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.

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