A new linear optimized time–space domain spatial implicit and temporal high-order finite-difference scheme for scalar wave modeling

Abstract

Suppressing the numerical dispersion is one of the key items for the finite-difference (FD) method. Usually, approximating the spatial derivatives by the implicit FD stencil is an effective approach to suppress the spatial dispersion for acoustic wave modeling. However, the temporal accuracy is still limited. To tackle this issue, we propose a new time–space domain (TS-D) implicit FD scheme, which could reach the arbitrary even-order temporal and spatial accuracy by adding a few additional grid points to the original implicit FD stencil. Compared with the existing spatial implicit and temporal high-order methods in the TS-D, our new scheme reduces 4N + 1 grid points, while reaches equivalent temporal and spatial high-order accuracy. To further enhance the simulation accuracy, a linear optimization strategy is developed by combining the Taylor series expansion (TE) and the least-squares methods. Our linear optimization strategy avoids the non-linear iterative optimization of the current spatial implicit and temporal high-order methods. Comparisons of the conventional TE- and optimization-based implicit methods demonstrate the accuracy and efficiency superiorities of our new linear optimized FD scheme.