  We present an approach to simulate the 3D isotropic elastic wave propagation
using nonuniform finite difference discretization on staggered grids.
Specifically, we consider simulation domains composed of layers of uniform
grids with different grid spacings, separated by nonconforming interfaces. We
demonstrate that this layer-wise finite difference discretization has the
potential to significantly reduce the simulation cost, compared to its fully
uniform counterpart. Stability of such a discretization is achieved by using
specially designed difference operators, which are variants of the standard
difference operators with adaptations near boundaries or interfaces, and
penalty terms, which are appended to the discretized wave system to weakly
impose boundary or interface conditions. Combined with specially designed
interpolation operators, the discretized wave system is shown to preserve the
energy conserving property of the continuous elastic wave equation, and
$\textit{a fortiori}$ ensure the stability of the simulation. Numerical
examples are presented to demonstrate the efficacy of the proposed simulation
approach.
