On shear-wave triplication in transversely isotropic media

Thomsen, Leon; Dellinger, Joe

doi:10.1016/j.jappgeo.2003.08.008

Cited by 43 publications

(48 citation statements)

References 11 publications

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“…The formulas are simple but approximate the exact solution with a high accuracy. The best results are obtained using the third-order approximation, which yields accuracy at least 30 times higher than the formulas presented by Thomsen and Dellinger (2003 …”

Section: Introductionmentioning

confidence: 85%

“…23), (c) first-order approximation (16), (d) second-order approximation (17). Figure 5 shows the relative errors of the Thomsen and Dellinger (2003) approximations together with the first-and second-order approximations (16) and (17) calculated for κ ∈〈2, 4〉, and Fig. 6 shows the same for κ ∈〈4, 9〉, respectively.…”

Section: Tests Of Accuracymentioning

confidence: 93%

“…were also derived by Thomsen and Dellinger (2003). They obtained the following approximate formulas for σ c (Thomsen and Dellinger, 2003, Eq.…”

Section: Approximate Triplication Conditionsmentioning

confidence: 99%

“…23) In the next section, we shall examine accuracy of the derived formulas together with formulas (19) and (20) presented by Thomsen and Dellinger (2003).…”

Section: Approximate Triplication Conditionsmentioning

confidence: 99%

“…For this case, several authors proposed simpler but approximate triplication conditions (McCurdy, 1974;Musgrave, 1979;Musgrave and Payton, 1984;Alshits and Chadwick, 1997;Thomsen and Dellinger, 2003). Among these conditions, the condition proposed by Thomsen and Dellinger (2003) is particularly interesting, because it is far simpler than the other approximations, and provides an insight into which parameters control the off-axis triplication. The validity of the formula is, however, restricted to a limited interval of anisotropy parameters.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

Vavryčuk¹

2004

Studia Geophysica et Geodaetica

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The presented approximate formulas yield a critical value of anisotropy parameter σ, for which an incipient off-axis SV-wave triplication occurs in transversely isotropic media. The formulas are simple but approximate the exact solution with a high accuracy. The best results are obtained using the third-order approximation, which yields accuracy at least 30 times higher than the formulas presented by Thomsen and Dellinger (2003

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Section: Introductionmentioning

confidence: 85%

Section: Tests Of Accuracymentioning

confidence: 93%

“…were also derived by Thomsen and Dellinger (2003). They obtained the following approximate formulas for σ c (Thomsen and Dellinger, 2003, Eq.…”

Section: Approximate Triplication Conditionsmentioning

confidence: 99%

“…23) In the next section, we shall examine accuracy of the derived formulas together with formulas (19) and (20) presented by Thomsen and Dellinger (2003).…”

Section: Approximate Triplication Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

Vavryčuk¹

2004

Studia Geophysica et Geodaetica

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The Role of Texture, Cracks, and Fractures in Highly Anisotropic Shales

et al. 2017

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Organic shales generally have low permeability unless fractures are present. However, how gas, oil, and water flows into these fractures remains enigmatic. The alignment of clay minerals and the alignment of fractures and cracks are effective means to produce seismic anisotropy. Thus, the detection and characterization of this anisotropy can be used to infer details about lithology, rock fabric, and fracture and crack properties within the subsurface. We present a study characterizing anisotropy using S wave splitting from microseismic sources in a highly anisotropic shale. We observe very strong anisotropy (up to 30%) with predominantly VTI (vertical transverse isotropy) symmetry, but with evidence of an HTI (horizontal transverse isotropy) overprint due to a NE striking vertical fracture set parallel to the maximum horizontal compressive stress. We observe clear evidence of a shear wave triplication due to anisotropy, which to our knowledge is one of only a very few observations of such triplications in field‐scale data. We use modal proportions of minerals derived from X‐ray fluorescence data combined with realistic textures to estimate the contribution of intrinsic anisotropy as well as possible contributions of horizontally aligned cracks. We find that aligned clays can explain much of the observed anisotropy and that any cracks contributing to the vertical transverse isotropy (VTI) must have a low ratio of normal to tangential compliance (ZN/ZT), typical of isolated cracks with low hydraulic connectivity. Subhorizontal cracks have also been observed in the reservoir, and we propose that their reactivation during hydraulic fracturing may be an important mechanism to facilitate gas flow.

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Constraints on Anisotropic Parameters in Transversely Isotropic Media and the Extensions to Orthorhombic Media

Li¹,

Chen²

2011

Chinese J of Geophysics

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The presence of anisotropy in earth materials is common. Due to its high symmetry and relative simplicity in mathematical formulae, transversely isotropic (TI) medium has become one of the most important anisotropic media in seismology. In theoretical study and real‐data processing, anisotropic parameters proposed by Thomsen has been widely adopted. The selection of elastic constants and Thomsen's parameters is not free. Constraints exist among these parameters. Results based on inappropriate parameters might be physically meaningless and misleading. In this study, based on the stability condition of material as well as theoretical and experimental investigations on anisotropic parameters, we proposed a set of concise inequalities about Thomsen's anisotropic parameters, i.e. 1/4 < f = 1 − β20/α20 < 1, ε > −f/2, 1/2f − 1 < δ 2(1/f − 1), and −1/2 < γ < (1 + 2ε)/4(1 − f) − 1/2. It was shown that (1) ε, δ and γ can be either positive or negative, with their ranges mainly constrained by the P‐to‐S velocity ratio β0/α0; (2) the ranges of δ, γ and β0/α0 are bounded; (3) the value of ε has no upper limit; (4) ε and γ are positively correlated, and the upper limit of is related to ε (5) no evident constraint exists between ε and δ, nor between δ and γ. Besides, constraints on anisotropic parameters for some special TI media and physical phenomena were reviewed. We also extend constraints on elastic constants and anisotropic parameters of TI media to those of orthorhombic media.

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On shear-wave triplication in transversely isotropic media

Cited by 43 publications

References 11 publications

Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

The Role of Texture, Cracks, and Fractures in Highly Anisotropic Shales

Constraints on Anisotropic Parameters in Transversely Isotropic Media and the Extensions to Orthorhombic Media

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