A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves
Yu Shi-Jian1, Liu Run-Ze2, and Cheng Jiu-Long3
1. Key Laboratory of Mine Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao 266510, China.
2. Wuhan Changjiang Engineering Geophysical Exploration Co., Wuhan 430010, China.
3. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, China).
Abstract To address the problem of subdividing inflexible rectangular grid models and their poor definition of velocity interfaces, we propose a complex structure triangular net for a minimum traveltime ray tracing global algorithm. Our procedure is: (1) Subdivide a triangle grid based on the Delaunay triangular subdivision criterion and the relationships of the points, lines, and the surfaces in the subdividing area. (2) Define the topology relationships and related concepts of triangular unit ray tracing. (3) The source point and wave arrival points at any time compose the propagating plane wave and the minimum traveltime and secondary source positions are calculated during the plane wave propagation. We adopt the hyperbolic approximation global algorithm for secondary source retrieving. (4) By minimum traveltime ray tracing, collect the path from receiver to source points with the neighborhood point’s traveltime and the direction of the secondary source. Numerical simulation examples are given to test the algorithm. The results show that the triangular net ray tracing method demonstrates model subdivision flexibility, precise velocity discontinuity interfaces, and accurate computations.
This work is supported financially by the National Natural Science Foundation of China (Grant Nos. 50974081, 50774051, 51034003), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant No. 200958), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0843), and the Open Research Fund Program of the State Key Laboratory of Coal Resources and Safe Mining (China University of Mining and Technology, Beijing) (No. 2007-07).
Cite this article:
YU Shi-Jian,LIU Run-Ze,CHENG Jiu-Long. A minimum traveltime ray tracing global algorithm on a triangular net for propagating plane waves[J]. APPLIED GEOPHYSICS, 2010, 7(4): 348-356.
[1]
Cao, S, and Greenhalgh, S., 1993, Calculation of the seismic first-break time field and its ray path distribution using a minimum traveltime tree algorithm: Geohys. J. Int, 114(3), 593 - 600.
[2]
Gao, E. G., Xu, G. M., Li, G. P., Tu, S. J., and Zhao, Y., 2002, A new total iterative tracing method in random interfaces: Acta Acustica (in Chinese), 27(3), 282 - 287.
[3]
Julian, B.R., and Gubbins, D., 1977, Three-dimensional seismic ray tracing: J. Geophys, 43, 95 - 114.
[4]
Klimes, L., and Kvasnicha, M., 1994, 3-D network ray tracing: Geophys. J. Int., 116, 726 - 738.
[5]
Liu, H., Meng, F. L., and Li, Y. M., 1995, The interface grid method for seeking global minimum travel-time and the correspondent ray path: Chinese Journal of Geophysics (in Chinese), 38(6), 823 - 832.
[6]
Moser, T. J., 1991, Shortest path calculation of seismic ray: Geophysics, 56(1), 59 - 67.
[7]
Um, J., and Thurber, C., 1987, A fast algorithm for two-points seismic ray tracing: Bull. Seis. Soc. Am, 79, 972 - 986.
[8]
van Trier, J., and Symes, W. W, 1991, Upwind finite-difference calculation of travel times: Geophysics, 56, 812 - 821.
[9]
Vidale, J. E., 1988, Finite-difference calculation of travel times: Bull. Seis. Soc. Am., 78, 2062 - 2076.
[10]
Vidale, J. E., 1990, Finite-difference calculation of traveltimes in three dimensions: Geophysics, 55, 521 - 526.
[11]
Wang, H., and Chang, X., 2000, 3-D ray tracing method based on graphic structure: Chinese Journal of Geophysics (in Chinese), 43(4), 534 - 541.
[12]
Xu, T., Xu, G. M., Gao, E. G., Zhu, L. B., and Jiang, X. Y., 2004, Block modeling and shooting ray tracing in complex 3-D media: Chinese J. Geophys. (in Chinese), 47(6), 1118 - 1126.
[13]
Xu, T., Zhang, Z., Zhao, A., Zhang, X., Zhang, H., 2008, Sub-triangle shooting ray tracing in complex 3D VTI media: Journal of Seismic Exploration, 17, 131 - 144.
[14]
Zhang, J. Z., Chen, S. J., and Xu, C. W., 2004, A method of shortest path raytracing with dynamic networks: Chinese J. Geophysics (in Chinese), 47(5), 899 - 904.
[15]
Zhang, M. G., Jia, Y. G., Wang, M. Y., and Li, X, F., 2006, A global minimum traveltime raytracing algorithm of wavefront expanding with interface points as secondary sources: Chinese J. Geophys. (in Chinese), 49(4), 1169 - 1175.
[16]
Zhao, A. H., Zhang, Z. J., and Teng, J. W., 2004, Minimum travel time tree algorithm for seismic ray tracing: improvement in efficiency: Journal of Geophysics and Engineering, 1(4), 245 - 251.
[17]
Zhao, R., and Bai, C.Y., 2010, Fast multiple ray tracing within complex layered media: The shortest path method based on irregular grid cells: Acta Seismologica Sinica, 32(4), 433 - 444.
2010, Vol. 7 
