Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes - Liu, Wei; Hu, Ziduo; Yong, Xueshan; Peng, Gengxin; Xu, Zhonghua; Han, Linghe (Frontiers in Earth Science, 2022)
Conventional staggered-grid finite-difference schemes (C-SFD) can make the spatial finite-difference (FD) operator to achieve (2M)th-order accuracy, but the corresponding FD discrete wave equation can only reach 2nd-order accuracy, which leads to low modeling accuracy and poor stability. In this paper, by constructing a spatial FD operator using the axial and off-axial grid points jointly to approximate the first order spatial partial derivative, we propose a new kind of mixed staggered-grid finite-difference schemes (M-SFD), which is suitable for the stress-velocity acoustic and elastic wave equation numerical modeling. And then based on the time-space domain dispersion relation and the Taylor series expansion, we derive the analytical expression of the FD coefficients. The FD discrete acoustic wave equation and P-wave or S-wave in the FD discrete elastic wave equation given by M-SFD can reach 4th-order, 6th-order, 8th-order, or arbitrary even-order accuracy. For acoustic wave modeling, compared to C-SFD, M-SFD can suppress the numerical dispersion more effectively to obtain higher modeling accuracy with almost the same computational efficiency. What’s more, M-SFD can achieve higher computational efficiency by adopting a larger time step and reach higher modeling accuracy at the same time. For elastic wave modeling, compared to C-SFD, M-SFD can obtain higher modeling accuracy with almost the same computational efficiency when the FD coefficients are calculated based on the S-wave time-space domain dispersion relation. Meanwhile, M-SFD can further improve the modeling accuracy by adopting the decomposed elastic wave equation, but which will increase the amount of calculation and memory. Stability analysis shows that the FD discrete acoustic and elastic wave equations given by M-SFD have better stability than C-SFD. We further extend M-SFD to RTM, and M-SFD can effectively eliminate the imaging artifacts caused by the numerical dispersion, which successfully improves the imaging accuracy and resolution of deep structure.