Abstract:In this paper,we use the fast marching method (FMM) algorithm to calculate the traveling time field.According to the definition of the function approximation and orthogonal polynomial,we use Chebyshev orthogonal polynomials to approximate the traveltime field so that the error minimizes in the least-square sense.Then the differential function in the Chebyshev interpolation function is directly used to calculate the gradient of the traveling field.And finally the ray path is obtained.Numerical experiments show that the proposed method improves greatly the accuracy and efficiency of ray path calculation.
Sun J,Sun Z,Han F.A finite difference scheme for solving the eikonal equation including surface topo-graphy.Geophysics,2011,76(4):T53-T63.
[2]
Vidale J E.Finite-difference calculation of traveltimes in 3-D.SEG Technical Program Expanded Abstracts,1989,8:1096-1098.
[3]
Vidale J.Finite-difference calculation of travel times.Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[4]
Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59-67.
[5]
唐小平,白超英,刘宽厚.分区多步最短路径极值法多值多次反射波追踪.地球物理学进展,2011,26(6):2064-2074.Tang Xiaoping,Bai Chaoying,Liu Kuanhou.Multiva-lued and multiple reflected raytracing with extreme value based on the multistage modified shortest-path method.Progress in Geophysics,2011,26(6):2064-2074.
[6]
赵后越,张美根.起伏地表条件下各向异性地震波最短路径射线追踪.地球物理学报,2014,57(9):2910-2917.Zhao Houyue,Zhang Meigen.Tracing seismic shortest path rays in anisotropic medium with roiling surface. Chinese Journal of Geophysics,2014,57(9):2910-2917.
[7]
李培明,梅胜全,马青坡.一种改进的双线性插值射线追踪方法.石油地球物理勘探,2013,48(4):553-558.Li Peiming,Mei Shengquan and Ma Qingbo.An improved bilinear interpolation travel-time ray-tracing method.OGP,2013,48(4):553-558.
[8]
韩复兴,孙建国,杨昊.基于二维三次卷积插值算法的波前构建射线追踪.吉林大学学报(地球科学版),2008, 38(2):336-340.Han Fuxing,Sun Jianguo,Yang Hao.Ray-tracing of wavefront construction by bicubic convolution interpolation.Journal of Jilin University (Earth Science Edition),2008,38(2):336-340.
[9]
张婷婷,张东,邱达.三维层状介质中基于旅行时梯度的多次波射线追踪.石油地球物理勘探,2014,49(6):1097-1105.Zhang Tingting,Zhang Dong and Qiu Da.Multiple ray tracing in 3D layered media using the traveltime gradient method.OGP,2014,49(6):1097-1105.
[10]
张东,张婷婷,乔友锋等.三维旅行时场B样条插值射线追踪方法.石油地球物理勘探,2013,48(4):559-566.Zhang Dong,Zhang Tingting,Qiao Youfeng et al.A 3-D ray tracing method based on B-spline traveltime interpolation.OGP,2013,48(4):559-566.
[11]
Asakawa E,Kanawa T.Seismic ray tracing using linear traveltime interpolation.Geophysical Prospecting,1993,41(1):99-111.
[12]
张东,傅相如,杨艳等.基于LTI和网格界面剖分的三维地震射线追踪算法.地球物理学报,2009,52(9):2370-2376.Zhang Dong,Fu Xiangru,Yang Yan et al.3-D seismic ray tracing algorithm based on LTI and partition of grid interface.Chinese Journa of Geophysics,2009,52(9):2370-2376.
[13]
刘锋,张东,杨艳等.三维LTI射线追踪极小值方程的快速数值解法.武汉大学学报(理学版),2012,58(5):395-400.Liu Feng,Zhang Dong,Yang Yan et al.A fast nume-rical solution to minimum equation in 3-D seismic LTI ray tracing.Journal of Wuhan University (Natural Science Edition).2012,58(5):395-400.
