Skip to main content

Improved Ray Tracing Method Based on the Snell’s Law

  • Conference paper
  • First Online:
Advances in Acoustic Emission Technology (WCAE 2017)

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 218))

Included in the following conference series:

  • 628 Accesses

Abstract

Passive wave tomography is one of the important techniques for microseismic monitoring in the complex underground mines. The resolution and reliability of tomography are influenced by the ray tracing method. Compared with other algorithms, the shortest path method is a robust global ray tracing algorithm, but there are still some problems. The study attempts to use the shortest path method to make the ray traced to satisfy the law of wave propagation, making it more realistic. The Snell’s law is introduced to improve the accuracy of the ray tracing method, and the disturbance of the points is considered so that the Snell’s law can modify the ray more effectively. The improved method is used to perform simulation in the grid model, and the result is compared with the traditional ones. The results show that the improved method combines the advantages of various methods and achieves good results, which indicates that the ray can jump out the original cell and bypass the empty area. The improved ray tracing method also can get a global optimal solution.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L.J. Dong, J. Wesseloo, Y. Potvin, X.B. Li, Discriminant models of blasts and seismic events in mine seismology. Int. J. Rock Mech. Min. Sci. 86, 282–291 (2016)

    Google Scholar 

  2. L.J. Dong, J. Wesseloo, Y. Potvin, X.B. Li, Discrimination of mine seismic events and blasts using the Fisher classifier, naive Bayesian classifier and logistic regression. Rock Mech. Rock Eng. 49(1), 183–211 (2016)

    ADS  Google Scholar 

  3. S. Lasocki, B. Orlecka-Sikora, Seismic hazard assessment under complex source size distribution of mining-induced seismicity. Tectonophysics 456(1), 28–37 (2008)

    ADS  Google Scholar 

  4. M.K. Abdul-Wahedab, M. Al Heiba, G. Senfaute, Mining-induced seismicity: Seismic measurement using multiplet approach and numerical modeling. Int. J. Coal Geol. 66(1-2), 137–147 (2006)

    Google Scholar 

  5. A. Leśniakab, Z. Isakow, Space–time clustering of seismic events and hazard assessment in the Zabrze-Bielszowice coal mine, Poland. Int. J. Rock Mech. Min. Sci. 46(5), 918–928 (2009)

    Google Scholar 

  6. L.J. Dong, D.Y. Sun, X.B. Li, J. Ma, L.Y. Zhang, X.J. Tong, Interval non-probabilistic reliability of surrounding jointed rockmass considering microseismic loads in mining tunnels. Tunn. Undergr. Sp. Tech. 81, 326–335 (2018)

    Google Scholar 

  7. J. Ma, L.J. Dong, G.Y. Zhao, X.B. Li, Discrimination of seismic sources in an underground mine using full waveform inversion. Int. J. Rock Mech. Min. Sci. 106, 213–222 (2018)

    Google Scholar 

  8. L.J. Dong, W. Zou, X.B. Li, W.W. Shu, Z.W. Wang, Collaborative localization method using analytical and iterative solutions for microseismic/acoustic emission sources in the rockmass structure for underground mining, Eng. Fract. Mech., https://doi.org/10.1016/j.engfracmech.2018.01.032

  9. R. Duraiswami, D. Zotkin, L. Davis, Exact solutions for the problem of source location from measured time differences of arrival. J. Acoust. Soc. Am. 106(4), 2277 (1999)

    Google Scholar 

  10. L.J. Dong, W.W. Shu, X.B. Li, G.J. Han, W. Zou, Three dimensional comprehensive analytical solutions for locating sources of sensor networks in unknown velocity mining system. IEEE Access 5, 11337–11351 (2017)

    Google Scholar 

  11. L.J. Dong, X.B. Li, Three-dimensional analytical solution of acoustic emission or microseismic source location under cube monitoring network. Trans. Nonferrous Met. Soc. Chin. 22(12), 3087–3094 (2012)

    Google Scholar 

  12. L.J. Dong, X.B. Li, Z.L. Zhou, G.H. Chen, J. Ma, Three-dimensional analytical solution of acoustic emission source location for cuboid monitoring network without pre-measured wave velocity. Trans. Nonferrous Met. Soc. Chin. 25(1), 293–302 (2015)

