Spatio-temporal higher-order finite-difference solution for the scalar acoustic wave equation based on the global difference coefficient

Abstract

The partial derivatives obtained through the difference approximation in the finite-difference method for solving the scalar acoustic wave equation may give rise to computational errors, which have the potential to induce numerical dispersion. Typically, the temporal or spatial higher-order difference format is employed, whereby the difference order between the computational region and the perfectly matched layer (PML) boundaries can result in boundary reflections. In this study, we derive the acoustic wave equation and its PML boundary conditions in the finite difference format of the temporal fourth-order and the spatial 2Nth-order, based on the Lax-Wendroff method. Subsequently, the stability conditions of the two finite difference formats are presented and analyzed under different parameters. This effectively addresses the issue of temporal dispersion. Furthermore, the high-order PML temporal boundary conditions effectively suppress the boundary reflection phenomenon generated by the computational regions and the different difference orders of the PML boundaries. Moreover, the time-space dispersion relation of the acoustic wave equation is employed to globally optimize the difference coefficients via the least-squares method, thereby suppressing the spatial dispersion. The numerical solution experiments of the acoustic wave equation for the horizontal laminar model and the Marmousi model demonstrate the efficacy of the presented algorithm.

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Funding

National Natural Science Foundation of China(42274149)

Natural Science Foundation of Shandong Province(ZR2022MD074)

RIGHTS & PERMISSIONS

The Author(s)