Cross-rhombus stencil-based finite-difference methods for 2D acoustic modeling and reverse-time migration on rectangular grids

Abstract

The recently developed cross-rhombus stencil-based time–space domain finite-difference (FD) method for modeling two-dimensional acoustic equations, controls the temporal and spatial dispersions synchronously and outperforms cross-stencil-based FD (CS-FD). However, it is only applicable to modeling on equally spaced grids and extensive application is hindered. In this work, we extend it further and develop novel cross-rhombus stencil-based FD (CRS-FD) for modeling on arbitrarily rectangular grids. Two kinds of rhombus stencils involving grid points both on and off the axis are developed first to achieve fourth order and sixth order FD accuracies, respectively, for solving the second order temporal derivative on rectangular grids. The plane wave theory is then used to derive the time–space-domain dispersion relations, when the temporal and spatial derivatives are solved by the new rhombus-stencil-based temporal high order FD and the cross-stencil-based spatial high order FD, respectively. The extrapolation stencil is a mixture of rhombus and cross stencils, and the involved FD coefficients are determined by applying the Tayler expansion on the time–space domain dispersion relation. Our new CRS-FD is high-order accurate in both time and space, and applicable to modeling on arbitrarily rectangular grids. Dispersion analysis, stability analysis and modeling examples on rectangular grids show that the CRS-FD is more accurate and stable than the CS-FD. Meanwhile, we develop the variable-length schemes for CRS-FD to further increase efficiency and apply them to extrapolate wavefields in reverse time migration. The results validate that the CRS-FD is more efficient than the CS-FD because much larger time steps can be used while reaching a similar accuracy. The variable-length scheme further reduces the computational time in comparison with the fixed-length scheme.