Abstract
ABSTRACTDegeneracies of the slowness surfaces of shear (and compressional) waves in low‐symmetry anisotropic media (such as orthorhombic), known as point singularities, pose difficulties during modelling and inversion, but can be potentially used in the latter as model parameter constraints. I analyse the quantity and spatial arrangement of point singularities in orthorhombic media, as well as their relation to the overall strength of velocity anisotropy. A classification scheme based on the number and spatial distribution of singularity directions is proposed. In normal orthorhombic models (where the principal shear moduli are smaller than the principal compressional moduli), point singularities can only be arranged in three distinct patterns, and media with the theoretical minimum (0) and maximum (16) number of singularities are not possible. In orthorhombic models resulting from embedding vertical fractures in transversely isotropic background, only two singularity distributions are possible, in contrast to what was previously thought. Although the total number of singularities is independent of the overall anisotropy strength, for general (non‐normal) orthorhombic models, different spatial distributions of singularities become more probable with increasing magnitude of anisotropy.
Highlights
Seismic wave propagation in anisotropic media is characterized by many interesting and challenging features, among which are so-called singularity directions—points in the phase space where the slowness surfaces of two or more wave modes come in contact
The relationship between the anisotropy strength and the number and distribution of conical singularities in orthorhombic media is studied. It is demonstrated theoretically and confirmed numerically that for models in which the principal compressional stiffnesses are larger than the shear stiffnesses, the singularities can be distributed in only three different patterns, and all singularities are associated with the shear waves only
The distribution of singularity directions between the classes in normal orthorhombic media does not depend on the anisotropy strength due to a limited number of possible relations between the stiffness moduli
Summary
Seismic wave propagation in anisotropic media is characterized by many interesting and challenging features, among which are so-called singularity directions ( degeneracies, acoustic axes)—points in the phase space where the slowness surfaces of two or more wave modes come in contact. Due to increasing interest in microseismic monitoring, in which a recorded wavefield from small-scale earthquakes contains direct shear waves of high energy, and the medium symmetry is often lower than hexagonal (e.g. orthorhombic or monoclinic as that of fractured shale), the conical singularities have to be treated with care in both modelling and inversion (Grechka and Yaskevich 2014; Grechka 2015). Geophysical Prospecting published by John Wiley & Sons Ltd on behalf of European Association of Geoscientists & Engineers. I use lower case indices to describe the former and capital indices for the latter, and no summation over repeated indices is assumed
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