Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation

doi:10.1190/GEO2018-0447.1

CORC > 地质与地球物理研究所 > 中国科学院地质与地球物理研究所 > 中国科学院地球与行星物理重点实验室

	Removing the stability limit of the explicit finite-difference scheme with eigenvalue perturbation
	Gao, Yingjie 1,2; Zhang, Jinhai 1,2; Yao, Zhenxing 1,2
刊名	GEOPHYSICS
	2018-11-01
卷号	83 期号:6 页码:A93-A98
ISSN号	0016-8033
DOI	10.1190/GEO2018-0447.1
英文摘要	The 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.
资助项目	National 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
WOS关键词	STABLE FDTD METHOD ; TIME DISPERSION
WOS研究方向	Geochemistry & Geophysics
语种	英语
出版者	SOC EXPLORATION GEOPHYSICISTS
WOS记录号	WOS:000457502000003
资助机构	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 ; 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
内容类型	期刊论文
源URL	[http://ir.iggcas.ac.cn/handle/132A11/90500]
专题	地质与地球物理研究所_中国科学院地球与行星物理重点实验室
通讯作者	Gao, Yingjie
作者单位	1.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
推荐引用方式 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.