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Modeling elastic wave velocities in porous media : frequency-dependent effects of heterogeneity at the pore- and patch-scale Taylor, Richard
Abstract
The prediction of relationships between elastic wave velocities in a porous medium and the properties of the fluid and solid constituents therein is a longstanding problem in geophysical exploration. Previous authors have shown that such relationships depend on both the wave frequency and degree of heterogeneity present. This frequency dependence arises via the state of relaxation of the pore fluids. At sufficiently low frequencies, deformation-induced flow leads to equilibration of the fluid pressure, and the pore fluids are said to be in a "relaxed" state. At sufficiently high frequencies, there is insufficient time for equilibration to occur, and the fluids are said to be "unrelaxed". Current models of elastic wave velocities in porous media are, for the most part, confined to either the relaxed limit (e.g., the poroelastic Biot-Gassmann theory) or the unrelaxed limit (e.g., inclusion-based effective medium theory). In this thesis we incorporate an explicit description of the relaxation mechanism into inclusion-based effective medium theory, so as to extend the theory toward the relaxed limit. Analysis of the mechanisms of relaxation leads to a description of the effective elastic behavior of the porous medium in terms of effective complex elastic moduli of the medium's constituents. Previous authors have identified two distinct scales of fluid distribution heterogeneity: the pore scale and the patch scale. Accordingly, we treat these scales separately, describing relaxation in terms of Poiseuille flow at the pore scale, and Darcy's law at the patch scale. The results of our analyses are effective medium theories that provide a consistent approach to the prediction of elastic wave velocities, as well as attenuation due to the relaxation mechanism, over a broad range of frequencies and length scales of heterogeneity. In particular, our model is applicable to the regime where the pore fluids are in a state of relaxation intermediate between the completely relaxed and completely unrelaxed end members.
Item Metadata
Title |
Modeling elastic wave velocities in porous media : frequency-dependent effects of heterogeneity at the pore- and patch-scale
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1999
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Description |
The prediction of relationships between elastic wave velocities in a porous medium and
the properties of the fluid and solid constituents therein is a longstanding problem in
geophysical exploration. Previous authors have shown that such relationships depend
on both the wave frequency and degree of heterogeneity present. This frequency dependence
arises via the state of relaxation of the pore fluids. At sufficiently low frequencies,
deformation-induced flow leads to equilibration of the fluid pressure, and the pore fluids
are said to be in a "relaxed" state. At sufficiently high frequencies, there is insufficient
time for equilibration to occur, and the fluids are said to be "unrelaxed".
Current models of elastic wave velocities in porous media are, for the most part,
confined to either the relaxed limit (e.g., the poroelastic Biot-Gassmann theory) or the
unrelaxed limit (e.g., inclusion-based effective medium theory). In this thesis we incorporate
an explicit description of the relaxation mechanism into inclusion-based effective
medium theory, so as to extend the theory toward the relaxed limit. Analysis of the
mechanisms of relaxation leads to a description of the effective elastic behavior of the
porous medium in terms of effective complex elastic moduli of the medium's constituents.
Previous authors have identified two distinct scales of fluid distribution heterogeneity:
the pore scale and the patch scale. Accordingly, we treat these scales separately,
describing relaxation in terms of Poiseuille flow at the pore scale, and Darcy's law at
the patch scale. The results of our analyses are effective medium theories that provide
a consistent approach to the prediction of elastic wave velocities, as well as attenuation
due to the relaxation mechanism, over a broad range of frequencies and length scales of
heterogeneity. In particular, our model is applicable to the regime where the pore fluids
are in a state of relaxation intermediate between the completely relaxed and completely
unrelaxed end members.
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Extent |
7760978 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-06-16
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0089086
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1999-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.