S-wave singularities in tilted orthorhombic media

Ivanov, Yuriy; Stovas, Alexey

doi:10.1190/geo2016-0642.1

Cited by 20 publications

(7 citation statements)

References 42 publications

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“…In this section, we would like to discuss some of the points that are omitted in the present study, but should be considered when dealing with orthorhombic models. First, orthorhombic models are characterized by existence (at least two and up to sixteen) of so-called shear-wave point singularitiesdirections along which the quasi-shear slowness sheets touch (Crampin 1981(Crampin , 1991Ivanov & Stovas 2017b). These degeneracies lead to discontinuities in the corresponding wave surfaces, multiple shear wave arrivals (triplications), and caustics.…”

Section: Discussionmentioning

confidence: 99%

Normal modes in orthorhombic media

Ivanov

Stovas

Kazei

2018

Geophysical Journal International

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Guided waves in a water layer overlaying an elastic half-space are known as normal modes. They are often present in seismic recordings at long offsets in shallow-water environment and generally considered coherent noise. The normal modes, however, carry important information about the near-surface and, as demonstrated by a number of authors, can be used to obtain the shallow velocity model. There is a growing evidence that the latter needs not to be isotropic due to various geological reasons. Motivated by that, we consider the normal-mode propagation in case the elastic half-space exhibits orthorhombic anisotropy. We derive the period equation that describes the normal-mode phase velocity dispersion. To simplify the complicated expression, we present acoustic and ellipsoidal orthorhombic approximations. We also outline the approach towards the group velocity and group azimuth calculation and apply it to the ellipsoidal case to obtain concise and intuitive expressions. Using numerical test, we study the relation between phase and group domains in elastic orthorhombic case. The deviation between velocities and azimuths in these domains is the strongest for low frequencies and it rapidly decreases with increasing frequency. For higher frequencies, the anisotropy effects of the underlaying halfspace are barely detectable since the observed signal is composed mainly of the direct acoustic wave, resulting in the two domains being nearly indistinguishable.

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Section: Discussionmentioning

confidence: 99%

Normal modes in orthorhombic media

Ivanov

Stovas

Kazei

2018

Geophysical Journal International

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“…Many scholars note the complicated shape of these surfaces in the vicinity of singularity points in orthorhombic and lower‐symmetry media (Crampin ; Brown et al . ; Grechka and Obolentseva ; Vavryčuk ; Grechka , ; Ivanov and Stovas ). Conical points and anomalous curvatures of the slowness sheets associated with them cause multi‐valued wave fronts, caustics and strongly non‐linear and rapidly varying particle motion (polarization) directions.…”

Section: Numerical Experimentsmentioning

confidence: 98%

“…As a final remark, I would like to illustrate the peculiar behaviour and complexity of the slowness and group-velocity surfaces in some of the orthorhombic media encountered in numerical experiments. Many scholars note the complicated shape of these surfaces in the vicinity of singularity points in orthorhombic and lower-symmetry media (Crampin 1991;Brown et al 1993;Grechka and Obolentseva 1993;Vavryčuk 2005;Grechka 2015Grechka , 2017Ivanov and Stovas 2017). Conical points and anomalous curvatures of the slowness sheets associated with them cause multi-valued wave fronts, caustics and strongly non-linear and rapidly varying particle motion (polarization) directions.…”

Section: Examples Of Phase and Group Surfacesmentioning

confidence: 99%

“…In orthorhombic media, the singularity directions form a pattern that is symmetric about the coordinate planes, and, taking into account the symmetry about the origin, the maximum allowed number of real‐valued singularity directions is 16 (Musgrave ; Ivanov and Stovas ). In fact, that is also the maximum number for any symmetry lower than orthorhombic (Khatkevich ; Vavryčuk ; Grechka ).…”

Section: Theorymentioning

confidence: 99%

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On occurrence of point singularities in orthorhombic media

Ivanov

2019

Geophysical Prospecting

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Degeneracies 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.

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“…Composing series in terms of the contrasts, we obtain

\tilde{boldA} (ω) = {boldR}_{bold0} + {boldR}_{1} + {boldR}_{2},

where the zero‐, first‐ and second–order contrast matrices are, respectively, given by

\begin{matrix} true \\ right {boldR}_{bold0} & = & left A_{0}, \\ right {boldR}_{1} & = & left - ((), 1 - 2 α) Δ A + i ω H α ((), 1 - α) ([], Δ A, A_{0}) \\ left + {(i ω H)}^{2} \frac{α ((), 1 - α) ((), 1 - 2 α)}{6} ([], A_{0}, ([], Δ A, A_{0})), \\ right {boldR}_{2} & = & left Δ^{2} boldA - {(i ω H)}^{2} \frac{α ((), 1 - α)}{6} ([], Δ A, ([], Δ A, A_{0})) . \end{matrix}

Let us assume that

γ_{2} > γ_{1}

c_{55} > c_{44}

(if

c_{55} = c_{44}

, there is an on vertical axis singularity point (Ivanov and Stovas ; Stovas )). In this case, there is an area in the vicinity of the point

p_{1} = p_{2} = 0

, where the S1 and S2 wave slowness surfaces are not crossing, and S1 and S2 waves are polarized in the vicinity of the axes OX and OY, respectively, for every point of this area.…”

Section: Introductionmentioning

confidence: 99%

Low‐frequency layer‐induced dispersion in a weak‐contrast vertically heterogeneous orthorhombic medium

Roganov¹,

Stovas

Roganov

2019

Geophysical Prospecting

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In this paper, we consider wave propagation in a periodically layered medium with orthorhombic symmetry. The weak‐contrast approximation is utilized to derive the low‐frequency dispersion in effective properties for P, S1 and S2 waves. We show that the dispersion term for all effective properties is controlled by the second‐order contrasts in elastic properties from the layers. We also compute the sensitivity matrices for second‐ and fourth‐order coefficients from eigenvalues of frequency‐dependent system matrix associated with kinematic parameters for individual wave modes.

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S-wave singularities in tilted orthorhombic media

Cited by 20 publications

References 42 publications

Normal modes in orthorhombic media

Normal modes in orthorhombic media

On occurrence of point singularities in orthorhombic media

Low‐frequency layer‐induced dispersion in a weak‐contrast vertically heterogeneous orthorhombic medium

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