Time-space Domain Finite-difference Method with Arbitrary Even-order Accuracy for the 2D Acoustic Wave Equation

High-order finite-difference (FD) methods have been widely used in numerically solving seismic wave equations. It has been reported that the modeling accuracy is 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 for the 2D acoustic wave equation can improve the accuracy from second-order to (2M)th-order accuracy along eight directions. To increase the accuracy further, we propose a new FD stencil for the 2D acoustic wave equation modeling. This new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order 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.