Modeling 3D acoustic-wave propagation using modified cuboid-based staggered-grid finite-difference methods with temporal
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Department of Geophysics, School of Geology Engineering and Geomatics, Chang’an University, Xi’an 710054, China ([email protected]) State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China
Received: February 18, 2020; Revised: July 26, 2020; Accepted: October 3, 2020
ABSTRACT To improve the modeling accuracy and adaptability of traditional temporal secondorder staggered-grid finite-difference (SFD) methods for 3D acoustic-wave modeling, we propose a modified time-space-domain temporal and spatial high-order SFD stencil on a cuboid grid. The grid nodes on a double-pyramid stencil and the standard orthogonality stencil are used to approximate temporal and spatial derivatives. This stencil can adopt different grid spacing in each spatial axis, and thus it is more flexible than the existing one with the same grid spacing. Based on the time-space-domain dispersion relation, the high-order FD coefficients are generated by using Taylor expansion and least squares. Numerical analyses and modeling examples demonstrate that our proposed schemes have higher accuracy and better stability than other conventional schemes, and thus larger time steps can be used to improve the computational efficiency in 3D case. K e y w o r d s : wave propagation, finite-difference, staggered-grid, high accuracy, numerical optimization
1. INTRODUCTION Over the past few decades, various finite-difference (FD) methods have been developed to improve the accuracy and effiency for seismic-wave modeling (e.g., Alford et al., 1974; Carcione et al., 2002; Levander, 1988; Moczo et al., 2011; Song et al., 2013). Compared with the centered-grid FD (CFD), the staggered-grid FD (SFD) is widely used in numerically modeling seismic-wave propagation for its superiority in accuracy and stability (e.g., Etemadsaeed et al., 2016; Liu and Sen, 2011; Saenger et al., 2000; Virieux, 1984; Yan and Yang, 2017). Suppression of numerical dispersion is one of the biggest challenges for FD algorithms. Generally, high-order FD approximation to spatial derivatives are regarded as
Stud. Geophys. Geod., 64 (2020), DOI: 10.1007/s11200-020-1013-1, in print © 2020 Inst. Geophys. CAS, Prague
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S. Xu and Y. Liu
effective schemes to control spatial dispersion (e.g., Dablain, 1986; Di Bartolo et al., 2012; Etgen and O’Brien, 2007; Lele, 1992; Liu and Sen, 2011; Moczo et al., 2014). Using high-order FD discretization in the space domain and homogeneous medium, arbitrary even-order spatial accuracy can be reached by increasing the length of FD operator. The FD coefficients are usually computed by a Taylor expansion (TE) (e.g., Fornberg, 1998; Kindelan et al., 1990; Liu and Sen, 2011). TE-based FDs have high accuracy for small wavenumbers, and the dispersion error becomes strong for middle and large wavenumbers (e.g., Holberg, 1987). To mitigate this issue, many optimization-based algorithms, including scaled binomial windows (e.g., Chu and Stoffa, 2012), linear least squares (LS) (e.g., Liu, 2014), simulated annealing (
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