On singularity point for acoustic orthorhombic model

The singularity points are very important for elastic waves propagation in low-symmetry anisotropic media (Stovas et al., 2021a). Being converted into the group velocity domain, they result in internal refraction cone with anomalous amplitudes and very complicated polarization fields. I analyze the conditional singularity point in acoustic orthorhombic (ORT) model which is very popular in processing and analysis of 3D seismic data. The elliptic ORT model has one singularity point in one of the symmetry planes (Stovas et al., 2021b). The elastic ORT model has 1 to 6 singularity points. It is shown that for acoustic ORT model the only one S1-S2 wave singularity point (per quadrant) can conditionally be defined in-between the symmetry planes. The required conditions and position of singularity point are computed. The projection of the slowness vector    for singularity point are given by

where are the elements of the stiffness coefficients matrix. I show that the singularity point for this model has the stable conical type of degeneracy (Shuvalov, 1998), which means that the internal refraction cone is always represented by ellipse in 3D space. The slowness surface for acoustic orthorhombic model that consists of three sheets corresponding to P (the inner one) and S1-S2 waves. The image of singularity point in the group domain and its three projections on the symmetry planes can be computed analytically.

 

References

Shuvalov, A.L., 1998, Topological features of the polarization fields of plane acoustic waves in anisotropic media, Proc. R. Soc. Lond., A., 454, 2911–2947.

Stovas, A., Roganov, Yu., and V. Roganov, 2021a, Geometrical characteristics of P and S wave phase and group velocity surfaces in anisotropic media, Geophysical Prospecting, 68(1), 53-69.

Stovas, A., Roganov, Yu., and V. Roganov, 2021b, Wave characteristics in elliptical orthorhombic medium, Geophysics, 86(3), C89-C99.