Before revision:  Using the energy method we prove that the numerical method is numerically stable , and energy conserving. Furthermore, computational results show the robustness of the scheme. We present numerical simulations of the 3D elastic wave equation in heterogeneous media with complex non-planar free surface topography  , including numerical simulations of community developed seismological benchmark problems.
After revision:  Using the energy method we prove that the semi-discrete approximation is stable and energy-conserving. We derive a priori error estimate and prove the convergence of the numerical error. Numerical experiments for the 3D elastic wave equation in complex geometries corroborate the theoretical analysis. Numerical simulations of the 3D elastic wave equation in heterogeneous media with complex non-planar free surface topography , including numerical simulations of community developed seismological benchmark problems.