三维最短路径法射线追踪及改进
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摘要
射线追踪技术在地震学领域有着广泛的应用,其中以最短路径算法在复杂介质中走时计算稳定性最好。理论上最短路径法的误差来源为速度模型采样误差、空间离散化误差和角度离散化的误差,由此造成网格稀疏时射线路径呈之字形,计算走时比实际走时偏大。弯曲法追踪精度高,但是射线追踪速度受初始路径与真实射线路径逼近程度制约,在复杂介质中可能找不到全局最小走时路径。最短路径法追踪出来的网格射线路径,可以作为较理想的初始路径,供弯曲法迭代优化。将最短路径法和弯曲法结合,通过射线在初始路径附近的扰动得到Fermat原理约束下的最短路径。文章对常速模型的试算,显示了改进方法对射线路径优化的作用,在模型网格稀疏的情况下效果尤其明显。本算法适用于计算三维任意复杂介质中初至波走时和射线路径,可应用于三维走时层析成像等领域。
Ray tracing techniques are widely applied in seismology, among which the shortest path method (SPM) is robust for 3-D ray tracing in complex velocity structures. Errors of SPM are mainly caused by three factors, namely sampling of velocity field, space discretization and angle discretization. When sparse calculating nodes are used in SPM ray tracing, raypath runs zigzag and the computed travel time is larger than the actual time between two nodes. Although ray bending method has relatively high tracing accuracy, the velocity of ray tracing is constrained by the approximation of the initial raypath to the real raypath, thus the path with the shortest travel time cannot be found in complex media. The raypath traced with SPM can be used as an ideal initial path for optimization with ray bending method. When SPM is combined with ray bending method, the shortest path under the constraints of Fermat's principle can be obtained through perturbation of ray near the initial raypath. Test of the combined method in a constant velocity model shows it can optimize raypath, especially in a network with coarse node spacing. The algorithm can be used to calculate the travel time and raypath of the first break in any complex 3-D media and can be applied to 3-D travel time tomography.
Ray tracing techniques are widely applied in seismology, among which the shortest path method (SPM) is robust for 3-D ray tracing in complex velocity structures. Errors of SPM are mainly caused by three factors, namely sampling of velocity field, space discretization and angle discretization. When sparse calculating nodes are used in SPM ray tracing, raypath runs zigzag and the computed travel time is larger than the actual time between two nodes. Although ray bending method has relatively high tracing accuracy, the velocity of ray tracing is constrained by the approximation of the initial raypath to the real raypath, thus the path with the shortest travel time cannot be found in complex media. The raypath traced with SPM can be used as an ideal initial path for optimization with ray bending method. When SPM is combined with ray bending method, the shortest path under the constraints of Fermat's principle can be obtained through perturbation of ray near the initial raypath. Test of the combined method in a constant velocity model shows it can optimize raypath, especially in a network with coarse node spacing. The algorithm can be used to calculate the travel time and raypath of the first break in any complex 3-D media and can be applied to 3-D travel time tomography.
引文
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[5]VAN AVENDONK HJ A,HARDING AJ,ORCUTT J A.Hybrid shortest path and ray bending method for travelti me and raypath calculations[J].Geophysics,2001,66:648-653.
[2]任文福,等.变速介质条件下三维叠前深度偏移成像及应用效果[J].天然气工业,2005,25(10):41-43.
[3]陈国金,等.井间地震层析成像中自动生成初始速度模型的方法研究[J].石油物探,2005,44(4):339-342.
[4]MOSER T J.Shortest path calculation of seismic rays[J].Geophysics,1991,56:59-67.
[5]VAN AVENDONK HJ A,HARDING AJ,ORCUTT J A.Hybrid shortest path and ray bending method for travelti me and raypath calculations[J].Geophysics,2001,66:648-653.
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