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各向异性介质主要表现为横向各向同性特征，而具有倾斜对称轴的横向各向同性介质更具有一般性。本文首先对横向各向同性介质进行分类；然后根据势能与坐标系无关的原理，推导出在一般坐标系下TI介质的弹性参数，这种方法适用于建立不同坐标系下弹性参数之间的相互关系；最后从各向异性介质中的波动方程出发，进行TI介质的相速度分析和波场正演模拟。计算结果表明，当对称轴倾斜时，介质在沿测线方向的错直平面内，均呈现出各向异性；当测线方向与走向垂直时，波前面两个对称轴的方向分别指示着介质对称轴的倾斜方向和垂直于对称轴的方向.
Anisotropic media are mainly transversely isotropic, whereas transversely isotropic media with oblique axes of symmetry are more general. In this paper, we classify transversely isotropic media first. Then, based on the principle that potential energy has nothing to do with the coordinate system, we deduce the elastic parameters of TI media in the general coordinate system. This method is suitable for establishing the interaction between the elastic parameters in different coordinate systems Finally, from the wave equation in anisotropic media, phase velocity analysis and wavefield forward modeling of TI media are carried out. The results show that when the axis of symmetry is tilted, the anisotropy of the medium appears in the wrong plane along the line direction. When the line direction and the strike are perpendicular, the directions of the two symmetry axes in the front of the wavefront indicate the medium The direction of tilt of the axis of symmetry and the direction perpendicular to the axis of symmetry.