Wave Propagation in Infinituple‐Porosity Media

The fractal texture (or fabric) of porous media, which supports fluid flow at different scales, is the main cause of wave anelasticity (dispersion and attenuation) on a wide range of frequencies. To model this phenomenon, we develop a theory of wave propagation in a fluid saturated infinituple‐poros...

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Bibliographic Details
Published in:Journal of geophysical research. Solid earth 2021-04, Vol.126 (4), p.n/a
Main Authors: Zhang, Lin, Ba, Jing, Carcione, José M.
Format: Article
Language:English
Subjects:
Anelasticity
Attenuation
Carbonates
Coefficients
Computational fluid dynamics
Dimensions
dispersion
Elasticity
First principles
Fluid flow
Fractal geometry
fractal porous media
Fractals
Gaussian distribution
Geophysics
Inclusions
infinituple‐porosity media
Marine sediments
Normal distribution
Porosity
Porous media
Porous media flow
Probability distribution functions
Propagation
random porous media
Sandstone
Sedimentary rocks
Sediments
Stiffness
Theories
wave anelasticity
Wave attenuation
Wave dispersion
Wave propagation
wave propagation equation
Wave velocity
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Summary:The fractal texture (or fabric) of porous media, which supports fluid flow at different scales, is the main cause of wave anelasticity (dispersion and attenuation) on a wide range of frequencies. To model this phenomenon, we develop a theory of wave propagation in a fluid saturated infinituple‐porosity media containing inclusions at multiple scales, based on the differential effective medium (DEM) theory of solid composites and Biot‐Rayleigh theory for double‐porosity media. The dynamical equations are derived from first principles, that is, based on the strain (potential), kinetic, and dissipation energies, leading to generalized stiffness and density coefficients. The scale of the inclusions can be characterized by different distributions. The theory shows that the anelasticity depends on the size (radius) of the inclusions, parameter θ (exponential distribution), mean radius r0 and variance σr2 (Gaussian distribution) and the fractal dimension Df (self‐similar distribution). When Df = 2, θ = 1 and σr2 = 4, the three distributions give the same P‐wave velocities and attenuation, since each added inclusion phase has nearly the same volume fraction. For the modeling results, the range of anelasticity of Df = 2.99/θ = 1/σr2 = 4 is broader than that of Df 
ISSN:2169-9313
2169-9356
DOI:10.1029/2020JB021266