Numerical modeling of elastic wave in frequency-domain by using staggered grid fourth-order finite-difference scheme

Abstract

Simulation of elastic wave propagation is an important method for oil and gas exploration. Accuracy and efficiency of elastic wave simulation in complex geological environment are always the focus issue. In order to improve the accuracy and efficient in numerical modeling of elastic modeling, a staggered grid fourth-order finite-difference scheme of modeling elastic wave in frequency-domain is developed, which can provide stable numerical solution with fewer number of grid points per wavelength. The method is implemented on first-order velocity-stress equation and a parsimonious spatial staggered-grid with fourth-order approximation of the first-order derivative operator. Numerical tests show that the accuracy of the fourth-order staggered-grid stencil is superior to that of the mixed-grid and other conventional finite difference stencils, especially in terms of shear-wave phase velocity. Measures of mass averaging acceleration and optimization of finite difference coefficients are taken to improve the accuracy of numerical results. Meanwhile, the numerical accuracy of the finite difference scheme can be further improved by enlarging the mass averaging area at the price of expanding the bandwidth of the impedance matrix that results in the reduction of the number of grid points to 3 per shear wavelength and computer storage requirement in simulation of practical models. In our scheme, the phase velocities of compressional and shear wave are insensitive to Poisson's ratio that does not occur to conventional finite difference scheme in most cases, and also the elastic wave modeling can degenerate to acoustic case automatically when the medium is pure fluid or gas. Furthermore, the staggered grid scheme developed in this study is suitable for modeling waves propagating in media with coupling fluid-solid interfaces that are not resolved very well for previous finite difference method. Cited as : Ma, C., Gao, Y., Lu, C. Numerical modeling of elastic wave in frequency-domain by using staggered grid fourth-order fifinite-difference scheme. Advances in Geo-Energy Research, 2019, 3(4): 410-423, doi: 10.26804/ager.2019.04.08