A general optimal method for a 2D frequency-domain finite-difference solution of scalar wave equation

Abstract

We have developed a general optimal method for 2D frequency-domain finite-difference simulation of the scalar wave equation. For a given finite-difference stencil, this method can generate the dispersion equation and optimize the expansion coefficients. Many commonly used frequency-domain finite-difference schemes (e.g., grids with different numbers of points, rotated grids, and grid spaces with different aspect ratios) can be derived as special cases under this framework. The possibility of expanding this method to 3D does exist. Based on the 2D scalar wave equation, the optimized coefficients of 25-point, 9-point, 17-point, and 15-point schemes have been worked out. The dispersion analysis indicates that our 25-point scheme has much higher accuracy than the average-derivative method 25-point scheme. The number of grid points per the smallest wavelength is reduced from 2.78 to 2.13 for a maximum phase velocity errors of 1%. The synthetic seismograms and the wavefield snapshots calculated using our optimal 25-point finite-different scheme give smaller dispersions than other finite-difference schemes.