Behavior of S waves in vicinity of singularity point in elliptic orthorhombic media

In low-symmetry anisotropic models, the S waves are generally coupled and have very complex behavior due to triplications and singularity points. The presence of singularity point affects S-wave phase and group velocity surface in a simple elliptical orthorhombic model. This model has no triplications but has a singularity point in one of the symmetry planes. We find that the slowness ellipse (defined by the zero Gaussian curvature) is the image of a singularity point on the group velocity surface, and the group velocity ellipse (also known as the internal refraction cone) is the image of a singularity point on the slowness surface. The equations for the slowness and group velocity ellipses are explicitly defined. The square of S1- and S2-wave lacunae also is computed.