An elongated finite-difference scheme for 2D acoustic and elastic wave simulations in the frequency domain

Abstract

We have developed a novel scheme to simulate acoustic and elastic wave propagation in the frequency-domain using a rectangular finite-difference (FD) stencil. One of the main problem of the frequency-domain modeling is its huge computational costs, i.e., the calculation time and memory usage. To overcome this problem, researchers have proposed many schemes to reduce the number of grid points in a wavelength. In general, high-accuracy schemes require large-sized stencils that cause increment in the bandwidth of the impedance matrix. It is, therefore, important to improve the accuracy of numerical schemes without increasing the bandwidth. We have applied an elongated stencil with different sampling ratio between horizontal and vertical directions to circumvent extra numerical bandwidth in the impedance matrix. Optimal FD coefficients and the aspect ratio of the grid cell are determined to minimize the error of the phase velocity. We investigate the dispersion property of the proposed scheme using plane-wave analysis. The dispersion analysis indicates that we could reduce the number of grid points in a wavelength by approximately 2.78 for acoustic wave modeling and by approximately 3.15 for elastic wave modeling so that the error of the phase velocity is less than 1%. We also conduct numerical simulations using homogeneous and inhomogeneous models to demonstrate the effectiveness of our scheme. The comparison of numerical accuracy and computational costs between our scheme and the conventional ones indicates that the computational costs (calculation time, memory usage) can be reduced with high numerical accuracy especially in elastic wave modeling. Because our technique is a simple and a powerful cost-efficient frequency-domain method, the elongated stencil can be an alternative scheme to the conventional ones for acoustic and elastic wave modeling.