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介质的弹性常数为三维四阶张量的分量，共有８１个，由于应力张量和应变张量的对称性及能量密度是应变的二次函数，一般各向异常性介质的独立弹性常数可减为２１个，如果介质具有较高的对称性，独立弹性常数的数目会更少。 对于地壳和上地幔，具有５个独立弹性常数的横向各向同性介质是一个非常好的近似，本研究中横向各向同性介质的对称轴方向可以是任意的（即对称轴可以不平等于铅直方向），在此情况下，需要进行坐标变换，如果已知介质在某一坐标系（其坐标轴平行或垂直于介质的对称轴）中的弹性常数，我们能够容易地利用变换公式得到变换后新坐标系中的弹性常数。 本文提出了一种方案，利用伪谱法既能模拟横向各向同性介质中的平面波，也能模拟点源激发的波场。在勘探地球物理和地震学中，模拟横向各向同性介拮中传播的平面波及区域源产生的波是最重要的研究课题之一。然而在一般各向异性介质中，很难或不可能确定弹性波的相速度和偏振方向，但在横向各向同性介质中，则可以通过坐标变换来实现，这里我们所提出的方法可以用于横向各向同性介质中弹性波的模拟。
The elastic constants of the medium are the components of the fourth-order three-dimensional tensor, a total of 81, due to the symmetry of the stress tensor and strain tensor and the energy density is quadratic function of strain, the independent elastic constants of the general anisotropic medium can be reduced Is 21. If the medium has higher symmetry, the number of independent elastic constants will be less. For the crust and the upper mantle, a transversely isotropic medium with five independent elastic constants is a very good approximation. In this study, the direction of the symmetric axis of the transversely isotropic medium can be arbitrary (ie, the axis of symmetry can not equal the vertical Direction). In this case, coordinate transformation is needed. If the elastic constant of a medium in a coordinate system whose axes are parallel or perpendicular to the symmetry axis of the medium is known, we can easily use the transformation formula to obtain the transformed Elastic constants in the new coordinate system. In this paper, a scheme is proposed, which can simulate both the plane wave in a transversely isotropic medium and the wave field excited by a point source using the pseudospectral method. In exploration geophysics and seismology, it is one of the most important research topics to simulate the plane waves propagating in transversally isotropic medium and the waves generated by regional sources. However, in general anisotropic media, it is difficult or impossible to determine the phase velocity and polarization direction of the elastic wave, but in the transversely isotropic medium, it can be realized by coordinate transformation. Our proposed method here can be applied to Simulation of elastic wave in transversely isotropic medium.