[14]
金昌昆,张建中.共接收面元三维折射旅行时反演方法.石油地球物理勘探,2016,51(4):751-759.Jin Changkun and Zhang Jianzhong.3D refraction traveltime inversion in common receiver-bins. OGP,2016,51(4):751-759.
[15]
Rawlinson N,Sambridge M.Wave front evolution in strongly heterogeneous layered media using the fast marching method.Geophysical Journal International,2004,156(3):631-647.
[16]
Rawlinson N,Sambridge M.Multiple reflection and transmission phases in complex layered media using a multistage fast marching method.Geophysics,2004,69(5):1338-1350.
[17]
张婷婷,邱达,张东.一种改进的三维旅行时梯度射线追踪方法.石油地球物理勘探,2016,51(5):916-923.Zhang Tingting,Qiu Da and Zhang Dong.A modified 3D traveltime gradient ray tracing method.OGP,2016,51(5):916-923.
[18]
Sethian J A.Evolution,implementation and applica-tion of level set and fast marching methods for advancing fronts.Journal of Computational Physics,2001,169(2):503-555.
[19]
Sethian J A.A fast marching level set method for monotonically advancing fronts.Proceedings of the National Academy of Sciences,1996,93(4):1591-1595.
[20]
黄兴国,孙建国,孙章庆等.基于复程函方程和改进的快速推进法的复旅行时计算方法.石油地球物理勘探,2016,51(6):1109-1118.Huang Xingguo,Sun Jianguo,Sun Zhangqing et al.A perturbation approach for solving the TTI complex eikonal equation.OGP,2016,51(6):1109-1118.
[21]
李永博,李庆春,吴琼等.快速行进法射线追踪提高旅行时计算精度和效率的改进措施.石油地球物理勘探,2016,51(3):467-473.Li Yongbo,Li Qingchun,Wu Qiong et al.Improved fast marching method for higher calculation accuracy and efficiency of traveltime.OGP,2016,51(3):467-473.
[22]
王飞,曲昕馨,刘四新等.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.石油地球物理勘探,2014,49(6):1106-1114.Wang Fei,Qu Xinxin,Liu Sixin et al.A new ray tra-cing approach based on both multi-stencils fast mar-ching and the steepest descent.OGP,2014,49(6):1106-1114.
[23]
张风雪,吴庆举,李永华等.FMM射线追踪方法在地震学正演和反演中的应用.地球物理学进展,2010,25(4):1197-1205.Zhang Fengxue,Wu Qingju,Li Yonghua et al.Application of FMM ray tracing to forward and inverse problems of seismology.Progress in Geophysics,2010,25(4):1197-1205.
[24]
邓飞,刘超颖.三维射线快速追踪及高斯射线束正演.石油地球物理勘探,2009,44(2):158-165.Deng Fei,Liu Chaoying.3-D rapid ray tracing and Gaussian ray beam forward simulation.OGP,2009,44(2):158-165.
[25]
李晓玲,白超英,胡光义.起伏层状TI介质中多次波射线追踪.石油地球物理勘探,2013,48(6):924-931.Li Xiaoling,Bai Chaoying and Hu Guangyi.Multiple ray tracing in an undulated layered TI media.OGP,2013,48(6):924-931.
[26]
唐秋惠,薛霆虓,何诚.三维多步FMM射线追踪在正态分布速度地层模型中的应用.工程地球物理学报,2017,14(3):346-352.Tang Qiuhui,Xue Tingxiao,He Cheng.The application of multi-stage 3D fast marching method of ray tracing in normal distribution speed model.Chinese Journal of Engineering Geophysics,2017,14(3):346-352.
[27]
孙章庆,孙建国,岳玉波等.复杂山地随机介质GMM-ULTI法射线追踪.地球物理学报,2016,59(7):2615-2627.Sun Zhangqing,Sun Jianguo,Yue Yubo et al.Ray tracing using GMM-ULTI method in the random media with complex topography.Chinese Journal of Geophysics,2016,59(7):2615-2627.