We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media. Specifically, one medium is a transversely isotropic medium with a vertical axis of symmetry (VTI medium) and the other one is a transversely isotropic medium with a tilt axis of symmetry (TTI medium). By solving the Kelvin-Christoffel equation, an eighth-order polynomial is established for reflection and refraction angles, which is confirmed from Snell’s law. Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions. An effective algorithm has been developed for numerical analysis of the polarization coefficients. Applying characteristic anisotropic parameters reported in the literature, the influencing factors on reflection and refraction coefficients are analyzed, e.g., the anisotropy, the tilt-angle of rock-layer, and the incident-angle. The calculated reflection and refraction coefficients have been rechecked for energy conservation.

中文翻译：

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VTI-TTI介质界面上弹性波的反射和折射

我们探讨了在两种不同的各向异性岩石介质之间的界面处引起的声波的物理现象。具体而言，一种介质是具有垂直对称轴的横向各向同性介质（VTI介质），另一种介质是具有倾斜对称轴的横向各向同性介质（TTI介质）。通过求解开尔文-克里斯托夫尔方程，可以建立反射角和折射角的八阶多项式，这可以从斯涅尔定律得到证实。获得了对应于不同入射角区域的三种感应波偏振系数的解析表达式。已经开发出一种有效的算法来对偏振系数进行数值分析。应用文献中报道的各向异性特征参数，分析了反射率和折射系数的影响因素，如各向异性，岩层倾斜角和入射角。计算出来的反射系数和折射系数已经过重新检查以节约能源。