  We consider the numerical simulation of the acoustic wave equations arising
from seismic applications, for which staggered grid finite difference methods
are popular choices due to their simplicity and efficiency. We relax the
uniform grid restriction on finite difference methods and allow the grids to be
block-wise uniform with nonconforming interfaces. In doing so, variations in
the wave speeds of the subterranean media can be accounted for more
efficiently. Staggered grid finite difference operators satisfying the
summation-by-parts (SBP) property are devised to approximate the spatial
derivatives appearing in the acoustic wave equation. These operators are
applied within each block independently. The coupling between blocks is
achieved through simultaneous approximation terms (SATs), which impose the
interface condition weakly, i.e., by penalty. Ratio of the grid spacing of
neighboring blocks is allowed to be rational number, for which specially
designed interpolation formulas are presented. These interpolation formulas
constitute key pieces of the simultaneous approximation terms. The overall
discretization is shown to be energy-conserving and examined on test cases of
both theoretical and practical interests, delivering accurate and stable
simulation results.
