Traveltime Calculations for qP, qSV, and qSH Waves in Two‐Dimensional Tilted Transversely Isotropic Media
Traveltime Calculations for qP, qSV, and qSH Waves in Two‐Dimensional Tilted Transversely Isotropic Media
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DOI：
10.1029/2019jb018868
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发表时间：
2020-07
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通讯作者：
Guangnan Huang;S. Luo;Juzhi Deng;V. Vavryčuk
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作者：
Guangnan Huang;S. Luo;Juzhi Deng;V. Vavryčuk
本文提出了一种快速扫描方法（FSM）来计算二维（2D）横向各向同性介质中qP、qSV和qSH波的初至走时，该介质的对称轴可以具有任意方向（倾斜横向各向同性[TTI]）。该方法在矩形网格上用有限差分近似离散各向异性程函方程，并用高斯-赛德尔迭代法沿着交替扫描顺序迭代求解离散系统。在每个网格点处，求解高度非线性方程以更新数值解直到其收敛。对于非线性方程的求解，首先确定一个包含解的区间，并将其划分为若干个子区间，使得每个子区间包含一个解，然后在这些子区间上应用伪位置法计算解;之后，在离散化方程的所有可能解中，施加因果关系条件，并且选择满足因果关系条件的最小解来更新解。对于具有点源条件的问题，在应用因式分解技术来解决源奇异性之后，FSM被扩展用于求解各向异性程函方程，这产生了干净的一阶精度。当处理qSV波的三倍时，选择对应于最小群速度的解，使得计算连续解。数值实验证明了该方法的精度、效率和性能。
This paper presents a fast sweeping method (FSM) to calculate the first‐arrival traveltimes of the qP, qSV, and qSH waves in two‐dimensional (2D) transversely isotropic media, whose symmetry axis may have an arbitrary orientation (tilted transverse isotropy [TTI]). The method discretizes the anisotropic eikonal equation with finite difference approximations on a rectangular mesh and solves the discretized system iteratively with the Gauss‐Seidel iterations along alternating sweeping orderings. At each mesh point, a highly nonlinear equation is solved to update the numerical solution until its convergence. For solving the nonlinear equation, an interval that contains the solutions is first determined and partitioned into few subintervals such that each subinterval contains one solution; then, the false position method is applied on these subintervals to compute the solutions; after that, among all possible solutions for the discretized equation, a causality condition is imposed, and the minimum solution satisfying the causality condition is chosen to update the solution. For problems with a point‐source condition, the FSM is extended for solving the anisotropic eikonal equation after a factorization technique is applied to resolve the source singularities, which yields clean first‐order accuracy. When dealing with the triplication of the qSV wave, solutions corresponding to the minimal group velocity are chosen such that continuous solutions are computed. The accuracy, efficiency, and capability of the proposed method are demonstrated with numerical experiments.