An improved 25‐point finite‐difference scheme for frequency‐domain elastic wave modelling

Abstract

Frequency‐domain finite‐difference modelling is widely used in exploration geophysics. However, it involves solving a large system of linear algebraic equations, which may cause huge computational costs, especially for large‐scale models. To address this issue, we have proposed an improved 25‐point finite‐difference scheme for wavefield modelling of two‐dimensional frequency‐domain elastic wave equations. The biggest difference between the improved 25‐point scheme with other 25‐point schemes is the finite‐difference formulas for spatial derivatives. The proposed 25‐point scheme applies to equal and unequal grid intervals, and its optimization coefficients depend on the grid‐spacing ratio and Poisson's ratio. The dispersion analysis indicates that within the phase velocity errors of 1% and 2%, the improved 25‐point scheme only requires approximately 2.3 and 2.2 grid points per shear wavelength, which has greater accuracy than the existing schemes. To eliminate artificial boundary reflections, we apply the perfectly matched layer boundary conditions to the model edges. Several numerical examples are presented to prove the validity of the improved 25‐point scheme.