An optimal method for frequency-domain finite-difference solution of 3D scalar wave equation

To increase the computational accuracy and efficiency of frequency-domain finite difference (FD) modeling method, the optimal FD scheme with rotated coordinate system were widely used. It requires the same spatial sampling intervals in horizontal and vertical directions, which limited their applications in practice. Later the average-derivative method (ADM) was proposed to work with the rectangular-grid modeling. However, these frequency-domain FD operators, unlike the time-domain FD operators of which the coefficients can be determined by a general optimal method even with different stencils, usually have their own forms of differential equations with different distributions of optimized coefficients. In this paper, we develop a general optimal method for frequency-domain FD modeling based on 3D acoustic wave equation. For a given finite-difference stencil, this method can generate the dispersion equation and optimize the expansion coefficients. The advantage of this method is that the optimized coefficients correspond to the grid nodes of FD stencil and it is very easy to expand to other FD schemes. We computed the optimized coefficients of 27- and 7-point schemes with different aspect ratios. Numerical experiments demonstrate that our optimal 27-point scheme have the same accuracy with ADM 27-point scheme and our optimal 7-point scheme have higher accuracy than the classical 7-point scheme.