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Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation
Gao, Yingjie1,2; Zhang, Jinhai1,2; Yao, Zhenxing1,2
2018-11-01
Source PublicationGEOPHYSICS
ISSN0016-8033
Volume83Issue:6Pages:A93-A98
AbstractThe explicit finite-difference scheme is popular for solving the wave equation in the field of seismic exploration due to its simplicity in numerical implementation. However, its maximum time step is strictly restricted by the Courant-Friedrichs-Lewy (CFL) stability limit, which leads to a heavy computational burden in the presence of small-scale structures and high-velocity targets. We remove the CFL stability limit of the explicit finite-difference scheme using the eigenvalue perturbation, which allows us to use a much larger time step beyond the CFL stability limit. For a given time step that is within the CFL stability limit, the eigenvalues of the update matrix would be distributed along the unit circle; otherwise, some eigenvalues would be distributed outside of the unit circle, which introduces unstable phenomena. The eigenvalue perturbation can normalize the unstable eigenvalues and guarantee the stability of the update matrix by using an arbitrary time step. The update matrix can be preprocessed before the numerical simulation, thus retaining the computational efficiency well. We further incorporate the forward time-dispersion transform (FTDT) and the inverse time-dispersion transform (ITDT) to reduce the time-dispersion error caused by using an unusually large time step. Our numerical experiments indicate that the combination of the eigenvalue perturbation, the FTDT method, and the ITDT method can simulate highly accurate waveforms when applying a time step beyond the CFL stability limit. The time step can be extended even toward the Nyquist limit. This means that we could save many iteration steps without suffering from time-dispersion error and stability problems.
DOI10.1190/GEO2018-0447.1
Funding OrganizationNational Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences
WOS KeywordSTABLE FDTD METHOD ; TIME DISPERSION
Language英语
Funding ProjectNational Major Project of China[2017ZX05008-007] ; National Natural Science Foundation of China[41704063] ; General Financial Grant from the China Postdoctoral Science Foundation[2017M610980] ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences[XDA15011700] ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences
Funding OrganizationNational Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; National Major Project of China ; National Major Project of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; General Financial Grant from the China Postdoctoral Science Foundation ; General Financial Grant from the China Postdoctoral Science Foundation ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Strategic Pioneer Program on Space Science, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences ; Foundation for Excellent Member of the Youth Innovation Promotion Association, Chinese Academy of Sciences
WOS Research AreaGeochemistry & Geophysics
WOS SubjectGeochemistry & Geophysics
WOS IDWOS:000457502000003
PublisherSOC EXPLORATION GEOPHYSICISTS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.iggcas.ac.cn/handle/132A11/90500
Collection地球与行星物理院重点实验室
Corresponding AuthorGao, Yingjie
Affiliation1.Chinese Acad Sci, Inst Geol & Geophys, Key Lab Earth & Planetary Phys, Beijing 100029, Peoples R China
2.Chinese Acad Sci, Inst Earth Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Gao, Yingjie,Zhang, Jinhai,Yao, Zhenxing. Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation[J]. GEOPHYSICS,2018,83(6):A93-A98.
APA Gao, Yingjie,Zhang, Jinhai,&Yao, Zhenxing.(2018).Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation.GEOPHYSICS,83(6),A93-A98.
MLA Gao, Yingjie,et al."Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation".GEOPHYSICS 83.6(2018):A93-A98.
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