Effective finite-difference modelling methods with 2-D acoustic wave equation using a combination of cross and rhombus stencils

Wang, Enjiang; Liu, Yang; Sen, Mrinal K.

doi:10.1093/gji/ggw250

Cited by 57 publications

(14 citation statements)

References 49 publications

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“…The basic idea of Hu et al (2016) is to express the Laplace FD operator as the weighted mean of the Laplace FD operators constructed in the general and rotated Cartesian coordinate system. The resulting mixed-grid FD scheme is similar to that of Wang et al (2016). Hu et al (2021) derived how to construct a 3D Laplace FD operator with the off-axial grid points and further proposed a 3D mixed-grid FD scheme, which improved the accuracy and stability of 3D scalar wave equation simulation.…”

Section: Introductionmentioning

confidence: 95%

“…However, the length of the spatial FD operator increases rapidly with M, which makes it very computationally expensive. Wang et al (2016) proposed an FD scheme by combining the C-FD and rhombus FD schemes, which balanced the accuracy and efficiency. Motivated by the widely used mixed-grid FD scheme in the frequency domain (Jo et al, 1996;Shin and Sohn, 1998), Hu et al (2016) proposed a mixed-grid FD scheme for 2D scalar wave equation modeling in the time-space domain.…”

Section: Introductionmentioning

confidence: 99%

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Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes

Liu

Hu²,

Yong³

et al. 2022

Front. Earth Sci.

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For the conventional staggered-grid finite-difference scheme (C-SFD), although the spatial finite-difference (FD) operator can reach 2Mth-order accuracy, the FD discrete wave equation is the only second-order accuracy, leading to low modeling accuracy and poor stability. We proposed a new mixed staggered-grid finite-difference scheme (M-SFD) by constructing the spatial FD operator using axial and off-axial grid points jointly to approximate the first-order spatial partial derivative. This scheme is suitable for modeling the stress–velocity acoustic and elastic wave equation. Then, based on the time–space domain dispersion relation and the Taylor series expansion, we derived the analytical expression of the FD coefficients. Theoretically, the FD discrete acoustic wave equation and P- or S-wave in the FD discrete elastic wave equation given by M-SFD can reach the arbitrary even-order accuracy. For acoustic wave modeling, with almost identical computational costs, M-SFD can achieve higher modeling accuracy than C-SFD. Moreover, with a larger time step used in M-SFD than that used in C-SFD, M-SFD can achieve higher computational efficiency and reach higher modeling accuracy. For elastic wave simulation, 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. Solving the split elastic wave equation with M-SFD can further improve the modeling accuracy but will decrease the efficiency and increase the memory usage as well. Stability analysis shows that M-SFD has better stability than C-SFD for both acoustic and elastic wave simulations. Applying M-SFD to reverse time migration (RTM), the imaging artifacts caused by the numerical dispersion are effectively eliminated, which improves the imaging accuracy and resolution of deep formation.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes

Liu

Hu²,

Yong³

et al. 2022

Front. Earth Sci.

View full text Add to dashboard Cite

show abstract

“…As the reverse-time migration imaging method is based on the two-way wave equation, which can accurately describe the dynamic and kinematic characteristics of a seismic wavefield propagating underground, reversetime migration has no inclination angle limit and can adapt to the imaging of complex structural areas, especially for structures with clear lateral velocity changes [1][2][3][4]. The finite difference scheme is widely used in the numerical simulation of the elastic-wave equation because of its simplicity and flexibility, high calculation efficiency, and small memory requirement [5][6][7][8][9][10][11][12][13]. On the one hand, with the development of multicomponent seismic exploration in recent years, particularly shear-wave seismic exploration, in order to minimize computational costs, there is a need to increase the time and spatial steps used in finite difference modeling while maintaining sufficient accuracy during numerical simulation [14].…”

Section: Introductionmentioning

confidence: 99%

The Combined Compact Difference Scheme Applied to Shear-Wave Reverse-Time Migration

Zhou

Sun

et al. 2022

Applied Sciences

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In this paper, the combined compact difference scheme (CCD) and the combined supercompact difference scheme (CSCD) are used in the numerical simulation of the shear-wave equation. According to the Taylor series expansion and shear-wave equation, the fourth-order discrete scheme of the displacement field is established; then, the CCD and CSCD schemes are used to calculate the spatial derivative of the displacement field. Additionally, the accuracy, dispersion, and stability of the CCD and CSCD are analyzed, and numerical simulation analyses are carried out using 1D uniform models. Lastly, based on the processing of artificial boundary reflection using PML boundary conditions, shear-wave reverse-time migrations are carried out using synthetic data. The results show that (1) CCD and CSCD have smaller truncation errors, higher simulation precision, and lower numerical dispersion than other normal difference schemes; (2) CCD and CSCD can use the coarse grid and larger time step to calculate, with less memory and high computational efficiency; (3) finally, the result of the shear-wave reverse-time migration of the 2D synthetic data model show that the reverse-time migration imaging is clear, and the proposed method for shear-wave reverse-time migration is practical and effective.

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“…Later, they [29,31] further developed several NAD-type approaches to restrain numerical dispersion. Recently, many research works [15,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] have been done to develop higher-order finite difference methods for the above mentioned wave equations. Furthermore, it has been demonstrated that high accuracy numerical approaches and techniques are very effective in restraining the dispersion errors [5,8,21,31].…”

Section: Introductionmentioning

confidence: 99%

An explicit fourth-order compact difference scheme for solving the 2D wave equation

Jiang

2020

Adv Differ Equ

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In this paper, an explicit fourth-order compact (EFOC) difference scheme is proposed for solving the two-dimensional(2D) wave equation. The truncation error of the EFOC scheme is O(τ 4 + τ 2 h 2 + h 4), i.e., the scheme has an overall fourth-order accuracy in both time and space. Because the scheme is explicit, it does not need any iterative processes. Afterwards, the stability condition of the scheme is obtained by using the Fourier analysis method, which has a wider stability range than other explicit or alternation direction implicit (ADI) schemes. Finally, some numerical experiments are carried out to verify the accuracy and stability of the present scheme.

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Effective finite-difference modelling methods with 2-D acoustic wave equation using a combination of cross and rhombus stencils

Cited by 57 publications

References 49 publications

Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes

Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes

The Combined Compact Difference Scheme Applied to Shear-Wave Reverse-Time Migration

An explicit fourth-order compact difference scheme for solving the 2D wave equation

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