Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Central South University of Technology Aims and scope Submit manuscript

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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.

    Article  Google Scholar 

  2. DUVENECK E. 3D tomographic velocity model estimation with kinematic wavefield attributes [J]. Geophysical Prospecting, 2004, 52(6): 535–545.

    Article  Google Scholar 

  3. IVANSSON S. Seismic borehole tomography theory and computational methods [J]. Proc IEEE, 1986, 74(2): 328–338.

    Article  Google Scholar 

  4. SCHUSTER G T. Fermat’s interferometric principle for target-oriented traveltime tomography [J]. Geophysics, 2005, 70(4): U47–50.

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  13. BUSKE S, KÄSTNER U. Efficient and accurate computation of seismic traveltimes and amplitudes [J]. Geophysical Prospecting, 2004, 52(4): 313–322.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  18. GOLUB G H, van LOAN C F. Matrix computation [M]. Baltimore: Johns Hopkins University Press, 1983.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Earth and Space Sciences, University of Science and Technology of China, Hefei, 230026, China

    Er-gen Gao  (高尔根), Shu-yun Song  (宋淑云) & Yong-bo Zhai  (翟永波)

  2. Research Center of Oil and Nature Gases, University of Science and Technology of China, Hefei, 230026, China

    Er-gen Gao  (高尔根)

  3. Institute of Geophysics, Chinese Academy of Sciences, Beijing, 100101, China

    An-jia Zhang  (张安家)

  4. Department of Environmental Sciences, Korea Military Academy, Seoul, 139799, Korea

    Uk Han

Authors
  1. Er-gen Gao  (高尔根)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. An-jia Zhang  (张安家)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Uk Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shu-yun Song  (宋淑云)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yong-bo Zhai  (翟永波)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Er-gen Gao  (高尔根).

Additional information

Foundation item: Project(40674071) supported by the National Natural Science Foundation of China; Project(KFAS2002-2003) supported by the Korea Foundation for Advanced Studies

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Eg., Zhang, Aj., Han, U. et al. Fast algorithm and numerical simulation for ray-tracing in 3D structure. J. Cent. South Univ. Technol. 15, 901–905 (2008). https://doi.org/10.1007/s11771-008-0164-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-008-0164-y

Key words

Search

Navigation