基于快速拟合算法的二维TTI介质qP波和qSV波走时计算  

Traveltime calculation for qP and qSV waves based on fast fitting algorithm in 2D TTI media

作　　者：芦永明 杨建勋 张剑锋 杨凯 李正伟 LU YongMing;YANG JianXun;ZHANG JianFeng;YANG Kai;LI ZhengWei(MSU-BIT-SMBU Joint Research Center of Applied Mathematics,Shenzhen MSU-BIT University,Shenzhen 518100,China;Faculty of Computational Mathematics and Cybernetics Shenzhen MSU-BIT University,Shenzhen 518100,China;Department of Earth and Space Sciences,Southern University of Science and Technology,Shenzhen 518055,China)

机构地区：[1]深圳北理莫斯科大学,莫大-北理工-深北莫应用数学联合研究中心,深圳518100 [2]深圳北理莫斯科大学计算数学与控制系,深圳518100 [3]南方科技大学地球与空间科学系,深圳518055

出　　处：《地球物理学报》2025年第5期1911-1921,共11页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(42104119,42104106,42204130);河北省地震科技星火计划重点项目(2025091100001);广东省教育厅项目“地震面波的数学模型及机器学习算法”(2021KTSCX145)联合资助.

摘　　要：快速准确的计算地震波走时在地球物理学中有重要的应用.然而,各向异性程函方程由于其复杂的非线性,导致走时求解具有极大的挑战性.在倾斜横向各向同性(TTI)介质中求解程函方程,传统方法通常需要使用迭代算法.面对大规模的偏移成像,高效率的走时计算显得尤为重要,但传统方法由于高昂的计算成本和复杂的方程求解难以满足实际应用需求.因此,发展了一种基于拟合算法的快速解决弱各向异性介质程函方程的方法.首先,在局部解中分析了qP波和qSV波对应的TTI介质慢度方程,研究表明在弱各向异性条件下,慢度方程的根与其对应的拟合二次函数的根相近,可以作为迭代法的一个初始点.据此提出在局部解的走时范围内使用二次曲线拟合对应的慢度方程,快速求解二次方程获取走时根.在获得走时解后,通过检查因果关系以保留满足条件的解.然后,将提出的这个算法与快速扫描法(FSM)相结合解决弱TTI介质的走时问题.最后,通过三个数值实验验证了提出算法在二维弱各向异性介质走时计算中的高效性和准确性.The fast and accurate calculation of seismic wave traveltimes has important applications in geophysics.However,solving the eikonal equations in transversely isotropic with a tilted axis(TTI)media presents significant challenges due to its complex nonlinearity.Traditional methods for solving these equations in TTI media involve using various iterative algorithms in combination with Fast Sweeping Methods(FSM).Efficient traveltime calculations are particularly important for large-scale migration imaging,but the high computational cost and complexity of equation solving in traditional methods need improvement to meet practical application demands.To address this problem,we have developed a fast solution for the eikonal equations in weakly anisotropic media based on a fitting algorithm.First,we analyzed the slowness equations of qP and qSV waves in TTI media in the local solver.The study revealed that under weakly anisotropic conditions,the slowness function differs only slightly from a quadratic function fitted to it.Therefore,we proposed to utilize quadratic curve fitting within the traveltime range of local solutions for the corresponding slowness equations,enabling the fast solution of the quadratic equation to obtain two roots.After obtaining the traveltime solutions,causality checks are performed to retain solutions that satisfy the conditions.By combining the above algorithm with the FSM to compute traveltimes in weakly TTI media,we further validated the efficiency and accuracy of this algorithm using three numerical experiments for traveltime calculations in two-dimensional weakly anisotropic media.

关 键 词：弱各向异性介质 拟合慢度方程 快速扫描法 

分 类 号：P631[天文地球—地质矿产勘探]