Poroelastic Backus averaging for anisotropic layered fluid‐ and gas‐saturated sediments

Gelinsky, Stephan; Shapiro, Serge A.

doi:10.1190/1.1444287

Cited by 106 publications

(77 citation statements)

References 48 publications

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“…The effective VTI model for wave propagation in layered media at arbitrary angle was presented by Krzikalla and Müller (2011). This effective model makes use of the poroelastic Backus averaging (Gelinsky and Shapiro, 1997) and the effective plane-wave modulus obtained for a periodic 1D medium (White et al, 1975). The resulting equations in the effective medium are equations of elasticity with frequency-dependent coefficients.…”

Section: Effective Viscoelastic Vti Modelmentioning

confidence: 99%

“…In this section, we introduce the effective poroelastic model based on the poroelastic Backus averaging (Gelinsky and Shapiro, 1997) and the effective plane-wave moduli obtained for P-wave propagation at normal incidence in a periodically layered porous medium (Kudarova et al, 2013). These effective moduli result from using the boundary conditions at the interfaces of the periodic cell different from those used in White's et al (1975) model.…”

Section: Effective Poroelastic Vti Modelmentioning

confidence: 99%

“…The expressions for the effective stiffnesseŝ A,F,Ĉ, andD were obtained by Gelinsky and Shapiro (1997) in two limiting cases of relaxed and unrelaxed pore pressures (the expressions are given in Appendix C). These limits are referred to as quasistatic and no-flow limits, respectively.…”

Section: Effective Viscoelastic Vti Modelmentioning

confidence: 99%

“…In this paper, we combine the effective constants from the poroelastic Backus averaging (Gelinsky and Shapiro, 1997) and the method proposed by Krzikalla and Müller (2011). We use the effective P-wave moduli introduced by Kudarova et al (2013).…”

Section: Introductionmentioning

confidence: 99%

“…Krzikalla and Müller (2011) introduce an effective vertical transverse isotropic (VTI) medium to describe propagation of quasi-P (qP) and quasi-S (qS) waves at different angles. In their model, the low-and high-frequency elastic moduli from poroelastic Backus averaging by Gelinsky and Shapiro (1997) are connected by a frequency-dependent function -the effective P-wave modulus of White et al (1975) for periodic layering and normal incidence. For a randomly layered medium with a small fluctuation of parameters, the frequency-dependent function can be derived from Gelinsky et al (1998).…”

Section: Introductionmentioning

confidence: 99%

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An effective anisotropic poroelastic model for elastic wave propagation in finely layered media

2016

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Mesoscopic-scale heterogeneities in porous media cause attenuation and dispersion at seismic frequencies. Effective models are often used to account for this. We have developed a new effective poroelastic model for finely layered media, and we evaluated its impact focusing on the angle-dependent attenuation behavior. To enable this, an exact solution was obtained for the response of a periodically layered medium to a surface point load using Floquet’s theory. We compared this solution with that of the new model and the equivalent viscoelastic vertical transverse isotropic medium available from existing literature. We have observed that the quasi-P (qP) wave dispersion and attenuation was predicted with high accuracy by the new effective poroelastic model. For the quasi-S (qS) wave, the effective poroelastic model provides a perceptibly better prediction of the attenuation, resulting in closer to the exact waveforms. The qS-wave attenuation is underestimated by the effective viscoelastic model, whereas for the qP-wave, the model gives accurate predictions in all cases except for highly permeable weak-frame media.

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Section: Effective Viscoelastic Vti Modelmentioning

confidence: 99%

Section: Effective Poroelastic Vti Modelmentioning

confidence: 99%

Section: Effective Viscoelastic Vti Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An effective anisotropic poroelastic model for elastic wave propagation in finely layered media

2016

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Brown and Korringa constants for heterogeneous thinly layered poroelastic media

Wollner

Mavko

2017

JGR Solid Earth

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Macromechanical characterization of a layered poroelastic package treated as a homogeneous (upscaled) medium is presented. The characterization is based on the knowledge of the poroelastic properties of the package's constituents. Specifically, we provide closed‐form expressions for the sum of the fourth‐order average elastic compliances tensor Sijkk′ of the solid frame and pore space compressibility 1/Kϕ, previously defined in Brown and Korringa's extended formulation of the Gassmann's fluid substitution equations. These constants allow, thus, to perform fluid substitution on an upscaled composite consisting of poroelastic layers. Each layer within the layered package is assumed to have isotropic symmetry, uniform porosity, and single pore‐filling fluid and composed of several homogeneously distributed mineral phases such that each layer is approximately Gassmann consistent; however, the fluid and mineral phases as well as the porosity may vary from one layer to the next along the package. In addition, we obtain insights into the sensitivity of Sijkk′ and 1/Kϕ when an approximate fluid substitution operation is used. Moreover, it is shown that the Sijkl′ of the upscaled medium can have transverse isotropy symmetry. The degree of anisotropy is controlled by the volume fractions of individual layers and the contrast of elastic properties between the layers. The results for Sijkk′ and 1/Kϕ are compared to those obtained by Berryman and Milton (BM) for a two‐phase isotropic composite. At a limiting case of an effectively isotropic medium, this paper's results coincide with those of BM.

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Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

et al. 2017

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Many researchers have analyzed seismic attenuation and velocity dispersion due to wave‐induced fluid flow (WIFF) related to the presence of fluid‐saturated fractures embedded in an isotropic porous background. Most fractured formations do, however, exhibit some degree of intrinsic elastic and hydraulic anisotropy of the background, and the impact of which on the effective seismic properties remains largely unexplored. In this work, we extend a numerical upscaling procedure to account for the potential intrinsic elastic and hydraulic anisotropy of the background. To do this, we represent the background of a representative sample of the fractured formation of interest with an anisotropic poroelastic medium and apply a set of relaxation experiments to compute the effective anisotropic seismic properties. A comprehensive numerical analysis allows us to observe that, for samples containing hydraulically connected fractures, the anisotropic behavior of both P and S waves differs significantly from that observed for an isotropic background. The anisotropy of the stiffness of the background plays a fundamental role for WIFF between the fractures and the background as well as for WIFF between connected fractures. Conversely, the anisotropy of the background permeability affects the characteristic frequency, the angle dependence, and the magnitude of the effects related to WIFF between fractures and background. In addition, different correlations between hydraulic and elastic background anisotropy lead to different degrees of effective seismic anisotropy. Our results therefore indicate that accounting for the effects of intrinsic background anisotropy on WIFF is crucial for a quantitative interpretation of seismic anisotropy measurements in fluid‐saturated fractured formations.

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Poroelastic Backus averaging for anisotropic layered fluid‐ and gas‐saturated sediments

Cited by 106 publications

References 48 publications

An effective anisotropic poroelastic model for elastic wave propagation in finely layered media

An effective anisotropic poroelastic model for elastic wave propagation in finely layered media

Brown and Korringa constants for heterogeneous thinly layered poroelastic media

Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

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