Dynamic poroelasticity of thinly layered structures

Gelinsky, Stephan; Shapiro, Serge A.; Müller, Tobias M.; Gurevich, Boris

doi:10.1016/s0020-7683(98)00092-4

Cited by 92 publications

(41 citation statements)

References 15 publications

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“…Second, the numerical results for a random system ͑uniform distribution͒ of fractures also show a reasonably good agreement with the analytical model for periodic fractures, especially in the vicinity of the attenuation peak. This latter finding appears to contradict earlier observations ͑Lopatnikov and Gurevich, 1988;Gurevic and Lopatnikov, 1995;Gurevich et al, 1997;Gelinsky, 1998͒ that show ͑both analytically and numerically͒ random and periodic systems of poroelastic layers exhibiting very different frequency dependencies of attenuation. However, our more detailed analysis, which involves a higher degree of fracturing ͑Figure 5͒, shows that periodic and random systems of fractures do exhibit different asymptotic behavior at low frequencies.…”

Section: Discussioncontrasting

confidence: 56%

Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

2006

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To explore the validity and limitations of the theoretical model of wave propagation in porous rocks with periodic distribution of planar fractures, we perform numerical simulation using a poroelastic reflectivity algorithm. The numerical results are found to be in good agreement with the analytical model, not only for periodic fractures, but also for random distribution of constant thickness fractures.

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Section: Discussioncontrasting

confidence: 56%

Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

2006

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“…Biot's theory is not adequate for rocks and hydrocarbon reservoir models in view of microinhomogeneity leading to scattering and fast-to-slow wave conversion [19,16]. In this case an effective dispersion relation for the fast longitudinal wave accounting for the fast-to-slow conversion has been derived for the fast P wave for frequencies in the range between a characteristic frequency lu0 and wb [19].…”

Section: Formulationmentioning

confidence: 99%

Asymptotic and exact fundamental solutions in hereditary media with singular memory kernels

Hanyga¹,

Seredyńska²

2002

Quart. Appl. Math.

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“…2) Macroscopically inhomogeneous porous medium, i.e., a micro-porous medium with some macroscopically heterogeneous structure. Examples of such media include a randomly layered porous medium (Gurevich and Lopatnikov, 1995;Gelinsky et al, 1998), a porous medium with macroscopic inclusions , and a double-porosity medium (Auriault and Boutin, 1994). Any such medium is characterized by two characteristic length parameters: a characteristic pore size d and a characteristic size b d of the macroscopic heterogeneities (layers, inclusions, fractures).…”

Section: Materials With Multiple Length Scalesmentioning

confidence: 99%

“…Clearly, a rigid relationship between the characteristic frequencies for macroscopically inhomogeneous porous media is no longer relevant. Analysis of the characteristic frequencies of the dominant attenuation mechanisms in heterogeneous porous media can be found in Gurevich et al (1997), Gelinsky et al (1998), and Shapiro and Mueller (1999).…”

Section: Materials With Multiple Length Scalesmentioning

confidence: 99%

Effect of fluid viscosity on elastic wave attenuation in porous rocks

Gurevich

1999

SEG Technical Program Expanded Abstracts 1999

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Attenuation and dispersion of elastic waves in fluidsaturated rocks due to pore fluid viscosity is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies can be studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of the shear wave in the fluid (viscous skin depth) is much smaller than the wavelength of the shear or compressional waves in the solid, the presence of viscous fluid layers requires a consideration of higher-order terms in the low-frequency asymptotic expansions. This expansion leads to asymptotic lowfrequency dispersion equations. For a shear wave with the directions of propagation and of particle motion in the bedding plane, the dispersion equation yields the low-frequency attenuation (inverse quality factor) as a sum of two terms which are both proportional to frequency ω but have different dependencies on viscosity η: one term is proportional to ω/η, the other to ωη. The lowfrequency dispersion equation for compressional waves allows for the propagation of two waves corresponding to Biot's fast and slow waves. Attenuation of the fast wave has the same two-term structure as that of the shear wave. The slow wave is a rapidly attenuating diffusiontype wave, whose squared complex velocity again consists of two terms which scale with iω/η and iωη.For all three waves, the terms proportional to η are responsible for the viscoelastc phenomena (viscous shear relaxation), whereas the terms proportional to η −1 account for the visco-inertial (poroelastic) mechanism of Biot's type. Furthermore, the characteristic frequencies of visco-elastic ω V and poroelastic ω B attenuation mechanisms obey the relation ω V ω B = Aω 2 R , where ω R is the resonant frequency of the layered system, and A is a dimensionless constant of order 1. This result explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic theories that imply ω ω R . The poroelastic mechanism dominates over the visco-elastic one when the frequencyindepenent parameter B = ω B

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Dynamic poroelasticity of thinly layered structures

Cited by 92 publications

References 15 publications

Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

Attenuation and dispersion of P-waves in porous rocks with planar fractures: Comparison of theory and numerical simulations

Asymptotic and exact fundamental solutions in hereditary media with singular memory kernels

Effect of fluid viscosity on elastic wave attenuation in porous rocks

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