Journal of Central South University of Technology

, Volume 15, Issue 6, pp 901–905 | Cite as

Fast algorithm and numerical simulation for ray-tracing in 3D structure

  • Er-gen Gao (高尔根)Email author
  • An-jia Zhang (张安家)
  • Uk Han
  • Shu-yun Song (宋淑云)
  • Yong-bo Zhai (翟永波)


Beginning with the method of whole path iterative ray-tracing and according to the positive definiteness of the coefficient matrix of the systems of linear equations, a symmetry block tridiagonal matrix was decomposed into the product of block bidiagonal triangular matrix and its transpose by means of Cholesky decomposition. Then an algorithm for solving systems of block bidiagonal triangular linear equations was given, which is not necessary to treat with the zero elements out of banded systems. A fast algorithm for solving the systems of symmetry block tridiagonal linear equations was deduced, which can quicken the speed of ray-tracing. Finally, the simulation based on this algorithm for ray-tracing in three dimensional media was carried out. Meanwhile, the segmentally-iterative ray-tracing method and banded method for solving the systems of block tridiagonal linear equations were compared in the same model mentioned above. The convergence condition was assumed that the L-2 norm summation for mk, 1 and mk, 2 in the whole ray path was limited in 10−6. And the calculating speeds of these methods were compared. The results show that the calculating speed of this algorithm is faster than that of conventional method and the calculated results are accurate enough. In addition, its precision can be controlled according to the requirement of ray-tracing

Key words

ray-tracing seismic migration Cholesky decomposition tomography 


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Copyright information

© Central South University Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  • Er-gen Gao (高尔根)
    • 1
    • 2
    Email author
  • An-jia Zhang (张安家)
    • 3
  • Uk Han
    • 4
  • Shu-yun Song (宋淑云)
    • 1
  • Yong-bo Zhai (翟永波)
    • 1
  1. 1.School of Earth and Space SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Research Center of Oil and Nature GasesUniversity of Science and Technology of ChinaHefeiChina
  3. 3.Institute of GeophysicsChinese Academy of SciencesBeijingChina
  4. 4.Department of Environmental SciencesKorea Military AcademySeoulKorea

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