Temporal and spatial high-order accuracy implicit finite-difference method for modeling acoustic wave equation on rectangular staggered-grid

The Finite-Difference (FD) method has become one of the most popular numerical simulation methods for seismic exploration due to its easy implementation and low computational consumption. However, using discrete difference explicit operators to numerically approximate the continuous derivatives of the seismic wave equation will lead to numerical dispersion easily. Besides, the extensive application is hindered by the square-grid discretization. For the numerical simulation of the first-order variable-density acoustic wave equation, we develop a more flexible rectangular-grid discretization-based temporal high-order and spatial implicit FD scheme, which can effectively suppress the temporal and spatial dispersions. Based on the time-space domain dispersion relation of our proposed new FD scheme, also combined with a variable substitution idea, we first use the Taylor series expansion method to solve the off-axial temporal and axial spatial FD coefficients in different directions to obtain arbitrary even-order temporal and spatial accuracy. In order to further improve the spatial accuracy of our proposed FD scheme in a large wavenumber region, a linear optimization method is adopted to obtain the optimized axial spatial FD coefficients of the first-order variable-density acoustic wave equation. Dispersion, stability analysis and numerical examples demonstrate that compared with the conventional cross-stencil-based FD scheme in the space domain, the newly proposed temporal high-order and spatial implicit FD scheme has obvious advantages in terms of simulation accuracy, stability and efficiency.