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The finite difference (FD) methods are widely used for approximating the partial derivatives in the acoustic/elastic wave equation. Grid dispersion is one of the key numerical problems and will directly influence the accuracy of the result because of the discretization of the partial derivatives in the wave equation. Therefore, it is of great importance to suppress the grid dispersion by optimizing the FD coefficient. Various optimized methods are introduced in this chapter to determine the FD coefficient. Usually, the identical staggered grid finite difference operator is used for all of the first-order spatial derivatives in the first-order wave equation. In this chapter, we introduce a new staggered grid FD scheme which can improve the efficiency while still preserving high accuracy for the firstorder acoustic/elastic wave equation modeling. It uses different staggered grid FD operators for different spatial derivatives in the first-order wave equation. The staggered grid FD coefficients of the new FD scheme can be obtained with a linear method. At last, numerical experiments were done to demonstrate the effectiveness of the introduced method.

Optimized Finite Difference Methods for Seismic Acoustic Wave Modeling