conditions weakly by a penalty technique. Here, we only use one pair in the
ghost point method. In numerical experiments, we demonstrate that the
convergence rate is optimal, and is the same as when a globally uniform mesh is
used in a single domain. In addition, with a predictor-corrector time
integration method, we obtain time stepping stability with stepsize almost the
same as given by the usual Courant-Friedrichs-Lewy condition.
