Frozen Gaussian approximation for 3-D elastic wave equation and seismic tomography
Frozen Gaussian approximation for 3-D elastic wave equation and seismic tomography
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DOI：
10.1093/gji/ggy498
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发表时间：
2018-10
影响因子：
2.8
通讯作者：
J. Hateley;L. Chai;P. Tong;Xu Yang
中科院分区：
文献类型：
--
作者：
J. Hateley;L. Chai;P. Tong;Xu Yang
本文将冻结高斯近似（FGA）理论推广到三维弹性波动方程的求解，并将其作为高频地震层析成像的正演模拟工具。FGA已被开发和验证为一个有效的解决方案，高频声波传播（P波）。本文的主要贡献包括三个方面：1.我们推导了三维弹性波方程的FGA公式。而不是标准的射线为基础的方法（如几何光学和高斯光束方法），推导需要做渐近展开在弱意义（积分形式），以便能够执行积分的部分。与声波方程的FGA理论相比，由于P波和S波的同时存在，以及SH波和SV波偏振方向的耦合，推导中的计算更具技术性。特别是，我们得到了非绝热耦合项SH-和SV-波，与形式密切相关的概念的Berry相位，深入研究量子力学和拓扑学（陈数）。通过与三维均匀介质弹性波动方程谱元法的比较，说明了FGA算法的精度和可并行性。基于欧拉方程和斯涅尔定律，推导了三维弹性波方程FGA的界面条件。我们通过模拟高频弹性波在1-D层状地球模型中的传播来验证这些条件。在这个例子中，我们还表明，它是自然的应用FGA算法的几何与非笛卡尔坐标; 3。将该算法分别应用于三维地震波方程走时层析成像和全波形反演
The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptotic expansion in the week sense (integral form) so that one is able to perform integration by parts. Compared to the FGA theory for acoustic wave equation, the calculations in the derivation are much more technically involved due to the existence of both P- and S-waves, and the coupling of the polarized directions for SH- and SV-waves. In particular, we obtain the diabatic coupling terms for SH- and SV-waves, with the form closely connecting to the concept of Berry phase that is intensively studied in quantum mechanics and topology (Chern number). The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method for 3-D elastic wave equation in homogeneous media; 2. We derive the interface conditions of FGA for 3-D elastic wave equation based on an Eulerian formulation and the Snell's law. We verify these conditions by simulating high-frequency elastic wave propagation in a 1-D layered Earth model. In this example, we also show that it is natural to apply the FGA algorithm to geometries with non-Cartesian coordinates; 3. We apply the developed FGA algorithm for 3-D seismic { wave-equation-based traveltime tomography and full waveform inversion, respectively