A modified 3D traveltime gradient ray tracing method
Zhang Tingting1, Qiu Da2, Zhang Dong2
1. School of Information Engineering, Hubei University for Nationalities, Enshi, Hubei 445000, China;
2. School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
摘要 最大旅行时梯度射线追踪（The Maximum Traveltime Gradient Ray Tracing，MTG）法利用三次B样条插值计算旅行时场的最大旅行时梯度,从而追踪初至波射线路径。但由于三次B样条插值是连续光滑的插值函数，在射线通过速度突变区域时，计算次级源点的旅行时和梯度会产生一定的误差。在分析MTG算法计算误差来源的基础上，提出了一种改进的B样条/线性联合插值的三维射线追踪（The Modified Maximum Traveltime Gradient Ray Tracing，简称MMTG）算法，即在速度均匀变化的区域采用B样条插值计算旅行时梯度确定下一个次级源点，在速度变化剧烈的区域利用线性插值法在网格界面上找出旅行时最小的入射点作为次级源点，从而保证射线在速度分界面上折射产生的不连续性。数值实验结果表明，MMTG算法在保持MTG算法优点的同时进一步提高了射线路径的计算精度，能够适应更复杂的速度介质模型。
Abstract：The maximum traveltime gradient (MTG) ray tracing method calculates the gradient of traveltime of cubic B-spline interpolation and traces the ray path with the gradient of travel time field. How-ever, the cubic B-spline interpolation is a smooth continuous interpolation function, so in the area with abrupt velocity change, it causes calculation error. In this study, we propose a 3D modified maximum traveltime gradient (MMTG) ray tracing method based on the analysis of the error of MTG. This MMTG method uses the B-spline/linear combined interpolation to calculate the ray path of seismic waves. In this process, we determine the next tracing point with the traveltime gradient calculated by the cubic B-spline interpolation in the area with slow-varying velocity; while in the region with an abrupt velocity change, we adopted a regional linear interpolation to find out the next secondary source to ensure only discontinuous refraction at interfaces is generated. Numerical experiment results show that the proposed MMTG ray tracing method can keep basic characteristics of the MTG method and achieve more accurate computation of traveltime in inhomogeneous and discontinuous media.
Clement W P,Knoll M D. Tomographic inversion of crosshole radar data:confidence in results. Proceedings of SAGEEP 2000,Environmental and Engineering Geophy-sical Society,2000,553-562.
[2]
Grunberg M,Genaud S,Mongenet C. Seismic ray-tracing and Earth mesh modeling on various parallel architectures. The Journal of Supercomputing,2004,29(1):27-44.
[3]
Serretti P,Morelli A. Seismic rays and traveltime tomography of strongly heterogeneous mantle structure:application to the Central Mediterranean. Geophysical Journal International,2011,187(3):1708-1724.
Sun Zhangqing,Sun Jianguo,Han Fuxing. The comparison of three schemes for computing seismic wave traveltime in complex topographical conditions. Chinese Journal of Geophysics,2012,55(2):560-568.
[10]
Hole J A,Zelt B C. 3-D finite-difference reflection travel times. Geophysical Journal International,1995,121(2):427-434.
[11]
Kim S,Cook R. 3D traveltime computation using second-order ENO scheme. Geophysics,1999,64(6):1867-1876.
[12]
Qin F,Luo Y,Olsen K B et al. Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics 1992,57(3):478-487.
[13]
Cao S,Greenhalgh S. Finite-difference solution of the eikonal equation using an efficient,first-arrival,wavefront tracking scheme. Geophysics,1994,59(4):632-643.
[14]
Asakawa E,Kanawa T. Seismic ray tracing using lin-ear traveltime interpolation. Geophysical Prospecting,1993,41(1):99-111.
Peng Zhixing,Shen Zhongmin. Computation of three dimensional seismic traveltime based on bilinear interpolation. Journal of Southwest Petroleum University (Science and Technology Edition),2008,30(5):85-87.
Mei Shengquan,Deng Fei,Zhong Benshan et al. The 3D ray tracing method based on the improved bilinear travetime interpolation. Computing Techniques for Geophysical and Geochemical Exploration,2010,32(2):152-157.
[17]
Zhang J Z,Huang Y Q,Song L P et al. Fast and accurate 3-D ray tracing using bilinear traveltime interpolation and the wave front group marching. Geophysical Journal International,2011,184(3):1327-1340.
Zhang Dong,Fu Xiangru,Yang Yan et al. 3-D seismic ray tracing algorithm based on LTI and partition of grid interface. Chinese Journal of Geophysics,2009,52(9):2370-2376.
Wang Fei,Qu Xinxin,Liu Sixin et al. A new ray tracing approach based on both multi-stencils fast marching and the steepest descent. OGP,2014,49(6):1106-1114
Zhang Dong,Zhang Tingting,Qiao Youfeng et al. A 3-D ray tracing method using B-spline traveltime interpolation. OGP,2013,48(4):559-566.
[21]
Zhang D,Zhang T T,Zhang X L et al. A new 3-D ray tracing method based on LTI using successive partitioning of cell interfaces and traveltime gradients. Journal of Applied Geophysics,2013,92:20-29.
