Seismic Wave Propagation in Composite Elastic Media

It has been known since the time of Biot–Gassman theory (Biot, J Acoust Soc Am 28:168–178, 1956, Gassmann, Naturf Ges Zurich 96:1–24, 1951) that additional seismic waves are predicted by a multicomponent theory. It is shown in this article that if the second or third phase is also an elastic medium...

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Bibliographic Details
Published in:Transport in porous media 2009-08, Vol.79 (1), p.135-148
Main Author: Spanos, T. J. T.
Format: Article
Language:English
Subjects:
Attenuation
Civil Engineering
Classical and Continuum Physics
Computational fluid dynamics
Dilatational waves
Earth and Environmental Science
Earth Sciences
Elastic limit
Elastic media
Elastic waves
Equations of motion
Fluid flow
Fluids
Geotechnical Engineering & Applied Earth Sciences
Heart
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Mathematical models
Media
Porous media
S waves
Seismic waves
Shear modulus
Viscosity
Wave attenuation
Wave propagation
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Summary:It has been known since the time of Biot–Gassman theory (Biot, J Acoust Soc Am 28:168–178, 1956, Gassmann, Naturf Ges Zurich 96:1–24, 1951) that additional seismic waves are predicted by a multicomponent theory. It is shown in this article that if the second or third phase is also an elastic medium then multiple p and s waves are predicted. Futhermore, since viscous dissipation no longer appears as an attenuation mechanism and the media are perfectly elastic, these waves propagate without attenuation. As well, these additional elastic waves contain information about the coupling of the elastic solids at the pore scale. Attempts to model such a medium as a single elastic solid causes this additional information to be misinterpreted. In the limit as the shear modulus of one of the solids tends to zero, it is shown that the equations of motion become identical to the equations of motion for a fluid filled porous medium when the viscosity of the fluid becomes zero. In this limit, an additional dilatational wave is predicted, which moves the fluid though the porous matrix much similar to a heart pumping blood through a body. This allows for a connection with studies which have been done on fluid-filled porous media (Spanos, 2002).
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-009-9448-4