Estimating optimal parameters of finite-difference scheme for wavefield modeling

The finite-difference (FD) method is widely used for simulating complex wavefield propagation because of its high accuracy and efficiency. However, it suffers from numerical dispersions caused by spatial discretization with coarse grid sizes. The dispersions affect the computational efficiency and modeling accuracy. This study investigates the relationship among numerical dispersion error, FD operators, and the number of samples per shortest wavelength. Based on the criterion of minimum computational cost, we propose a scheme to estimate the optimal FD parameters, i. e., the number of samples per shortest wavelength and the spatial order of FD operators. Firstly, we introduce a method called Forward Space Dispersion Transform (FSDT) to add spatial dispersion to the reference wavefield for various scenarios of grid spacing and FD orders; Secondly, we measure the normalized L2 norm of the error between the reference wavefield and dispersed wavefield, so we can estimate the dispersion error directly to set a proper error threshold; Finally, we study the relationship among FD coefficients, FD operator length, grid spacing, and computational cost to find out the optimal grid spacing and FD order for giving the minimum computational cost under a preset error threshold. We also show some numerical tests of the relationship among the FD operator length, grid points per shortest wavelength, and computational cost under an error threshold of 0. 01 with the finite-difference coefficients generated using the Remez Exchange (RE) method and Taylor-series Expansion (TE) method. Based on the tests, some FD parameters are recommended.