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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。
Based on the pure P-wave equation in vertical transversely isotropic (VTI) media with vertical axis of symmetry, the purely P-wave equation in the TTI media is deduced by projective transformation Quasi-P wave equation, the equation to fundamentally eliminate the impact of pseudo-shear wave. The equation is simple in form and stable in the case of δ> ε. The paper also gives a higher-order finite difference scheme for numerical solution of the pure P-wave equation in TTI media and derives the corresponding stability conditions. According to the splitting idea of Perfectly Matched Layer (PML) PML Absorption Boundary Conditions for P Wave Equations. Theoretical analysis and numerical results show that the pure P-wave equation deduced in this paper can better describe the quasi-P wave in TTI media. The forward algorithm given in this paper can also accurately simulate the P-wave propagation in TTI media .