An elliptical anisotropic medium is defined as a simplified representation of anisotropy in which the anelliptic parameters are set to zero in all symmetry planes. Despite the fact that this model is rather seldom observed for real rocks, it is often used as a reference model. The P-wave equations for an elliptical anisotropic medium are well known. However, the shear wave (S-wave) equations have not been derived. Thus, we have defined all wave modes in elliptical orthorhombic models focusing mostly on the S-wave properties. We determine that all wave modes in elliptical orthorhombic model are generally coupled and analyze the effect of the additive coupling term. As a result, there is an S-wave fundamental singularity point located in one of the symmetry planes depending on the relative magnitude of S-wave stiffness coefficients.

中文翻译：

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椭圆正交介质中的波动特征

椭圆各向异性介质被定义为各向异性的简化表示，其中在所有对称平面中将椭圆参数设置为零。尽管实际上很少观察到此模型，但通常将其用作参考模型。椭圆各向异性介质的P波方程是众所周知的。但是，尚未推导出剪切波（S波）方程。因此，我们在椭圆斜方模型中定义了所有波模式，主要侧重于S波特性。我们确定椭圆形正交模型中的所有波模通常都已耦合，并分析了加性耦合项的影响。结果，取决于S波刚度系数的相对大小，在对称平面之一中存在S波基本奇异点。