New analysis of attenuation in partially melted rock

Walsh, J. B.

doi:10.1029/jb074i017p04333

Cited by 350 publications

(176 citation statements)

References 13 publications

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“…The Eshelby theory neglects interactions between inhomogeneities, and so we require a dilute solution of cracks; i.e., the porosity must be numerically much less than a. In calculating the velocities we assume low-frequency disturbances in the sense defined by Walsh [1969]. In the direction perpendicular to the cracks the Vv/Vs ratio is nearly normal for liquid-filled cracks but decreases rapidly as the bulk modulus of the fluid phase approaches that of a gas.…”

Section: Theorymentioning

confidence: 99%

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The effect of oriented cracks on seismic velocities

Anderson¹,

Minster²,

Cole³

1974

J. Geophys. Res.

239

123

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We have considered the problem of elastic wave velocities in a matrix containing aligned ellipsoidal fluid-filled cracks. This problem is relevant to a variety of geophysical applications, including crustal and mantle seismology and the behavior of stressed and dilatant rock. When the cracks are ellipsoids of revolution, the composite is transversely isotropic and is describable with five elastic constants. For aligned oblate spheroids the major reduction in velocity occurs along the axis of symmetry. The opening of new cracks, the widening of old cracks, or the reduction of pore pressure accompanying crustal dilatancy can be expected to cause a large decrease in compressional velocity and considerable compressional wave anisotropy.Laboratory experiments indicate that crack porosity significantly depresses the seismic velocities even in lowporosity igneous rocks [Birch, 1960]. Anderson and Spetzle•' [1970], using the Eshelby-Walsh theory, showed that flat cracks were much more effective in reducing the elastic constants than spherical pores were. Thus they were able to show that the properties of the low-velocity zone could be explained with a small amount of partial melting. Likewise, the low velocities in crystalline rocks at low pressures can be under- Most of the work to date on the properties of composites or solids containing cracks has assumed isotropy, i.e., random orientation of grains and cracks. Geophysical aggregates can be expected to be anisotropic even if the matrix is isotropic, due to preferred orientation of cracks. The crack fabric of rock can be caused by tectonic stress fields or temperature gradients. Layering, recrystallization, cooling, and tectonic deformation can all be expected to result in cracks with a preferred orientation, both on microscopic (intergranular cracks) and on macroscopic (preferred orientation of dikes, joints) scales. Nur [1971] has discussed the problem of stressinduced crack orientation and gives a general treatment for velocities in a matrix containing oriented dry cracks.In the case of crustal deformation the orientation of cracks is controlled by the orientation of the principal stresses. In particular, the occurrence of dilatancy should be associated with cracks aligned in a statistical sense. We shall investigate here the extreme case in which the cracks are parallel.The overall elastic symmetry of a material containing parallel penny-shaped cracks is axial or transversely isotropic. Only five elastic constants are then independent. The extreme case of a laminated medium has been examined by Postma Copyright ¸ 1974 by the American Geophysical Union. •11ipsoidal inhomogeneities. This theory has been used by Walsh [1969] to calculate the elastic constants of a solid containing penny-shaped fluid-filled cracks with random orientation. Such a material is isotropic in the large and is described by two elastic constants.We consider an isotropic matrix containing ellipsoidal fluidfilled zones where the axial ratios are a/b = a/c = a < 1. The Eshelby theory neglects i...

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Section: Theorymentioning

confidence: 99%

“…•11ipsoidal inhomogeneities. This theory has been used by Walsh [1969] to calculate the elastic constants of a solid containing penny-shaped fluid-filled cracks with random orientation. Such a material is isotropic in the large and is described by two elastic constants.…”

mentioning

confidence: 99%

The effect of oriented cracks on seismic velocities

Anderson¹,

Minster²,

Cole³

1974

J. Geophys. Res.

239

123

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“…On it are shown theoretical curves for a solid containing dry ellipsoidal cracks and a solid containing ellipsoidal pockets of liquid. We assume that the aspect ratio, which is the ratio of the minor diameter to the major diameter, of each of the cracks and pockets is small (Walsh 1969;Anderson et centration of melt per unit volume is assumed to be approximately twice the value of the aspect ratio. For example, if the aspect ratio is 10", as suggested by Anderson et al (1972) for the low velocity zone in the apper mantle (Gutenberg 1959), a melt content of approximately 2% per unit volume is required.…”

Section: The South Islandmentioning

confidence: 99%

Seismic wave velocities in the uppermost mantle beneath New Zealand

Haines

1979

New Zealand Journal of Geology and Geophysics

112

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The extent of lateral inhomogeneity in the uppermost mantle beneath New Zealand has been studied by mapping the variation of Pn and Sn velocities. Ten regions of constant structure were required to model the distribution of velocities, which range from 7·4 km/s and 3' 95 km/s for Pn and Sn respectively, beneath the central North Island, to 8· 7 km/s and 4· 8 krn/s beneath Nelson. It is suggested that the regions partition the uppermost mantle according to whether its constituents are ultramafic or mafic and according to the concentrations of open cracks and melt.

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“…Most previous theoretical calculations were made for an isotropic case in which cracks are assumed to be distributed and oriented spatially at random in an isotropic medium (e.g., WU, 1966;WALSH, 1969;KUSTER and TOKSOZ, 1974;BUDIANSKY and O'CONNELL, 1976). However, some theoretical work has been accomplished on elastic anisotropy caused by preferred crack orientations.…”

mentioning

confidence: 99%

Seismic velocity anisotropy in a medium cotaining oriented cracks. Transversely isotropic case.

1982

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A new method was developed for calculating effective elastic parameters of a medium containing oblate spheroidal cracks having parallel planes. This new method is free from the restrictions of isotropic matrix material and low crack density. Velocity anisotropy was calculated for the case of oriented cracks filled with fluid. Effects of crack aspect ratio, fluid bulk modulus, and crack volume on velocity anisotropy were investigated. The present results showed smaller anisotropy than that given by ANDERSON et al. (1974) for a medium containing oriented spheroidal cracks. The relation between velocity and crack density parameter (ratio of porosity to aspect ratio of cracks divided

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New analysis of attenuation in partially melted rock

Cited by 350 publications

References 13 publications

The effect of oriented cracks on seismic velocities

The effect of oriented cracks on seismic velocities

Seismic wave velocities in the uppermost mantle beneath New Zealand

Seismic velocity anisotropy in a medium cotaining oriented cracks. Transversely isotropic case.

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