Energy-conserving 3D elastic wave simulation with finite difference discretization on staggered grids with nonconforming interfaces

In this work, we describe an approach to stably simulate the 3D isotropic elastic wave propagation using finite difference discretization on staggered grids with nonconforming interfaces. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by planar interfaces. This discretization setting is motivated by the observation that wave speeds of earth media tend to increase with depth due to sedimentation and consolidation processes. We demonstrate that the layer-wise finite difference discretization approach has the potential to significantly reduce the simulation cost, compared to its counterpart that uses holistically uniform grids. Such discretizations are enabled by summation-by-parts finite difference operators, which are standard finite difference operators with special adaptations near boundaries or interfaces, and simultaneous approximation terms, which are penalty terms appended to the discretized system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized system is shown to preserve the energy-conserving property of the continuous elastic wave equation, and a fortiori ensure the stability of the simulation. Numerical examples are presented to corroborate these analytical developments.