A new kind of optimal second-order symplectic scheme for seismic wave simulations

Liu, Shaolin; Li, Xiaofan; Wang, Wenshuai; Liu, Youshan; Zhang, Meigen; Zhang, Huan

doi:10.1007/s11430-013-4805-0

Cited by 19 publications

(4 citation statements)

References 26 publications

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“…In the past decades, researchers have studied a series of forward modeling methods, including finite difference methods (Kelly et al, 1976; Day, 1982; Igel et al, 1995; Yang DH et al, 2003, 2004, 2006; Liu SL et al, 2015, Ma X et al, 2018), finite element methods (Lysmer and Drake, 1972; Marfurt, 1984; Liu SL et al, 2014; He XJ et al, 2020), a pseudo‐spectral method (Kosloff and Baysal, 1982), and a spectral element method (Kosloff and Baysal, 1982; Seriani and Priolo, 1994; Komatitsch et al, 2005). These methods are designed to solve different types of questions.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

Zhang

Pan

Yang

et al. 2021

Earth and Planetary Physics

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Section: Introductionmentioning

confidence: 99%

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

Zhang

Pan

Yang

et al. 2021

Earth and Planetary Physics

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“…However, the nonuniform spacing of the interpolation points for algebraic polynomials imposes a tight constraint on the time‐step compared with a uniform spacing grid (Carcione and Wang PJ, ). As a consequence, the Courant–Friedrichs–Lewy (CFL) numbers decrease exponentially with the increasing degree of Lagrange polynomials (Liu SL et al, ; De Basabe and Sen, , ; Liu SL et al, ) (Figure ). This means that the SEM requires many more time steps for a given problem compared with the FD method (uniform grid).…”

Section: Introductionmentioning

confidence: 99%

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

Liu

Wang

et al. 2019

Earth and Planetary Physics

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In the adjoint‐state method, the forward‐propagated source wavefield and the backward‐propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory‐saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memory‐saving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced; therefore, in‐core memory storage is feasible even for large‐scale three‐dimensional adjoint inversion problems.

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“…Despite these advantages, the method is subject to serious numerical dispersion errors that limit its application in problems involving large time spans and narrow pulses for insufficient sampling. Apart from traditional methods for reducing numerical dispersion such as increasing sampling rate and using higher order degrees of accuracy, several other approaches that are able to produce small dispersive errors have also been proposed (Holberg, 1987;Lele, 1992;Tam and Webb, 1993;Yang et al, 2002;Yin et al 2006;Chu and Stoffa, 2012;Li et al, 2012;Liu, 2013;Yao, 2013a, 2013b;Liu et al, 2014a).…”

Section: Introductionmentioning

confidence: 99%

Dispersion-relation preserving stereo-modeling method beyond Nyquist frequency for acoustic wave equation

et al. 2017

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According to Nyquist-Shannon sampling theory, two sampling points of the displacements per minimal wavelength are required to reconstruct a wavefield. However, high-frequency components above the Nyquist frequency can be theoretically recovered by introducing spatial derivatives of the displacements. We have developed a new finitedifference scheme for solving the acoustic equation, named the dispersion-relation preserving stereo-modeling method, which is practical for seismic forward modeling beyond the Nyquist frequency. The key idea in this model is to approximate the high-order spatial derivatives with wavenumber-domain optimization in wavefields represented by the wave displacements and their gradients. We investigated the theoretical properties of this method, including the absolute error of spatial operators, numerical error, stability criterion, and computational efficiency. Our results indicated that the method can effectively suppress the numerical dispersion on extremely coarse grids with less than two grid points per minimal wavelength, surpassing the pseudospectral and high-order Lax-Wendroff correction methods. Numerical experiments for the homogeneous medium, layered medium, and 2D SEG/ EAGE salt model indicated that the new method performed well in terms of computational efficiency and simulation accuracy, making it a highly useful tool for seismic modeling.

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A new kind of optimal second-order symplectic scheme for seismic wave simulations

Cited by 19 publications

References 26 publications

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

Dispersion-relation preserving stereo-modeling method beyond Nyquist frequency for acoustic wave equation

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