In order to interpret seismic wave velocity, anisotropy, and attenuation
measurements for porous materials in terms of the concentration of fluid
and the underlying microstructure, we use a combined effective medium theory
(Hornby, 1994, and Jakobsen, 1999) to calculate the resulting material
properties for all porosities and a range of geometries of fluid inclusions
in an underlying solid matrix. Starting from a representative isotropic
solid and fluid phase we show the effect on bulk and shear moduli, P- and
S-wave velocity, and anisotropy of introducing varying amounts of spheroidal
fluid inclusions of a range of aspect ratios. For an isotropic material
where the fluid inclusions are introduced at random orientations, higher
inclusion aspect ratio results in lower elastic moduli, and hence seismic
velocities for a given fluid concentration. For an anisotropic effective
medium where the inclusions are aligned, seismic velocities are greater
or less than for the corresponding isotropic case for propagation parallel
or perpendicular to the direction of alignment, and increasing aspect ratio
accentuates this effect. A first order perturbation theory (Pointer
et al., 1999) is employed to simulate the attenuation resulting from the
solid-fluid composite, and both bulk and shear attenuation are found to
increase with porosity. Bulk attenuation is approximately an order
of magnitude greater than shear attenuation for parameters appropriate
to sedimentary rocks.
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