An upwind fastsweeping scheme for calculating seismic wave first-arrival traveltimes formodels with an irregular free surface
An upwind fastsweeping scheme for calculating seismic wave first-arrival traveltimes formodels with an irregular free surface
复制标题
不规则自由面模型地震波初至走时计算的逆风快扫方案
DOI：
10.1111/1365-2478.12513
复制
发表时间：
2018
影响因子：
2.6
通讯作者：
Chen. Ling
中科院分区：
文献类型：
--
作者：
Lan Haiqiang;Chen. Ling
最近建立了曲线坐标系中与地形有关的程控方程，并证明该方程在计算具有不规则自由面的地球模型中的地震波初至旅行时是有效的。Lax-Friedrichs扫掠格式在以往的研究中被广泛用于逼近地形相关的eikonal方程粘性解，它的耗散性更强，需要更多的迭代才能收敛。此外，所需的迭代次数随着网格的细化而增加，导致密集网格中的计算量很大，这阻碍了Lax-Friedrichs扫频格式在地震波走时计算和高分辨率成像中的应用。本文利用显式公式对地形相关方程的数值哈密顿量的勒让德变换进行离散化，提出了一种新的迎风快速扫掠求解器。对扫描格式中与勒让德变换有关的极小值问题进行了解析求解，证明了该算法在求解地形相关的方程时比Lax-Friedrichs算法要高效得多。数值实验表明，新的迎风快速扫掠方法在有限次迭代后收敛，并获得了更高的精度，与网格大小无关，这使得它成为计算非平坦自由面情况下旅行时的一种有效和稳健的工具。
The topography‐dependent eikonal equation formulated in a curvilinear coordinate system has recently been established and revealed as being effective in calculating first‐arrival travel times of seismic waves in an Earth model with an irregular free surface. The Lax–Friedrichs sweeping scheme, widely used in previous studies as for approximating the topography‐dependent eikonal equation viscosity solutions, is more dissipative and needs a much higher number of iterations to converge. Furthermore, the required number of iterations grows with the grid refinement and results in heavy computation in dense grids, which hampers the application of the Lax–Friedrichs sweeping scheme to seismic wave travel‐time calculation and high‐resolution imaging. In this paper, we introduce a new upwind fast sweeping solver by discretising the Legendre transform of the numerical Hamiltonian of the topography‐dependent eikonal equation using an explicit formula. The minimisation related to the Legendre transform in the sweeping scheme is solved analytically, which proved to be much more efficient than the Lax–Friedrichs algorithm in solving the topography‐dependent eikonal equation. Several numerical experiments demonstrate that the new upwind fast sweeping method converges and achieves much better accuracy after a finite number of iterations, independently of the mesh size, which makes it an efficient and robust tool for calculating travel times in the presence of a non‐flat free surface.