自然科学版 英文版
自然科学版 英文版
自然科学版 英文版

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中南大学学报(英文版)

Journal of Central South University

Vol. 14    No. 1    February 2007

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Fast ray tracing method in 3-D structure and its proof of positive definiteness
GAO Er-gen(高尔根)1, Uk HAN2, TENG Ji-wen(滕吉文)3

1. School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China;2. Department of Environmental Sciences, Korea Military Academy, Seoul 139799, Korea;3. Institute of Geophysics, Chinese Academy of Sciences, Beijing 100101, China

Abstract: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, the 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.

 

Key words: Fermat’s principle; ray tracing; ray path; positivity; seismic migration; tomography

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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