Fast ray tracing method in 3-D structure and its proof of positive definiteness

doi:10.1007/s11771-007-0020-5

	Fast ray tracing method in 3-D structure and its proof of positive definiteness
	Gao Er-gen ; Han, Uk ; Teng Ji-wen
刊名	JOURNAL OF CENTRAL SOUTH UNIVERSITY OF TECHNOLOGY
	2007-02-01
卷号	14 期号:1 页码:100-103
关键词	Fermat's principle ray tracing ray path positivity seismic migration tomography
ISSN号	1005-9784
DOI	10.1007/s11771-007-0020-5
文献子类	Article
英文摘要	Based on Fermat's principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor's incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, die positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.
WOS关键词	ALGORITHM ; MEDIA
WOS研究方向	Metallurgy & Metallurgical Engineering
语种	英语
出版者	JOURNAL OF CENTRAL SOUTH UNIV TECHNOLOGY
WOS记录号	WOS:000246083600020
内容类型	期刊论文
源URL	[http://ir.iggcas.ac.cn/handle/132A11/68154]
专题	中国科学院地质与地球物理研究所
通讯作者	Gao Er-gen
作者单位	1.Univ Sci & Technol China, Sch Earth & Space Sci, Hefei 230026, Peoples R China 2.Korea Mil Acad, Dept Environm Sci, Seoul 139799, South Korea 3.Chinese Acad Sci, Inst Geophys, Beijing 100101, Peoples R China
推荐引用方式 GB/T 7714	Gao Er-gen,Han, Uk,Teng Ji-wen. Fast ray tracing method in 3-D structure and its proof of positive definiteness[J]. JOURNAL OF CENTRAL SOUTH UNIVERSITY OF TECHNOLOGY,2007,14(1):100-103.
APA	Gao Er-gen,Han, Uk,&Teng Ji-wen.(2007).Fast ray tracing method in 3-D structure and its proof of positive definiteness.JOURNAL OF CENTRAL SOUTH UNIVERSITY OF TECHNOLOGY,14(1),100-103.
MLA	Gao Er-gen,et al."Fast ray tracing method in 3-D structure and its proof of positive definiteness".JOURNAL OF CENTRAL SOUTH UNIVERSITY OF TECHNOLOGY 14.1(2007):100-103.