The computation of the elastic constants of an anisotropic medium from the velocities of body waves

Klı́ma, Karel; Červený, Vlastislav

doi:10.1007/bf01613681

Cited by 25 publications

(12 citation statements)

References 4 publications

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“…The best correlation (R = 0.94) is observed for P-wave velocities. This means that velocities V P and, correspondingly, moduli C 11 , C 22 , and C 33 were determined with the highest accuracy [19]. The weak correlation for transverse waves (R = 0.6 and 0.2 for S2 and S1 waves, respectively) indicates low informativeness of experimental V s values in the calculation of elastic moduli.…”

Section: Discussionmentioning

confidence: 98%

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Application of a modified method of ultrasonic measurements for determination of elastic moduli of rocks

et al. 2015

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The velocities of elastic waves with quasi-longitudinal and quasi-transverse polarizations in a spherical rock sample have been measured. The experimental values of velocities are used to calculate 21 elastic moduli of the sample. For comparison, the effective elastic properties of the sample are simulated based on the data on the crystallographic textures of rock-forming minerals obtained by neutron diffraction. It is shown that the largest discrepancy between the model predictions and experimental velocity values is observed for transversely polarized waves.

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Section: Discussionmentioning

confidence: 98%

“…As it was shown in [19], to calculate 21 independent components of the elastic modulus tensor, along with the P-wave velocities in at least 15 directions, it is necessary to know the velocities of P, S1, and S2 waves in six additional directions.…”

Section: Calculation Of Elastic Moduli Based On Velocity Datamentioning

confidence: 99%

Application of a modified method of ultrasonic measurements for determination of elastic moduli of rocks

et al. 2015

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“…This method was employed to measure elastic constants of homogeneous monoclinicsymmetry media and of orthorhombic-symmetry rocks (Belikov et al 1970). A number of methods based on perturbation theory have been proposed to determine the elastic constants for weakly anisotropic homogeneous media with known symmetry in an arbitrary oriented coordinate system (Neighbours 1954;Backus 1970;Klima 1973). But these methods are not applicable to strongly anisotropic and inhomogeneous media.…”

Section: Theorymentioning

confidence: 99%

The Study of Elastic Symmetry and Anisotropy of Elastic Body Waves In Gneiss

Aleksandrov

Prodayvoda

1994

Geophysical Journal International

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S U M M A R YThis paper describes a method for determining the effective elastic constants of anisotropic rocks from the results of ultrasonic measurements of the phase velocity of elastic body waves with arbitrary directions of the wave normal in the absence of a priori information on the texture symmetry. For estimating the regular and fluctuating components of the effective tensor of elastic constants the method requires the measurement of phase velocities along nine directions in a sample having the form of a cuborhombododecahedron. The rock symmetry category is determined beforehand from the symmetry of the acoustic tensor, and a standard coordinate system is chosen along eigenvectors of the latter. Rules for selecting the standard acoustic coordinate system for rocks of any symmetry have been formulated. The initial approximation of elastic constants is found from exact equations connecting the elastic constants and the acoustic tensor components, as well as from equations connecting the elastic constants in the working and auxiliary coordinate systems. The fluctuational components of measured values of effective phase velocities are smoothed using the convolution property of the acoustic tensor. The mean elastic constants are calculated from a set of equations, which includes convolutions of the elastic tensor and a linearized set of equations with elastic displacement vectors. The proposed method has been applied to the results of ultrasonic measurements of a twice-deformed gneiss sample from the Lodogian series of the Baltic Shield. Experimental findings conform to triclinic symmetry.

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“…The computation procedure (Klima 1973) of elastic constants adopts a data-set of measured P-wave velocities. A common anisotropic body is characterized by 21 independent elastic parameters.…”

Section: Computation Of Elastic Constantsmentioning

confidence: 99%

Non-linearity in multidirectional P-wave velocity: confining pressure behaviour based on real 3D laboratory measurements, and its mathematical approximation

Přikryl

Klı́ma

Lokajı́ček

et al. 2005

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Experimental laboratory measurements of P-wave velocity confirm the superposition of linearity over non-linearity by a progressive increase in confining pressure. The increase in confining pressure diminishes the influence of microcracks that are partly or totally closed. At a certain stress level, the trend of P-wave velocity with applied confining pressure approaches that of a solid without cracks, and a linear increase in elastic wave velocity occurs under high confinement.Several studies have focused on the problem of mathematical approximation of this phenomenon (Carlson & Gangi 1985;Wepfer & Christensen 1991; Meglis et al. 1996). Although successful within a certain degree of error, they provide neither a multidirectional solution nor the comparison of results with rock fabric. In this study, an analytical relation was applied to describe the P-wave velocity-confining pressure behaviour of quasi-isotropic rocks (granites) and their anisotropic equivalents (orthogneisses). Two parameters of this relationship reflect the elastic properties of the rock matrix, and two others are related to the presence of microcracks, their density and genesis. The results of a mathematical approximation of the P-wave velocity-confining pressure behaviour show a favourable correlation to the measured data-sets. Comparison of individual fitted parameters with the rock fabric provides an improved understanding of the material's mechanical behaviour.

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The computation of the elastic constants of an anisotropic medium from the velocities of body waves

Cited by 25 publications

References 4 publications

Application of a modified method of ultrasonic measurements for determination of elastic moduli of rocks

Application of a modified method of ultrasonic measurements for determination of elastic moduli of rocks

The Study of Elastic Symmetry and Anisotropy of Elastic Body Waves In Gneiss

Non-linearity in multidirectional P-wave velocity: confining pressure behaviour based on real 3D laboratory measurements, and its mathematical approximation

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