Singularity lines for monoclinic media with a horizontal symmetry plane

A connected set of singularity points is called the singularity line. Along this line, the slowness surfaces (or phase velocity surfaces) of different wave modes coincide. For anisotropic models, the singularity lines are mostly known in transversely isotropic media (Crampin and Yedlin, 1981). Recently, it was shown that they also can be defined in the special types of orthorhombic media: degenerate (Stovas et al, 2023b) and pathological (Stovas et al, 2023a). Singularity line can also exist in the low symmetry anisotropic models, monoclinic and triclinic (Khatkevich, 1963; Vavrycuk, 2005; Roganov et al, 2019).

In this paper, we focus on singularity lines in monoclinic media with a horizontal symmetry plane. We define the singularity lines in all coordinate planes, and in vertical planes of arbitrary azimuthal orientation. Since the monoclinic anisotropic model can be considered as the transversely isotropic medium with a vertical symmetry axis being perturbed with the multiple azimuthally non-invariant fracture sets, identification of singularity lines can give additional constraints in inversion of seismic data for fracture prediction. The singularity lines being converted into the group velocity domain results in continuous bands in the group velocity surface (traveltime surface) shaping the lacunas for S1 wave and internal refraction cones for S2 wave associated with strong anomalies in wave amplitudes.

The singularity directions satisfy the following polynomial equations (Alshits, 2004; Roganov et al., 2019), , where  are the third-order polynomials given by the elements of the Christoffel matrix. Resolving this system of equations, we define the conditions (in terms of stiffness coefficients) for existence of singularity lines in vertical planes. The Sylvester criterion is applied to control the physical realizable model. Mostly, the obtained models have singularity lines formed by S1 and S2 waves, while one model has singularity line composed of S1S2 and PS1 legs connected by the triple PS1S2 singularity point.

 

 

References

Alshits, V.I., 2004, On the role of anisotropy in crystalloacoustics, In: Goldstein R.V., Maugin G.A. (eds) Surface Waves in Anisotropic and Laminated Bodies and Defects Detection. NATO Science Series II: Mathematics, Physics and Chemistry, vol 163. Springer, Dordrecht.

Crampin, S., and M. Yedlin, 1981, Shear-wave singularities of wave propagation in anisotropic media, J. Geophys., 49, 43–46.

Khatkevich, A.G., 1963 Acoustic axes in crystals, Sov. Phys. Crystallogr. 7, 601–604.

Stovas, A., Roganov, Yu., and V. Roganov, 2023a, On pathological orthorhombic models, Geophysical Prospecting, 71(8), 1523- 1539.                                                                    

Stovas, A., Roganov, Yu., and V. Roganov, 2023b, Degenerate orthorhombic models, Geophysical Journal International, accepted for publication.                  Roganov, Yu., Stovas, A., and V. Roganov, 2019, Properties of acoustic axes in triclinic media, Geophysical Journal, 41(3), 3-17.                                                    Vavrycuk, V., 2005, Acoustic axes in triclinic anisotropy, The Journal of the Acoustical Society of America 118, 647-653.