Abstract：We propose a new ray tracing approach in two steps. First wavefront propagation times of all grid points in a known velocity field are calculated using the multi-stencils fast marching method (MSFM). Then the ray path with the minimum traveltime can be easily obtained by following the steepest gradient direction from the receiver to the transmitter. Contrast to conventional fast marching method (FMM) and its improved algorithms, MSFM algorithm calculates traveltime using two stencils at the same time, and the information in diagonal direction can be included, thus the calculation accuracy and efficiency can be greatly improved. In order to verify the accuracy and efficiency of the new ray tracing method, we test the proposed scheme on two synthetic velocity models. We compared our result with those obtained by FMM and the high accuracy fast marching method(HAFMM).This comparison indicates that the proposed ray tracing technique is efficiency and achieves better results both on accuracy and efficiency compared to the FMM based and the HAFMM based steepest descent ray tracing methods.
王飞, 曲昕馨, 刘四新, 李彦鹏, 吴俊军. 一种新的基于多模板快速推进算法和最速下降法的射线追踪方法[J]. 石油地球物理勘探, 2014, 49(6): 1106-1114.
Wang Fei, Qu Xinxin, Liu Sixin, Li Yanpeng, Wu Junjun. A new ray tracing approach based on both multi-stencils fast marching and the steepest descent. OGP, 2014, 49(6): 1106-1114.
Aldridge D F,Oldenburg D W. Two-dimensional tomographic inversion with finite-difference traveltimes. Journal of Seismic Exploration,1993,2,257-274.
[2]
Clement W P,Knoll M D. Tomographic inversion of crosshole radar data:confidence in results. Proceedings of SAGEEP 2000,Environmental and Engineering Geophysical Society,2000,553-562.
[3]
Goktukler G,Balkaya C. Traveltime tomography ofcrosshole radar without raytracing. Journal of Applied Geophysics,2010,72(4):213-224.
[4]
Julian B R,Gubbins D. Three-dimensional seismic ray tracing. Journal of Geophysics Research,1977,43(1):95-114.
[5]
Um J,Thurber C. A fast algorithm for two-point seismic ray tracing. Bulletin of the Seismological Society of America,1987,77(3):972-986.
[6]
Prothero W A,Taylor W J,Eickemeyer J A. A fast,two-point,three-dimensional raytracing algorithm using a simple step search method. Bulletin of the Seismological Society of America,1988,78(3):1190-1198.
[7]
Nakanishi I,Yamaguchi K. A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure. Journal of Physics of the Earth,1986,34(2):195-201.
[8]
Moser T J. Shortest path calculation of seismic rays. Geophysics,1991,56(1):59-67.
[9]
Fischer R,Lees J M. Shortest path ray tracing with sparse graphs. Geophysics,1993,58(7):987-996.
[10]
Asakawa E,Kawanaka T. Seismic ray tracing using linear traveltime interpolation. Geophysical Prospecting,1993,41(1):99-111.
Li Peiming,Mei Shengquan,Ma Qingpo. An improved bilinear interpolation travel-time ray-tracing method. OGP,2013,48(4):553-558.
[13]
Vidale J E. Finite-difference calculation of travel-times. Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[14]
Vidale J E. Finite-difference calculation of traveltimes in three dimensions. Geophysics,1990,55(5):521-526.
[15]
Van T J,Symes W W. Upwind finite-difference cal-culation of traveltimes. Geophysics,1991,56(6):812-821.
[16]
Qin F,Luo Y,Olsen K B et al. Finite-difference solution of the eikonal equation along expanding wave fronts. Geophysics,1992,57(3):478-487.
[17]
Tsai Y R,Cheng L T,Osher S et al. Fast sweeping algorithm for a class of Hamilton-Jacobi equation. SIAM Journal on Numerical Analysis,2003,41(2):673-694.
[18]
Zhao H K. A fast sweeping method for eikonal equation. J Math and Computing,2004,74:603-627.
[19]
Zhang Y T,Zhao H K,Qina J. High order fast sweeping methods for static Hamilton-Jacobi equation. J Scientific Computing,2006,29:25-26.
[20]
Sethian J A. A fast marching level set methods for monotonically advancing fronts. Proc Natl Acad Sci,1996,93(4):1591-1595.
[21]
Sethian J A,Popovici A M. 3-D traveltime computation using the fast marching method. Geophysics,1999,64(2):516-523.
[22]
Gremaud P A,Kuster C M. Computational study of fast methods for the eikonal equation. SIAM J Scientific Computing,2006,27(6):1803-1816.
[23]
Kim S. An O(N) level set method for eikonal equations. SIAM J Scientific Computing,2001,22(6):2178-2193.
[24]
Yatziv L,Bartesaghi A,Sapiro G. O(N) implementation of the fast marching algorithm. Journal of Computational Physics,2006,212(2):393-399.
[25]
Sethian J A. Level Sets Methods and Fast Marching Methods(Second Edition). Cambridge Univ Press,1999.
[26]
Danielsson P E,Lin Q F. A modified fast marching method. Proc Scandinavian Conf Image Analysis,2003,2749:1154-1161.
[27]
Hassouna M S and Farag A A. Multistencils fast marching methods:A highly accurate solution to the eikonal equation on cartesian domains. IEEE Transactions on Pattern Analysis and Machine Inteligence,2007,29:1-12.
[28]
Slawinski R A and Slawinski M A. On raytracing in constant velocity-gradient media:calculus approach. Canadian Journal of Exploration Geophysics,1999,35(1-2):24-27.
