Time-space domain high-order finite-difference methods for seismic wave numerical simulation based on new stencils

The traditional finite-difference (FD) seismic wave simulation scheme adopts high order FD operators to discretize the spatial derivatives, and the second-order FD operator to discretize the temporal derivative. Therefore, the traditional high-order FD method only achieves high-order accuracy in space, but exhibits low-order accuracy in time. When a relatively large time step is applied, the traditional FD method suffers from visible temporal dispersion and even instability. This paper develops new time-space domain high-order FD methods that attain arbitrary even-order accuracy in space, fourth- and sixth-order accuracy in time. The new FD methods are developed based on new FD stencils and a centered-grid. The FD coefficients are determined from the discrete dispersion relation using the Taylor-series expansion (TE) approach. Dispersion analysis indicates that our temporal fourth- and sixth-order FD methods improve the accuracy of the traditional temporal second-order FD method significantly. Computational cost analysis demonstrates that our temporal high-order FD methods are more efficient than the traditional temporal second-order method. Numerical simulation of seismic waves in homogeneous and heterogeneous media further validates the effectiveness of our high-order FD methods.