    Google Scholar 

  13. X.B. Li, L.J. Dong, An efficient closed-form solution for acoustic emission source location in three-dimensional structures. AIP Adv. 4(2), 1–8 (2014)

    Google Scholar 

  14. X.H. Yang, J.S. He, D.Q. Xie, The forward and inversion technology for velocity tomography. Geophys. Geochem. Explor. 33(2), 217–219 (2009)

    Google Scholar 

  15. G. Ergen, X. Guoming, A new kind of step by step iterative ray-tracing method. Chin. J. Geophys. 39(Suppl), 302–308 (1996)

    Google Scholar 

  16. J.E. Vidale, Finite-difference calculation of travel times. Bull. Seism. Soc. Am 78(6), 2062–2076 (1988)

    Google Scholar 

  17. J.E. Vidale, Finite-difference calculation of travel times in three dimensions. Geophysics 55(5), 521–526 (1990)

    ADS  Google Scholar 

  18. F. Qin, Y. Luo, K.B. Olsen, W. Cai, G.T. Schuster, Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics 57(3), 478–487 (1992)

    ADS  Google Scholar 

  19. E. Asakawa, T. Kawanaka, Seismic ray tracing using linear traveltime interpolation. Geophys. Prospect. 41(1), 99–111 (1993)

    ADS  Google Scholar 

  20. E. Cardarelli, A. Cerreto, Ray tracing in elliptical anisotropic media using the linear travel time interpolation (LTI) method applied to travel time seismic tomography. Geophys. Prospect. 50(1), 55–72 (2002)

    ADS  Google Scholar 

  21. N. Jianxin, Y. Huizhu, Quadratic/linear travel time interpolation of seismic ray-tracing. J. Tsinghua Univ. (Sci. Tech.) 43(11), 1495–1498 (2003)

    Google Scholar 

  22. N. Ettrich, D. Gajewski, Wave front construction in smooth media for prestack depth migration. Pure Appl. Geophys. 148(3-4), 481–502 (1996)

    ADS  Google Scholar 

  23. K.J. Lee, R.L. Gibson, An improved mesh generation scheme for the wavefront construction method. Geophysics 72(72), 59–70 (2007)

    Google Scholar 

  24. V. Vinje, E. Iversen, H. Gjoystdal, Travel time and amplitude estimation using wavefront construction. Geophysics 58(8), 1157–1166 (1992)

    Google Scholar 

  25. I. Nakanishi, K. Yamaguchi, A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure. Earth Planets Space 34(2), 195–201 (1986)

    Google Scholar 

  26. T.J. Moser, Shortest path calculation of seismic rays. Geophysics 56(1), 59–67 (1991)

    ADS  Google Scholar 

  27. L. Klimeš, Kvasnička and Michal. “3-D network ray tracing,”. Geophys. J. Int. 116(3), 726–738 (1994)

    ADS  MathSciNet  Google Scholar 

  28. W. Hui, C. Xu, 3-D ray tracing method based on graphic structure. Chin. J. Geophys. 43(4), 534–541 (2000)

    Google Scholar 

  29. T.H. Cormen, C.E. Leiserson, R.L. Rivest, Stein and Clifford. Section 24.3: Dijkstra’s algorithm, in Introduction to Algorithms, 2nd edn., (MIT Press, McGraw–Hill, Cambridge, MA; Boston, MA, 2001), pp. 595–601

    MATH  Google Scholar 

  30. E.W. Dijkstra, A note on two problems in connection with graphs. Numer. Math. 1(1), 269–271 (1959)

    MathSciNet  MATH  Google Scholar 

  31. R.J. Schechter, Snell’s Law: optimum pathway analysis. Surv. Ophthalmol. 21(6), 464–466 (1977)

    Google Scholar 

Download references

Acknowledgment

The authors wish to acknowledge financial support from the Fundamental Research Funds for the Central Universities of Central South University (2018zzts722), The Young Elite Scientists Sponsorship Program by CAST (YESS20160175).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qingchun Hu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hu, Q. (2019). Improved Ray Tracing Method Based on the Snell’s Law. In: Shen, G., Zhang, J., Wu, Z. (eds) Advances in Acoustic Emission Technology. WCAE 2017. Springer Proceedings in Physics, vol 218. Springer, Cham. https://doi.org/10.1007/978-3-030-12111-2_40

Download citation

Publish with us

Policies and ethics