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We consider the numerical simulation of the acoustic wave equations arisingfrom seismic applications, for which staggered grid finite difference methodsare popular choices due to their simplicity and efficiency. We relax theuniform grid restriction on finite difference methods and allow the grids to beblock-wise uniform with nonconforming interfaces. In doing so, variations inthe wave speeds of the subterranean media can be accounted for moreefficiently. Staggered grid finite difference operators satisfying thesummation-by-parts (SBP) property are devised to approximate the spatialderivatives appearing in the acoustic wave equation. These operators areapplied within each block independently. The coupling between blocks isachieved through simultaneous approximation terms (SATs), which impose theinterface condition weakly, i.e., by penalty. Ratio of the grid spacing ofneighboring blocks is allowed to be rational number, for which speciallydesigned interpolation formulas are presented. These interpolation formulasconstitute key pieces of the simultaneous approximation terms. The overalldiscretization is shown to be energy-conserving and examined on test cases ofboth theoretical and practical interests, delivering accurate and stablesimulation results.

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids