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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)
Article

Abstract

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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References

  1. [1]
    AKI K, CHRISTOFFERSSON A, HUSEBYE E S. Determination of the three-dimensional seismic structure of the lithosphere [J]. J Geophys Res, 1977, 82(2): 277–296.CrossRefGoogle Scholar
  2. [2]
    DUVENECK E. 3D tomographic velocity model estimation with kinematic wavefield attributes [J]. Geophysical Prospecting, 2004, 52(6): 535–545.CrossRefGoogle Scholar
  3. [3]
    IVANSSON S. Seismic borehole tomography theory and computational methods [J]. Proc IEEE, 1986, 74(2): 328–338.CrossRefGoogle Scholar
  4. [4]
    SCHUSTER G T. Fermat’s interferometric principle for target-oriented traveltime tomography [J]. Geophysics, 2005, 70(4): U47–50.CrossRefGoogle Scholar
  5. [5]
    YANG Zhuo-xin, ZHANG Xian-kang, YANG Jian, ZHAO Jin-ren. Joint inversion of 3-D crustal structure and velocity distribution [J]. Geophysical Progress, 1997, 12(1): 41–52. (in Chinese)Google Scholar
  6. [6]
    ZHANG Zhong-jie, QIN Yi-long, CHEN Yun, ZHANG Chao-ying, SUN Shan-xue, ZHAO Bing, LIU Yi-feng, LIU Zhen-kuan. Reconstruction of the semblance section for the crust and mantle reflection structure by wide-angle reflection seismic data [J]. Chinese J Geophys, 2004, 47(3): 469–474. (in Chinese)CrossRefGoogle Scholar
  7. [7]
    ZHANG Zhong-jie, TENG Ji-wen, ZHANG Lin-bin, YANG Ding-hui. The modified Snell law for seismic ray in anisotropic media [J]. Chinese Science Bulletin, 1995, 40(20): 1724–1728.Google Scholar
  8. [8]
    XU Tao, XU Guo-ming, GAO Er-gen, ZHU Liang-bao, JIANG Xian-yi. Block modeling and shooting ray in complex 3-D media [J]. Chinese J Geophys, 2004, 47(3): 1118–1126. (in Chinese)Google Scholar
  9. [9]
    XU Tao, XU Guo-ming, GAO Er-gen, LI Ying-chun, JIANG Xian-yi, LUO Kai-yun. Block modeling and segmentally iterative ray tracing in complex 3D media [J]. Geophysics, 2006, 71(3): T41–51.CrossRefGoogle Scholar
  10. [10]
    XU Tao, XU Guo-ming, GAO Er-gen, JIANG Xian-yi. Refraction ray-tracing in complex medium [J]. Oil Geophysical Prospecting, 2004, 39(6): 690–693.Google Scholar
  11. [11]
    XU Tao, XU Guo-Ming, GAO Er-Gen, JIANG Xian-yi, LUO Kai-yun. 3-D shooting ray-tracing sub-triangle method [J]. Oil Geophysical Prospecting, 2005, 40(4): 391–399.Google Scholar
  12. [12]
    GJYSTDAL H, IVERSEN E, LECOMTE I, KASCHWICH T, DROTTNING A, MISPEL J. Improved applicability of ray tracing in seismic acquisition, imaging, and interpretation [J]. Geophysics, 2007, 72(5): SM261–271.CrossRefGoogle Scholar
  13. [13]
    BUSKE S, KÄSTNER U. Efficient and accurate computation of seismic traveltimes and amplitudes [J]. Geophysical Prospecting, 2004, 52(4): 313–322.CrossRefGoogle Scholar
  14. [14]
    GAO Er-gen, XU Guo-ming, LI Guang-pin, ZHAO Yi, TU Shi-jie. A new total iterative ray-tracing method in random interface [J]. Acta Custica, 2002, 27(3): 282–287. (in Chinese)Google Scholar
  15. [15]
    ZHOU Zhu-sheng, ZHANG Sai-min, CHEN Ling-jun. Seismic ray-tracing calculation based on parabolic travel-time interpolation [J]. J Cent South Univ Technol, 2004, 11(2): 199–205.CrossRefGoogle Scholar
  16. [16]
    GAO Er-gen, XU Guo-ming, JIANG Xian-yi, LUO Kai-yun, LIU Tong-qing, XIE Duan, SHI Jin-liang. Iterative ray-tracing method segment by segment under 3-D construction [J]. Oil Geophysical Prospecting, 2002, 37(1): 11–16. (in Chinese)Google Scholar
  17. [17]
    GAO Er-gen, Uk Han, TEN Ji-wen. Fast ray-tracing method in 3-D structure and its proof of positive definiteness [J]. J Cent South Univ Technol, 2007, 14(1): 100–103.CrossRefGoogle Scholar
  18. [18]
    GOLUB G H, van LOAN C F. Matrix computation [M]. Baltimore: Johns Hopkins University Press, 1983.zbMATHGoogle Scholar

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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