Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers
MetadataShow full item record
The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot's characteristic frequency to the viscoelastic characteristic frequency. If Biot's characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel-Biot theory of poroelasticity. In the opposite case when Biot's characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.
Gurevich, Boris and Ciz, Radim (2006) Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers , International Journal of Solids and Structures 43(25-26):7673-7683.
The link to this article is:
Copyright 2006 Elsevier B.V. All rights reserved
Showing items related by title, author, creator and subject.
Gurevich, Boris (2002)Attenuation and dispersion of elastic waves in fluidsaturated rocks due to pore fluid viscosity is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers.Waves ...
Pore scale numerical modeling of elastic wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layersCiz, Radim; Saenger, E.; Gurevich, Boris (2006)Numerical pore-scale simulation of elastic wave propagation is an emerging tool in the analysis of static and dynamic elastic properties of porous materials. Rotated staggered-grid (RSG) finite difference method has proved ...
Galvin, Robert (2007)Development of a hydrocarbon reservoir requires information about the type of fluid that saturates the pore space, and the permeability distribution that determines how the fluid can be extracted. The presence of fractures ...