Elastic Wave Velocities in Laminated Media

White, J. E.; Angona, F. A.

doi:10.1121/1.1928030

Cited by 6 publications

(8 citation statements)

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“…Transverse isotropy is a good model for (1) sedimentary rocks like shales which contain aligned clay minerals (Thomsen, 1986;Winterstein, 1986), (2) formations which consist of many beds that are thin relative to the wavelength of an elastic wave (Backus, 1962;White, 1955), and (3) rocks with aligned microfractures (Crampin, 1984). Orthorhombic anisotropy is a good model for some igneous and metamorphic rocks whose microcracks and minerals are aligned (Thill et al, 1973).…”

Section: Resultsmentioning

confidence: 99%

“…A hypothesis, which accounts for some of these discrepancies and which is now generally accepted, is that some parts of the Earth are anisotropic. This hypothesis is further substantiated by laboratory measurements and mathematical models of rocks (White and Angona, 1955;Backus, 1962;Thill et al, 1973;Thomsen, 1986). …”

Section: Introductionmentioning

confidence: 86%

“…Transverse isotropy is also called azimuthal isotropy, cross anisotropy, hexagonal anisotropy, and polar anisotropy. Transverse isotropy is used to model the elastic properties of sedimentary rocks (see e.g., Thomsen, 1986;Winterstein, 1986), of rocks with aligned fractures (see e.g., Crampin, 1984;Schoenberg and Douma, 1988), and of formations with beds which are thin compared to a wavelength of an elastic wave (see e.g., White and Angona, 1955;Backus, 1962). …”

Section: Elastic Symmetrymentioning

confidence: 99%

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Elastic wave propagation along a borehole in an anisotropic medium

Ellefsen

1990

SEG Technical Program Expanded Abstracts 1990

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In the first part of this thesis, several applications of perturbation theory are developed to study normal mode propagation along a borehole. This theory is used to relate first order perturbations in frequency, wavenumber, elastic moduli, densities, and locations of interfaces. Although the perturbation equation is derived for a general model with many fluid and solid layers which have any cross-sectional shape, the equation is applied to a two-layer model consisting of a fluid-filled borehole through a transversely isotropic solid (with its symmetry axis parallel to the borehole). Because analytical expressions for the displacements exist for this particular model, the terms in the perturbation equation simplify greatly. Formulas are derived to calculate (1) phase velocities for a model with slight, general anisotropy, (2) partial derivatives of either the wavenumber or frequency with respect to either an elastic modulus or density, (3) group velocity, and (4) phase velocities for a model with a slightly irregular borehole. These formulas are applicable also to models with an isotropic solid because it is a special case of a transversely isotropic solid.In the second part, the effects of anisotropy upon elastic wave propagation are determined. The wave equation is solved in the frequency-wavenumber domain with a variational method, and the solution yields the phase velocities, group velocities, pressures, and displacements for the normal modes. (The phase and group velocities obtained with this variational method match those obtained with the perturbation method indicating that both are correctly formulated and implemented.) These properties are studied for two cases: a transversely isotropic model for which the borehole has several different orientations with respect to the symmetry axis and an orthorhombic model for which the borehole is parallel to the intersection of two symmetry planes. The normal modes for these two cases show several effects which do not exist when the solid is isotropic or transversely isotropic with its symmetry axis parallel to the borehole:1. The phase velocities for the quasi-pseudo-Rayleigh, both quasi-flexural, and both quasi-screw waves do not exceed the phase velocity of the slowest qSwave. (The phase velocities of the leaky modes, which were not investigated, will exceed this threshold.)2. The two quasi-flexural waves have different phase and group velocities; the differences are greatest at low frequencies and diminish as the frequency increases. In general, the two quasi-screw waves behave similarly.3. The greater the difference between the the phase velocities of the qS-waves, the greater the difference between the phase velocities of the quasi-flexural waves at all frequencies. The two quasi-screw waves behave similarly.4. Near the limiting qS-wave velocity, the difference between the phase velocities of the two quasi-flexural waves is greater than that for the two quasi-screw waves.5. For the slow quasi-flexural wave, the particle displacements in the plane perpe...

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 86%

Section: Elastic Symmetrymentioning

confidence: 99%

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Elastic wave propagation along a borehole in an anisotropic medium

Ellefsen

1990

SEG Technical Program Expanded Abstracts 1990

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“…For the stratigraphic anisotropy caused by directional alignment of the cracks, many previous studies have been carried out, and a variety of simplified models are proposed, including a laminated media model 29 , a media model where cracks are embedded in the pores 30 , 31 , periodic thin interlayers and expansion model 32 , and so on. For the fracture-filling gas hydrate reservoir, some scholars have used the TCLM model to carry out the acoustic velocity simulation and gas hydrate saturation estimation study in several gas hydrate potential areas, and have obtained the better application effect 26 , 33 , 34 .…”

Section: Numerical Simulation Methodsmentioning

confidence: 99%

Gas hydrate saturations estimated from pore-and fracture-filling gas hydrate reservoirs in the Qilian Mountain permafrost, China

Xiao

Zou

Lü

et al. 2017

Sci Rep

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Accurate calculation of gas hydrate saturation is an important aspect of gas hydrate resource evaluation. The effective medium theory (EMT model), the velocity model based on two-phase medium theory (TPT model), and the two component laminated media model (TCLM model), are adopted to investigate the characteristics of acoustic velocity and gas hydrate saturation of pore- and fracture-filling reservoirs in the Qilian Mountain permafrost, China. The compressional wave (P-wave) velocity simulated by the EMT model is more consistent with actual log data than the TPT model in the pore-filling reservoir. The range of the gas hydrate saturation of the typical pore-filling reservoir in hole DKXX-13 is 13.0~85.0%, and the average value of the gas hydrate saturation is 61.9%, which is in accordance with the results by the standard Archie equation and actual core test. The P-wave phase velocity simulated by the TCLM model can be transformed directly into the P-wave transverse velocity in a fracture-filling reservoir. The range of the gas hydrate saturation of the typical fracture-filling reservoir in hole DKXX-19 is 14.1~89.9%, and the average value of the gas hydrate saturation is 69.4%, which is in accordance with actual core test results.

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“…where f(y) is the ^-periodic solution of where c,2 = 17,/p,, 1 = 1,2. Thus, we recover formula (2) in [16]. C. Homogenization via energy methods.…”

Section: Effective Properties Of Laminated Composites Via Homogenizatmentioning

confidence: 99%