三维旅行时场B样条插值射线追踪方法  

A 3-D ray tracing method based on B-spline traveltime interpolation

作　　者：张东[1] 张婷婷[1] 乔友锋[1] 杨艳[1] 胡英[2] 秦前清[3] 

机构地区：[1]武汉大学物理科学与技术学院,湖北武汉430072 [2]中国石油勘探开发研究院,北京100083 [3]武汉大学测绘遥感信息工程国家重点实验室,湖北武汉430072

出　　处：《石油地球物理勘探》2013年第4期559-566,676+501,共8页Oil Geophysical Prospecting

基　　金：国家科技重大专项课题(2008ZX05020-006)资助

摘　　要：传统的三维射线追踪算法由于受到计算区域网格离散化的限制,会导致追踪结果的射线路径出现不应有的弯折和相邻射线合并现象,进而影响追踪精度。本文根据地震初至波路径垂直于波前面的原理,提出基于B样条插值的旅行时场梯度反向射线追踪方法。该方法通过三次B样条插值得到空间连续的旅行时场,并计算旅行时场梯度;然后从检波点开始,沿着旅行时场梯度的负方向进行追踪,即可得到从震源到检波点的最小旅行时路径。由于通过样条插值能获得连续的旅行时场,故追踪步长不受网格尺寸的限制,从而克服计算区域离散化所带来的问题。应用具体算例对该方法的效果进行了验证,结果表明,该方法在计算精度和效率上都有明显改善。应用于地震初至波层析成像的正演计算时,能够使收敛误差更小。Grid dissection of computational areas in conventional 3-D seismic ray tracing algorithms always lead to some zigzags and unexpected mergence in ray paths which may bring lower precision to calculation.To solve these problems,a new ray tracing scheme based on B-spline interpolation in backward step is presented in this paper.We calculate traveltime at any point in the area by cubic B-spline interpolation,and then get the field of traveltime gradient.According to the Fermat's principle,the ray path is always perpendicular to the wavefront which is the same of the negative traveltime gradient.First arrival ray path then can be traced from receiver point to source point along the negative gradient step by step.Since the traveltime field reconstructed by cubic B-spline interpolation is continuous and smooth,the tracing step-size has no limitation of the grid size,and the tracing error introduced by area discretization can be reduced obviously.The results of two experimental models revealed the improvement in precision and efficiency of the new algorithm.And less convergence error can also be reached when the new algorithm is applied to forward modeling for seismic traveltime tomography.

关 键 词：射线追踪 三次B样条 旅行时线性插值 初至波 地震层析成像 

分 类 号：P631[天文地球—地质矿产勘探]