Reflection and Transmission of Waves at a Fluid/Porous-medium Boundary

Denneman, A.I.M.; Drijkoningen, G.G.; Smeulders, David; Wapenaar, Kees

doi:10.1007/0-306-46953-7_48

Cited by 3 publications

(4 citation statements)

References 10 publications

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“…The acoustic medium Ω 0 is water (ρ f = 1000 kg/m 3 , c = 1500 m/s). The poroelastic layers consist alternately of water-saturated sand in Ω 2j−1 [8], and Berea sandstone in Ω 2j [23]. The poroelastic properties of these media are summarized in Table 1.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Classical textbooks such as [4,5] can be consulted for a detailed analysis of Biot's equations (which involve a fast compressional wave and a shear wave, as in elastic media, and a slow compressional wave). In the case of a single fluid / porous interface, many theoretical studies have dealt with the reflection / transmission coefficients [6] and with the properties of the surface waves [7,8,9,10,11]. The aim of the present study is to solve this problem in the case of an arbitrary number of layers, using two radically different approaches: a semi-analytical approach and a purely numerical one.…”

Section: Introductionmentioning

confidence: 99%

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Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media

et al. 2012

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Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems. Special attention is paid to calculating the Fourier integrals. The numerical method is based on a high order finite-difference time-domain scheme. Mesh refinement is applied near the interfaces to discretize the slow compressional diffusive wave predicted by Biot's theory. Lastly, an immersed interface method is used to discretize the boundary conditions. The numerical benchmarks are based on realistic soil parameters and on various degrees of hydraulic contact at the fluid / porous boundary. The time evolution of the acoustic pressure and the porous velocity is plotted in the case of one and four interfaces. The excellent level of agreement found to exist between the two approaches confirms the validity of both methods, which cross-checks them and provides useful tools for future researches.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media

et al. 2012

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“…Third, acoustic/poroelastic interface contacts were also examined. For the open-pore interface, Denneman et al [39] derived closed-form expressions for reflection and transmission coefficients between acoustic and porous half-spaces. Lyu et al [21] calculated the reflection and transmission of plane waves at the interface between the ocean and the ocean floor.…”

Section: Introductionmentioning

confidence: 99%

Evanescent waves in hybrid poroelastic metamaterials with interface effects

Zhang

Luo

Wang

et al. 2023

International Journal of Mechanical Sciences

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“…Starting with Geertsma & Smit (1961), to Deresiewicz & Rice (1964), Wu et al (1990), Santos et al (1992), Albert (1993), and Cieszko & Kubik (1998), it is continued with Denneman et al (2002). In this last study, the closed form expressions of reflection and transmission coefficients (Denneman et al 2000; Denneman et al 2001) are calculated for the interfaces of water with water‐saturated and air‐filled porous layers. The work presented here, also, studies the reflection and transmission at the fluid/porous solid interface, however, the porous solid is considered anisotopic with arbitrary symmetry.…”

Section: Introductionmentioning

confidence: 99%

3-D wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid

Sharma

2004

Geophysical Journal International

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S U M M A R YReflection/refraction process is studied to calculate the energy distribution and transmission in a general anisotropic poroelastic solid half-space in contact with a fluid half-space. Biot's theory is used to study the propagation of plane harmonic waves in an anisotropic fluidsaturated porous solid. Snell's law for reflection/refraction at an interface between fluid and anisotropic poroelastic solid is calculated for the wave propagation in three dimensions. From the velocity and direction of incident wave in the fluid medium, Snell's law is used to find the phase velocities and phase directions of all the four refracted waves. The phase velocity and phase direction, thus, obtained are used to calculate the group velocity and ray direction of each of the refracted waves. The energy of the incident wave is distributed among one reflected wave and four quasi-waves refracted to the anisotropic poroelastic medium. Energy transmission with each of the reflected/refracted waves is studied along with their directions of travel in 3-D space. The variations of energy partition with the direction of the incident wave are computed for a particular model. The effect of azimuthal anisotropy on the partition and transmission of energy is observed.Dynamic behaviour of fluid-saturated porous media is attracting considerable attention as a result of its importance in earthquake engineering, oil exploration, soil dynamics and hydrology. The poroelastic equations formulated by Biot (1956) have long been regarded as standard and have formed the basis for solving wave-propagation problems in poroelasticity. Biot (1955) presented the stress-strain relations for an anisotropic poroelastic solid. Anisotropy in porous solids may be the result of propagation through distribution of aligned cracks, microcracks and preferentially-oriented pore space. Occasionally, anisotropy may be the result of some other phenomena, such as rock foliation or crystal alignment. Following Biot's theory, Schmitt (1989) and Sharma (1991) studied the wave propagation in transversely isotropic poroelastic solids. Thomsen (1995) related the anisotropy to crack parameters in a porous rock and suggested that amount and type of anisotropy in the porous rocks depend upon the crack density, crack shape, stiffness of interstitial fluid, equant porosity, frequency, fluid pressure and flow between cracks and pores. This work was supported by the experimental study of anisotropy of sandstone with controlled crack geometry by Rathore et al. (1995). Sharma (1996) discussed the coexistence of cracks and pores and its effect on surface wave propagation. Hudson et al. (1996) studied the effect of connection between cracks and of small-scale porosity within the solid material on the overall elastic properties of cracked solids.The study of anisotropic elasticity is also important for understanding the mechanical behaviour of composite materials (Braga 1990;Fan & Hwu 1998). Anisotropy in these materials results from the presence of crystals of particular symmetry ...

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Reflection and Transmission of Waves at a Fluid/Porous-medium Boundary

Cited by 3 publications

References 10 publications

Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media

Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media

Evanescent waves in hybrid poroelastic metamaterials with interface effects

3-D wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid

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