曲线坐标系因式分解程函方程及其走时计算  

The factored eikonal equation in curvilinear coordinate system and its numerical solution

作　　者：周小乐 兰海强[1,2] 陈凌 郭高山[1,2] ZHOU XiaoLe;LAN HaiQiang;CHEN Ling;GUO GaoShan(State Key Laboratory of Lithospheric Evolution,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;University of the Chinese Academy of Sciences,Beijing 100049,China;Chinese Academy of Sciences Center for Excellence in Tibetan Plateau Earth Sciences,Beijing 100101,China)

机构地区：[1]中国科学院地质与地球物理研究所,岩石圈演化国家重点实验室,北京100029 [2]中国科学院大学,北京100049 [3]中国科学院青藏高原地球科学卓越创新中心,北京100101

出　　处：《地球物理学报》2020年第2期638-651,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金(NSFC 41674095);岩石圈演化国家重点实验室自主研究课题(SKL-Z201704-11712180,SKLYT201802)共同资助

摘　　要：地震波走时广泛应用于静校正、层析成像、Kirchhoff偏移成像、地震定位等研究.复杂地表条件是影响走时计算精度的重要因素.近年来,发展的曲线坐标系程函方程为精细刻画起伏地表条件下的地震波走时场特征提供了新的思路.然而,基于有限差分程函方程的求解方法不可避免地受到震源奇异性的影响,即震源附近波前的曲率较大,此时使用平面波近似假设的差分格式会导致较大误差.而震源误差会随着波前的传播到达整个计算区域,从而影响整个区域的求解精度.针对该问题,本文借鉴因式分解的思想,推导建立了曲线坐标系因式分解程函方程,并针对性地发展了其数值求解方法,从根源上解决了复杂模型走时计算中的震源奇异性问题.数值实例表明因式分解法能够有效降低震源误差,显著提高起伏地表走时计算的精度和效率,为起伏地表地震波走时计算提供更佳的选择,在复杂模型的地震资料处理中展现出广泛的应用前景.The calculation of first-arrival traveltime plays an important role in many areas of seismology such as static correction,seismic tomography,pre-stack migration,earthquake location,etc.Complex surface conditions are important factors affecting the accuracy of traveltime calculation.In recent years,the development of eikonal equation in a curvilinear coordinate system paves a new way for calculating seismic traveltime with an irregular surface.However,the finite-differencebased eikonal solution is inevitably affected by the source singularity.Due to the high curvature of the wavefront around the source,using aplane wave to approximate the wavefront results in a large numerical error,which will propagate from the source to all computational domain.In order to solve this problem,we formulate the factored eikonal equation in the curvilinear coordinate system using factorization.Then,we develop a factored fast sweeping solver to address the source singularity problem for traveltime calculation with an irregular surface.Numerical examples show that the factored sweeping method can treat the source singularity successfully,improve the accuracy and efficiency of the traveltime calculation with an irregular surface significantly.It provides a better choice for the traveltime calculation with an irregular surface,showing a wide potential in the seismic data processing under complex topographical conditions.

关 键 词：曲线坐标系 因式分解 程函方程 震源奇异性 

分 类 号：P631[天文地球—地质矿产勘探]