2D/3D起伏地表多震相地震波走时的因式分解程函方程算法  

Multi⁃phase seismic traveltime computation in 2D/3D undulated surface model using factored eikonal equation

作　　者：张云 李夕海 白超英[2,3] 牛超 王艺婷 曾小牛 ZHANG Yun;LI Xihai;BAI Chaoying;NIU Chao;WANG Yiting;ZENG Xiaoniu(Rocket Force University of Engineering,Xi’an,Shaanxi 710025,China;Department of Geophysics,College of Geological Engineering and Geomatics,Chang’an University,Xi’an,Shaanxi 710054,China;Institute of Computational Geophysics,Chang’an University,Xi’an,Shaanxi 710054,China)

机构地区：[1]火箭军工程大学,陕西西安710025 [2]长安大学地质工程与测绘学院地球物理系,陕西西安710054 [3]长安大学计算地球物理研究所,陕西西安710054

出　　处：《石油地球物理勘探》2023年第4期857-871,共15页Oil Geophysical Prospecting

摘　　要：起伏地表条件的地震波走时计算方法是研究该类地表区地下结构的基础工具。快速行进法和快速扫描法均是基于有限差分求解程函方程而发展起来的地震波走时计算方法,由于震源附近波前曲率较大,这两种算法均存在震源奇异性问题。研究成果表明,对于复杂模型快速行进法的计算效率高于快速扫描法。为此,借鉴快速扫描法解决震源奇异性的思路,采用快速行进法求解因式分解程函方程,从而规避了震源奇异性问题。具体而言,将地震波走时分解为一个距离函数T0与一个走时扰动值T1乘积的形式,通过快速行进法求解T1,并与T0相乘,得到地震波走时;同时,为弥补规则网格迎风差分格式不适用于地表/界面起伏的缺陷,构建了适用于不规则网格的不等距迎风差分格式,进而结合分区多步技术形成了全局多震相地震波走时计算方法。2D和3D数值模拟实例表明,所提算法从根本上解决了快速行进法的震源奇异性问题,显著提高了原算法的计算精度与效率,可精确计算多震相地震波走时。The seismic traveltime computation scheme in undulating surface conditions is a basic tool to study the underground structures of such surface areas.The fast marching method(FMM)and the fast sweeping method(FSM)are both developed based on solving the eikonal equation with finite difference.They have the problem of source singularity due to the high curvature of the wavefront around the source.Previous studies show that the com‑putational efficiency of FMM is higher than FSM for complex models.Thus,this paper employs the FMM to solve the factorization equation and avoid source singularity.Specifically,the original eikonal equation can be transformed into the factored eikonal equation,in which the seismic traveltime can be regarded as the product of a distance function T0 and a correction factor T1 of traveltime.The correction factor T1 of traveltime can be solved by the FMM algorithm and then the distance function T0 is multiplied to obtain the traveltime(T).To address the problem that the upwind finite difference formula with even grid spacing is not applicable to surface/interface undulation,this paper constructs an upwind finite difference formula with uneven grid spacing.Finally,the multistage computational technique is adopted to propose a computation method for global multi‑phase seismic traveltime.The simulation tests indicate that the new algorithm solves the source singularity of FMM,significantly improves the computational accuracy and efficiency of the original algorithm,and can accurately calculate the multi‑phase seismic traveltime.

关 键 词：因式分解程函方程 走时扰动因子 不等距迎风差分格式 多震相地震波走时计算 

分 类 号：P631[天文地球—地质矿产勘探]