一般各向异性介质地震qP波,qSV波和qSH波的有限差分走时计算方法研究

现有的各向异性介质走时计算方法主要针对TI介质和正交各向异性介质，且求解过程中采用了简化的程函方程和简化的相、群速度公式，使得走时计算方法缺乏普遍适用性。另外，有限差分格式在直角坐标系中求解点震源的程函方程存在源点奇异性，制约了走时计算精度。本项目拟推导出一般各向异性介质的程函方程、相速度和群速度公式，且不对它们作简化和近似，然后推导出非线性程函方程的求根公式和因果关系条件，最后设计出求解一般各向异性介质程函方程的快速扫描数值解法。在此基础之上，借鉴因式分解的基本思想，推导出压制源点奇异性的各向异性介质因式分解程函方程、相应的非线性程函方程求根公式和因果关系条件，最终设计出求解因式分解程函方程的快速扫描数值解法，以得到更高精度的地震波走时场。该研究可以计算出不同（高、低）对称度各向异性介质的地震波走时场，对实现高效、高精度的一般各向异性介质地震波走时计算方法具有重要的理论意义和实用价值。

Most of well-developed anisotropic traveltime calculation methods aims to TI and orthorhombic media. Simplified eikonal equation, phase-and group- velocities are adopted, this makes these traveltime calculation methods lacks of universal applicability. In addition, the finite-difference scheme has source singularity problem when it solves a point-source eikonal equation in Cartesian coordinates, this restricts traveltime accuracy. In this project, eikonal equation, phase- and group- velocities will be deduced for general anisotropic media without simplification and approximation. Then, a root-finding expression for the nonlinear eikonal equation and a causality condition will be given. Finally, a series of numerical schemes will be proposed for the fast sweeping method solving the general anisotropic eikonal equation. In order to improve traveltime accuracy, a factored eikonal equation will be deduced. Then, a root-finding expression and a causality condition will be derived. Finally, a series of numerical schemes for the fast sweeping method solving the factored eikonal equation will be given. The research can calculate traveltime for general anisotropic media (including TI, orthorhombic, and triclinic media, etc.), it has great theoretical significance and practical value for a highly efficient and accurate traveltime calculation method in general anisotropic media.