Hybrid Fast Sweeping Methods for Anisotropic Eikonal Equation in Two-Dimensional Tilted Transversely Isotropic Media
Hybrid Fast Sweeping Methods for Anisotropic Eikonal Equation in Two-Dimensional Tilted Transversely Isotropic Media
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DOI：
10.1007/s10915-020-01280-3
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发表时间：
2020-07
影响因子：
2.5
通讯作者：
Guangnan Huang;S. Luo
中科院分区：
文献类型：
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作者：
Guangnan Huang;S. Luo
在求解各向异性斜向方程的基础上，提出了计算二维倾斜横向各向同性介质中qP、qSV和qSH波初到传播时的混合快速扫描方法。采用因式分解方法求解点源附近的源奇点，得到了一个因式各向异性方程，该方程的求解精度较高。该方法在点源的一个邻域内求解分解方程，邻域的大小与网格无关，在邻域外求解原方程。该方法具有常用快速扫描方法的效率、准确性和收敛性等优点。此外，由于一阶快速扫描方法的“超收敛”性质，即其数值解和梯度都是一阶精确的，使得我们可以设计基于线性不连续Galerkin公式的二阶快速扫描方法。二阶方法作为一阶方法的后处理过程，将线性不连续Galerkin公式中的局部自由度由3个降为1个，使得局部更新公式简单，是一种高效的二阶格式。数值实验证明了所提出的方法。
We present hybrid fast sweeping methods for computing first-arrival traveltime of the qP, qSV and qSH waves in two-dimensional tilted transversely isotropic media, based on solving the anisotropic eikonal equation. A factorization approach is applied to resolve the source singularity near the point source, which leads to a factored anisotropic eikonal equation whose solutions can be computed with high accuracy. The proposed methods solve the factored equation in a neighborhood of the point source with the size of the neighborhood independent of the mesh, and solve the original equation outside the neighborhood. The methods enjoy all the appealing features, such as efficiency, accuracy and convergence, of the usual fast sweeping method. Furthermore, the “super-convergence” property of the first-order fast sweeping method, i.e., both its numerical solution and gradient are first-order accurate, allows us to design a second-order fast sweeping method based on a linear discontinuous Galerkin formulation. As a post-processing procedure of the first-order method, the second-order method reduces the local degrees of freedom from three to one in the linear discontinuous Galerkin formulation, which implies a simple local updating formula, hence an efficient second-order scheme. Numerical experiments are presented to demonstrate the proposed methods.