An optimized 13-point finite-difference operator for 2D frequency-domain acoustic wave modeling

Abstract The finite-difference method has seen widespread application in frequency-domain forward modeling, but the scheme for the finite-difference (FD) operator shows a negative correlation between the accuracy and computational speed of numerical simulation. How to design an optimal difference operator is crucial for enhancing the accuracy and efficiency of the simulation. In this study, we propose a new 13-point stencil based on combining the fourth-order 9-point FD operator in a 0° coordinate system with the second-order 5-point FD operator in a 45° rotated coordinate system. The new FD coefficients are optimized by the sequential genetic algorithm and Broyden–Fletcher–Goldfarb–Shanno algorithm. We analyze dispersion, accuracy, and efficiency for 9-, 13-, and 17-point stencils. The tests show that the 13-point stencil necessitates 2.55 grid points for the smallest wavelength with a phase velocity deviation <1%, and the ability to suppress dispersion is comparable to the 17-point stencil. Numerical modeling with this 13-point FD stencil is applicable for both acoustic and viscoacoustic mediums, which can guarantee accuracy with only half the computation time of the 17-point stencil.