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.
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References
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)
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)
S. Lasocki, B. Orlecka-Sikora, Seismic hazard assessment under complex source size distribution of mining-induced seismicity. Tectonophysics 456(1), 28–37 (2008)
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)
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)
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)
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)
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
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)
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)
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)
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)
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)
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)
G. Ergen, X. Guoming, A new kind of step by step iterative ray-tracing method. Chin. J. Geophys. 39(Suppl), 302–308 (1996)
J.E. Vidale, Finite-difference calculation of travel times. Bull. Seism. Soc. Am 78(6), 2062–2076 (1988)
J.E. Vidale, Finite-difference calculation of travel times in three dimensions. Geophysics 55(5), 521–526 (1990)
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)
E. Asakawa, T. Kawanaka, Seismic ray tracing using linear traveltime interpolation. Geophys. Prospect. 41(1), 99–111 (1993)
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)
N. Jianxin, Y. Huizhu, Quadratic/linear travel time interpolation of seismic ray-tracing. J. Tsinghua Univ. (Sci. Tech.) 43(11), 1495–1498 (2003)
N. Ettrich, D. Gajewski, Wave front construction in smooth media for prestack depth migration. Pure Appl. Geophys. 148(3-4), 481–502 (1996)
K.J. Lee, R.L. Gibson, An improved mesh generation scheme for the wavefront construction method. Geophysics 72(72), 59–70 (2007)
V. Vinje, E. Iversen, H. Gjoystdal, Travel time and amplitude estimation using wavefront construction. Geophysics 58(8), 1157–1166 (1992)
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)
T.J. Moser, Shortest path calculation of seismic rays. Geophysics 56(1), 59–67 (1991)
L. Klimeš, Kvasnička and Michal. “3-D network ray tracing,”. Geophys. J. Int. 116(3), 726–738 (1994)
W. Hui, C. Xu, 3-D ray tracing method based on graphic structure. Chin. J. Geophys. 43(4), 534–541 (2000)
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
E.W. Dijkstra, A note on two problems in connection with graphs. Numer. Math. 1(1), 269–271 (1959)
R.J. Schechter, Snell’s Law: optimum pathway analysis. Surv. Ophthalmol. 21(6), 464–466 (1977)
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).
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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
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DOI: https://doi.org/10.1007/978-3-030-12111-2_40
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