Time–space domain dispersion-relation-based finite-difference method with arbitrary even-order accuracy for the 2D acoustic wave equation

High-order finite-difference (FD) methods have been widely used for numerical solution of acoustic wave equations. It has been reported that the modeling accuracy is of 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. Under the same discretization, the present version of time–space domain dispersion-relation-based FD method can improve the accuracy from 2nd-order to (2M)th-order along eight directions for the 2D acoustic wave equation. To increase the accuracy further, we propose a new FD stencil for 2D acoustic wave equation modeling. This new time–space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order accuracy along all directions, and is more accurate and more stable than the conventional one for the same M. Dispersion analysis and modeling examples demonstrate its advantages.