scholarly journals Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method

Geophysics ◽  
2014 ◽  
Vol 79 (5) ◽  
pp. T277-T285 ◽  
Author(s):  
Yanfei Wang ◽  
Wenquan Liang ◽  
Zuhair Nashed ◽  
Xiao Li ◽  
Guanghe Liang ◽  
...  
Keyword(s):  
Finite Difference ◽  
Staggered Grid ◽  
Difference Operators ◽  
Seismic Modeling ◽  
Space Domain ◽  
Dispersion Relationship ◽  
Time Space

Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T17-T40 ◽  
Author(s):  
Zhiming Ren ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Stability Condition ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Equation Modeling ◽  
Optimal Time ◽  
Finite Difference Schemes ◽  
Space Domain ◽  
Time Space

Staggered-grid finite-difference (SFD) methods are widely used in modeling seismic-wave propagation, and the coefficients of finite-difference (FD) operators can be estimated by minimizing dispersion errors using Taylor-series expansion (TE) or optimization. We developed novel optimal time-space-domain SFD schemes for acoustic- and elastic-wave-equation modeling. In our schemes, a fourth-order multiextreme value objective function with respect to FD coefficients was involved. To yield the globally optimal solution with low computational cost, we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least-squares (LS) to derive the optimal SFD coefficients by minimizing the relative error of time-space-domain dispersion relations over a given frequency range. To ensure the robustness of our schemes, a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold. Moreover, the hybrid absorbing boundary condition was applied to remove artificial boundary reflections. We compared our optimal SFD with the conventional, TE-based time-space-domain, and LS-based SFD schemes. Dispersion analysis and numerical simulation results suggested that the new SFD schemes had a smaller numerical dispersion than the other three schemes when the same operator lengths were adopted. In addition, our LS-based time-space-domain SFD can obtain the same modeling accuracy with shorter spatial operator lengths. We also derived the stability condition of our schemes. The experiment results revealed that our new LS-based SFD schemes needed a slightly stricter stability condition.

Acoustic Wave Equation Modeling with New Time-Space Domain Finite Difference Operators

2013 ◽  
Vol 56 (6) ◽  
pp. 840-850 ◽  
Author(s):  
LIANG Wen-Quan ◽  
YANG Chang-Chun ◽  
WANG Yan-Fei ◽  
LIU Hong-Wei
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Equation Modeling ◽  
Difference Operators ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
New Time

Time-space-domain temporal high-order staggered-grid finite-difference schemes by combining orthogonality and pyramid stencils for 3D elastic-wave propagation

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. T259-T282 ◽  
Author(s):  
Shigang Xu ◽  
Yang Liu ◽  
Zhiming Ren ◽  
Hongyu Zhou
Keyword(s):  
Dispersion Relation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Large Time ◽  
High Order ◽  
Staggered Grid ◽  
Elastic Wave Equation ◽  
Space Domain ◽  
First Order ◽  
Time Space

The presently available staggered-grid finite-difference (SGFD) schemes for the 3D first-order elastic-wave equation can only achieve high-order spatial accuracy, but they exhibit second-order temporal accuracy. Therefore, the commonly used SGFD methods may suffer from visible temporal dispersion and even instability when relatively large time steps are involved. To increase the temporal accuracy and stability, we have developed a novel time-space-domain high-order SGFD stencil, characterized by ([Formula: see text])th-order spatial and ([Formula: see text])th-order temporal accuracies ([Formula: see text]), to numerically solve the 3D first-order elastic-wave equation. The core idea of this new stencil is to use a double-pyramid stencil with an operator length parameter [Formula: see text] together with the conventional second-order SGFD to approximate the temporal derivatives. At the same time, the spatial derivatives are discretized by the orthogonality stencil with an operator length parameter [Formula: see text]. We derive the time-space-domain dispersion relation of this new stencil and determine finite-difference (FD) coefficients using the Taylor-series expansion. In addition, we further optimize the spatial FD coefficients by using a least-squares (LS) algorithm to minimize the time-space-domain dispersion relation. To create accurate and reasonable P-, S-, and converted wavefields, we introduce the 3D wavefield-separation technique into our temporal high-order SGFD schemes. The decoupled P- and S-wavefields are extrapolated by using the P- and S-wave dispersion-relation-based FD coefficients, respectively. Moreover, we design an adaptive variable-length operator scheme, including operators [Formula: see text] and [Formula: see text], to reduce the extra computational cost arising from adopting this new stencil. Dispersion and stability analyses indicate that our new methods have higher accuracy and better stability than the conventional ones. Using several 3D modeling examples, we demonstrate that our SGFD schemes can yield greater temporal accuracy on the premise of guaranteeing high-order spatial accuracy. Through effectively combining our new stencil, LS-based optimization, large time step, variable-length operator, and graphic processing unit, the computational efficiency can be significantly improved for the 3D case.

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