Waves in alternating solid and viscous fluid layers

Boris Gurevich

doi:10.1071/ASEG2001ab050

ISSN: 2202-0586
E-ISSN:

oa Waves in alternating solid and viscous fluid layers
Authors Boris Gurevich^a
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^a Curtin University of Technology, , Australia, [email protected]
Publisher: Australian Society of Exploration Geophysicists
Source: ASEG Extended Abstracts, Volume 2001, Issue ASEG2001 - 15th Geophysical Conference, Dec 2001, p. 1 - 4
DOI: https://doi.org/10.1071/ASEG2001ab050
- Published online: 01 Dec 2001

Abstract

Explicit expressions for the frequency dependence of the velocity and attenuation of shear waves in a periodic system of flat solid and viscous fluid layers have been derived by solving exact Rytov’s dispersion equation in the long-wavelength approximation. The dispersion and attenuation are related to the well known mechanisms of dissipation in porous media: viscoelastic mechanism (viscous shear relaxation) and visco-inertial Biot’s mechanism. The expressions describing the effects of these two mechanisms in a broad frequency range have been derived from the same standpoint. The asymptotic expressions for various limiting cases coincide with the results of previous studies.

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References

Auriault, J.-L. and Boutin, C, 1994, Deformable porous media with double porosity. Ill: Acoustics, Transport in Porous Media, 14, 143-162.
Bedford, A., 1986, Application of Biot’s equations to a medium of alternating fluid and solid layers. Journal of Wave-Material Interaction, 1, 34-53.
Berryman, J. G., 1985, Scattering by a spherical inhomogeneity in a fluid-saturated porous medium. Journal of Mathematical Physics, 26, 1408-1419.
Boutin, C. and Auriault, J.-L., 1990, Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concrete, International Journal of Engineering Science, 28, 1157-1181.
Brekhovskikh, L. M., 1981, Waves in Layered Media. Academic Press.
Gelinsky, S., Shapiro, S.A., Mueller, T, and Gurevich, B., 1997, Dynamic poroelasticity of thinly layered structures: International Journal of Solids and Structures, 35, 4739-4751.
Gurevich, B., Sadovnichaja, A.P., Lopatnikov, S.L., and Shapiro, S.A. 1998, Scattering of a compressional wave in a poroelastic medium by an ellipsoidal inclusion: Geophysical Journal International, 133, 91-103.
Gurevich, B. and Lopatnikov, S.L. 1995. Velocity and attenuation of elastic waves in finely layered porous rocks: Geophysical Journal International, 121, 933-947.
Gurevich, B., 1999, Low-frequency shear wave propagation in periodic systems of alternating solid and viscous fluid layers. Journal of the Acoustical Society of America, 106, 57-60.
Gurevich, B., 2001, Effect of fluid viscosity on the elastic wave attenuation in porous rocks. Geophysics. In press.
Molotkov, L. A. and Bakulin, A. V., 1998, Effective model of solid-fluid layers as a partial case of Biot model. Journal of Mathematical Sciences, 91, 2812-2827.
Rytov, S. M., 1956, Acoustical properties of a thinly laminated medium. Soviet Physics Acoustics, 2, 68-80.
Schoenberg, M., 1984, Wave propagation in alternating fluid/solid layers. Wave Motion, 6, 303-320.
Schoenberg, M. and Sen, P. N., 1986, Wave propagation in alternating solid and viscous fluid layers: Size effects in attenuation and dispersion of fast and slow waves. Applied Physics Letters, 48, 1249-1251.

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Article Type: Research Article

Keyword(s): attenuation; Biot’s theory; dispersion; porous media

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