Abstract
Equivalent staggered-grid (ESG) as a new family of schemes has been utilized in seismic modeling, imaging, and inversion. Traditionally, the Taylor series expansion is often applied to calculate finite-difference (FD) coefficients on spatial derivatives, but the simulation results suffer serious numerical dispersion on a large frequency zone. We develop an optimized equivalent staggered-grid (OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3D elastic wave equation. On the one hand, we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave, S-wave, and converted-wave (C-wave) terms. On the other hand, a novel plane wave solution for the 3D elastic wave equation is derived from the matrix decomposition method to construct the time–space dispersion relations. FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method. Finally, we construct a new objective function to analyze P-wave, S-wave, and C-wave dispersion concerning frequencies. The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method. The synthetic examples demonstrate the effectiveness and superiority of the presented method.
Highlights
Numerical modeling for elastic wave propagation is a powerful tool in seismic data processing and interpretation (Duan et al 2013)
We obtain FD coefficients using the Newton iteration method based on new time–space dispersion equations
With a local constant velocity assumption, we simulate the propagation of elastic waves in the 3D homogeneous and heterogeneous media using the optimized equivalent staggered-grid (OESG) method
Summary
Numerical modeling for elastic wave propagation is a powerful tool in seismic data processing and interpretation (Duan et al 2013). The first category consumes a lower computational cost than the other one for solving the dispersion equations, and it usually provides high accuracy on a small frequency zone (Ren and Liu 2015). Several new truncation windows have gradually been developed, such as a Chebyshev’s autoconvolution window (Wang et al 2015) and a truncation window based on the least-squares algorithm (Ren et al 2018) These methods based on truncated windows can partially suppress numerical dispersion. Some optimized FD methods based on the staggered-grid scheme are gradually applied to solve the elastic wave equation (Ma and Zhu 2003; Kosloff et al 2010; Yang et al 2014). We construct an optimized equivalent staggeredgrid scheme (OESG) to improve the accuracy of elastic wave simulation. We analyze the dispersion characteristics and give several results of numerical modeling, proving the validity and superiority of the presented method
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