Dynamic Green's function for homogeneous and isotropic porous media

Sahay, Pratap N.

doi:10.1046/j.1365-246x.2001.01562.x

Cited by 25 publications

(52 citation statements)

References 16 publications

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“…As mentioned previously, the 2-D Green's function for the porous medium can be derived systematically using Kupradze's method (Kupradze, 1979) as in the paper of Sahay (2001). However, the Green's function obtained by Kupradze's method has a complicated form.…”

Section: Two-dimensional (2-d) Green's Function For the Porous Mediummentioning

confidence: 99%

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

Jeng

Williams

2008

International Journal of Solids and Structures

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Based on Biot's theory, the dynamic 2.5-D Green's function for a saturated porous medium is obtained using the Fourier transform and the potential decomposition methods. The 2.5-D Green's function corresponds to the solutions for the following two problems: the point force applied to the solid skeleton, and the dilatation source applied within the pore fluid. By performing the Fourier transform on the governing equations for the 3-D Green's function, the governing differential equations for the two parts of the 2.5-D Green's function are established and then solved to obtain the dynamic 2.5-D Green's function. The derived 2.5-D Green's function for saturated porous media is verified through comparison with the existing solution for 2.5-D Green's function for the elastodynamic case and the closed-form 3-D Green's function for saturated porous media. It is further demonstrated that a simple form 2-D Green's function for saturated porous media can be been obtained using the potential decomposition method.

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Section: Two-dimensional (2-d) Green's Function For the Porous Mediummentioning

confidence: 99%

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

Jeng

Williams

2008

International Journal of Solids and Structures

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“…In order to simplify this problem, we use the reciprocity theorem (eq. 9) (Pride and Haartsen, 1996;Sahay, 2001), and assume that the average force F 1 acting on the porous medium and fluid force F 2 are similar (Garambois and Dietrich, 2002). This simplification allows us to drop the j index of the Green's functions (eq.…”

Section: Coupled Second-order Equations For Plane P-sv Wavesmentioning

confidence: 99%

First‐order perturbations of the seismic response of fluid‐filled stratified poro‐elastic media

Barros

Dietrich

2006

SEG Technical Program Expanded Abstracts 2006

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SUMMARYWe derive analytical formulas for the first-order effects produced by plane inhomogeneities on the seismic response of a stratified porous medium. The approach used for the derivation is similar to the one employed in the elastic case; it is based on a perturbation analysis of the poro-elastic wave propagation equations. The final forms of the sensitivity operators, which are often referred to as the Fréchet derivatives, are expressed in terms of the Green's functions of the solid and fluid displacements in the frequency-ray parameter domain. We compute here the Fréchet derivatives with respect to eight parameters, namely, the fluid and mineral density and bulk moduli, porosity, permeability, consolidation parameter and shear modulus. The accuracy and stability of the derived expressions are checked by comparing differential seismograms computed from the analytical expressions of the Fréchet derivatives with solutions obtained by introducing discrete perturbations into the model properties. We find that the Fréchet derivative approach is generally accurate for perturbations of the medium properties of up to 10%, and for layer thicknesses less than one fifth of the dominant wavelength.

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“…Later solutions include Kaynia and Banerjee [25], who used Laplace transform and the «, -w¡ formulation to derive 3-D fundamental solutions of total and fluid body forces, Zimmerman and Stem [26], who used «, -p formulation in frequency domain to derive 3D fundamental solutions of total and fluid body forces, and Philippacopoulos [27] and Sahay [28], who used the «, -w,formulation to derive 3D fundamental solution of point force. Concise fundamental solutions in time domain for the low frequency range have been derived for saturated poroelastic medium [29].…”

Section: Introductionmentioning

confidence: 99%

Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition

Ding

Cheng

Chen

2013

Journal of Applied Mechanics

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for the point force and fluid source singularities in 2D and 3D, using an analogy betv^'een poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on the decomposition of a Dirac ô function into a rotational and a dilatational part. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken. These isolated wave fields may be useful in applications where it is desirable to separate the shear and compressional wave effects. These wave fields are evaluated and plotted.

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Dynamic Green's function for homogeneous and isotropic porous media

Cited by 25 publications

References 16 publications

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

First‐order perturbations of the seismic response of fluid‐filled stratified poro‐elastic media

Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition

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