Pure quasi-P wave equation and numerical solution in 3D TTI media  

三维TTI介质中的纯准P波方程及求解方法（英文）

作　　者：张建敏[1,2,3] 何兵寿[1,2,3] 唐怀谷 

机构地区：[1]中国海洋大学,山东青岛266100 [2]青岛海洋科学与技术国家实验室海洋矿产资源评价与探测技术功能实验室,山东青岛266071 [3]海底科学与探测技术教育部重点实验室,山东青岛266100

出　　处：《Applied Geophysics》2017年第1期125-132,191,共9页应用地球物理（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.41674118);the national science and technology major project(No.2016ZX05027-002)

摘　　要：Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI media）. This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer （PML） absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.以具有垂直对称轴的横向各向同性(Vertical Transversely Isotropic,简称VTI)介质中纯准P波方程为基础,通过投影变换推导出倾斜横向各向同性(Titled Transversely Isotropic,简称TTI)介质中的纯准P波方程,该方程从根本上消除伪横波的影响。方程形式简单并且在δ>ε的情况下仍能稳定求解。文章还给出TTI介质中纯准P波方程数值求解的高阶有限差分格式并推导对应的稳定性条件,依据完全匹配层(Perfectly Matched Layer,简称PML)的分裂思路给出TTI介质中纯准P波方程的PML吸收边界条件。理论分析和数值计算结果均表明:本文推导的纯准P波方程能更好地描述TTI介质中的准P波,文章给出的正演算法也能够准确模拟TTI介质中准P波的传播过程。

关 键 词：TTI media the pure quasi-P wave equation high-order finite PML boundary conditions BP model 

分 类 号：P631.4[天文地球—地质矿产勘探]