The analysis of singularity points in anisotropic models of low symmetry is very important for seismic modelling and seismic data processing. Ray tracing: the group velocity vector dramatically changes the orientation in vicinity of singularity point. Seismic amplitudes: the relative geometrical spreading of seismic wave tends to zero in singularity point. Seismic wave polarization: the polarization vectors dramatically change in vicinity of singularity point. Multiarrival: one of the waves has triplication associated with singularity point, another wave has a lacuna.The singularity points are considered for elastic anisotropic model with orthorhombic symmetry. The conditions for the presence of singularity points are derived depending on location of these points, in symmetry plane and in-between the symmetry planes. The explicit equations for images of the singularity points in group velocity domain are derived. The conditions for different types of degeneracy of these images are defined. We also perform the analysis of interaction of the group velocity images of different singularity points.

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 of 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 is well known. However, the S-wave equations have not been derived. Thus, we define all wave modes in elliptical orthorhombic models focusing mostly on the S-wave properties. We show that all wave modes in elliptical orthorhombic model are generally coupled and analyze the effect of additive coupling term. As the 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.

In low-symmetry anisotropic models, the S waves are generally coupled and have very complex behavior due to triplications and singularity points. We focus on the effect of singularity points on S waves phase and group velocities in a simple elliptical orthorhombic model with no triplications and only one fundamental singularity point located in one of the symmetry planes. We show 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 waves lacunae is also computed.

The phase and group velocity surfaces are essential for wave propagation in anisotropic media. These surfaces have certain features that, especially, for shear waves result in complications for modelling and inversion of recorded wavefields. To analyse wave propagation in an anisotropic model, it is important to identify these features in both the phase and group domains. We propose few characteristics for this analysis: the energy flux angle, decomposed in the polar and azimuth angle correction angles and enhancement factor, which is able to characterize both singularity points and triplication zones. The very simple equation that controls the triplications is derived in the phase domain. The proposed characteristics are illustrated for elastic and acoustic anisotropic models of different symmetry classes.

The presence of S waves singularity points in low‐symmetry anisotropic models significantly affects the topology of the slowness surfaces of S waves in the vicinity of these points and, consequently, results in complications in the geometrical spreading. Thus, we analyse the effect of a singularity point in a simple elliptical orthorhombic model with decoupled P wave.