Linear viscoelastic behaviour in rocks

Brennan, B.J.

doi:10.1029/gd004p0013

Cited by 22 publications

(9 citation statements)

References 21 publications

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“…Filling and emptying fluid from a pore system is itself a history dependent phenomena that can be described using the P-M space picture [Smith et al, 1987;Guyer, 1993]. (6) For a pressure fluctuation associated with an acoustic disturbance, the timescale is 10-2-10 -6 s. For a pressure fluctuation associated with a quasi-static measurement [Boitnott, 1992;Gist, 1994], the timescale is 1-10 s. The hysteretic response of a system may well depend on timescale [Brennan, 1981]. We have made no attempt to add this frequency dependence to our model.…”

Section: Discussionmentioning

confidence: 99%

Equation of state and wave propagation in hysteretic nonlinear elastic materials

McCall¹,

Guyer²

1994

J. Geophys. Res.

233

153

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Heterogeneous materials, such as rock, have extreme nonlinear elastic behavior (the coefficient characterizing cubic anharmonicity is orders of magnitude greater than that of homogeneous materials) and striking hysteretic behavior (the stress‐strain equation of state has discrete memory). A model of these materials, taking their macroscopic elastic properties to result from many mesoscopic hysteretic elastic units, is developed. The Preisach‐Mayergoyz description of hysteretic systems and effective medium theory are combined to find the quasistatic stress‐strain equation of state, the quasistatic modulus‐stress relationship, and the dynamic modulus‐stress relationship. Hysteresis with discrete memory is inherent in all three relationships. The dynamic modulus‐stress relationship is characterized and used as input to the equation of motion for nonlinear elastic wave propagation. This equation of motion is examined for one‐dimensional propagation using a Green function method. The out‐of‐phase component of the dynamic modulus due to hysteresis is found to be responsible for the generation of odd harmonics and to determine the amplitude of the nonlinear attenuation.

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Section: Discussionmentioning

confidence: 99%

Equation of state and wave propagation in hysteretic nonlinear elastic materials

McCall¹,

Guyer²

1994

J. Geophys. Res.

233

153

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“…The input channels are 12 bits, so for a full scale signal, the digital limit on phase resolution is [4096] -1 = 2.4 x 10 -4 rad. Phase determination by the method of Lissajous figures can provide high resolution if the figure is expanded; the method is particularly useful at low frequency 21 . Improvements in mechanical aspects of phase resolution were achieved by reducing mechanical perturbations.…”

Section: Phase Measurementmentioning

confidence: 99%

Apparatus for measuring viscoelastic properties over ten decades: Refinements

Brodt

Cook

Lakes

1995

Review of Scientific Instruments

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This paper describes refinements to an instrument for determining the viscoelastic properties of a solid material isothermally, with a single apparatus, over 10 decades of time and frequency. Torque is applied electromagnetically to a specimen fixed at one end. Specimen deformation is determined via a Iaser beam reflected from the other end upon a split diode detector. Phase resolution is improved by the use of a lock-in amplifier at high frequency and by the use of Lissajous figures to measure phase, allowing the study of materials of moderate loss (0.008G tan SGO.2) in addition to materials with high loss (tan S-1). The rigidity of the instrument is increased by modifications in the specimen support geometry. The range of equivalent frequency for torsion is from less than 10M6 Hz to more than IO4 Hz. Digital methods are incorporated in the creep measurements and in the phase measurements. 0 1995 American Institute of Physics.

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“…Experimentally, what is mainly indicated for nonsaturated samples is a comprehensive approach using the established, bar resonance techniques that have been Seismologically , it would also be desirable to compare the results obtained from the bar resonance method, with comparable results from the approach of Stacey and his coworkers (see e.g. Brennan 1981), in which the common frequencies of experimental seismology are used in the laboratory.…”

Section: Discussionmentioning

confidence: 99%

“…Brennan 1981), in which the common frequencies of experimental seismology are used in the laboratory.…”

Section: (Rad S-')mentioning

confidence: 99%

Mechanism of Anelasticity

Schwab¹

1988

Geophysical Journal International

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S U M M A R YAccess to modem vector processors-'supercomputers'-now makes possible extremely large-scale seismological computations, in which the anelasticity of the earth can be treated in an exact manner. For this exact formalism to be physically meaningful, it must be shown to be consistent with a convincing physical model of anelasticity. Such a model is investigated for unsaturated, solid-earth materials. It is a scattering mechanism which is based on the nature of polycrystalline aggregates. For transverse waves, this linear mechanism of anelasticity isgiven by with where @, @, Y are the fractional volumes of pores, crystalline inhomogeneities, and lubricated crystals. The Lam& constants, density, and crystal velocity, A, p, p , Bc, describe the crystalline matrix exclusive of the pores and inhomogeneities; pint,, pincl describe the inhomogeneities; and, if all these parameters are identified with a reference frequency wo, the very simple approximation for the dispersion can be written. In this simple form, reasonably accurate predictions from the model are probably limited to values of the fractional scattering volumes that are individually no more than a few percent. Larger values of the fractional volumes appear to require either more detailed theoretical treatments, or empirically-based scaling laws that reduce the true fractional scattering volumes to smaller, effective ones before the formulae above are used. The formulae are presented as constant-QtJ representations of linear anelasticity; however, a Futterman type model, with Q,( o) inversely proportional to the dispersive velocity, is also a reasonable result from the development. In this case, the multiplicative factor B(w)/BC is added to the right-hand side of the expression for l/QtJ, and B ( 0 ) B ( w o ) [ l + (l/nQp) In (o/wo)l.

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Linear viscoelastic behaviour in rocks

Cited by 22 publications

References 21 publications

Equation of state and wave propagation in hysteretic nonlinear elastic materials

Equation of state and wave propagation in hysteretic nonlinear elastic materials

Apparatus for measuring viscoelastic properties over ten decades: Refinements

Mechanism of Anelasticity

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