Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

Hunziker, Jürg; Favino, Marco; Caspari, Eva; Quintal, Beatriz; Rubino, J. Germán; Krause, Rolf; Holliger, Klaus

doi:10.1002/2017jb014566

Cited by 52 publications

(43 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These observations are consistent with those of Guo, Rubino, Barbosa, et al, (), Guo, Rubino, Barbosa, et al, (), and Guo, Rubino, Glubokovskikh, et al, (), which found that the 3‐D (penny‐shaped cracks) theoretical predictions are in good agreement with the 2‐D (slit cracks) numerical simulations after scaling the elastic moduli in the low‐ and high‐frequency limits. Similar conclusions are also drawn by Barbosa et al () and Hunziker et al () through the comparison of the 2‐D and 3‐D numerical simulations for the aligned fracture cases. The comparison of the theoretical models for the slit and penny‐shaped cracks in this paper confirms that the seismic dispersion and attenuation due to WIFF for waves perpendicular to fractures are relatively insensitive to the largest dimension (“length”) of the fractures.…”

Section: Discussionsupporting

confidence: 87%

“…Guo et al (2017), Guo, Rubino, Barbosa, et al, (2018a), Guo, Rubino, Barbosa, et al, (2018b), and Guo, Rubino, Glubokovskikh, et al, (2018) compared the results of numerical simulations for slit fractures (2-D numerical simulation) against the theoretical model designed for the penny-shaped fractures ; a 3-D theoretical result) and found a surprisingly good agreement, despite the difference in underlying geometries. This phenomenon was further explored in recent numerical simulations of Hunziker et al (2018), which show that attenuation and dispersion caused by 3-D cracks is very close to that caused by 2-D cracks. Although there is no clear theoretical explanation as yet for this agreement, it implies that the seismic dispersion and attenuation due to WIFF is relatively insensitive to the largest dimension ("length") of the fractures.…”

mentioning

confidence: 91%

See 1 more Smart Citation

Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

Guo

et al. 2018

JGR Solid Earth

View full text Add to dashboard Cite

We estimate the seismic attenuation and velocity dispersion induced by fluid pressure diffusion in a saturated porous medium containing a sparse distribution of aligned slit fractures. This is done by solving the scattering problem for a single crack and using Waterman‐Truell scattering approximation for a distribution of cracks. This approach gives a numerical solution for the entire frequency range and analytical solutions for the low‐ and high‐frequency limits. Analysis of the results shows that the characteristics of the seismic dispersion and attenuation for the slit cracks are similar to known results for penny‐shaped crack. At high frequencies, the attenuation and dispersion are controlled by the crack density regardless of the crack geometry. At low frequencies, due to the different geometries of the slit and penny‐shaped cracks, the characteristics of seismic dispersion and attenuation are different. For both the slit and penny‐shaped crack case, the slope of the frequency dependence attenuation of factor (inverse quality factor) Q−1 tends to be 1. Yet the low‐frequency asymptotic solutions for these two cases are somewhat different. For penny‐shaped cracks, the Q−1(ω) on the bilogarithmic scale has a straight line asymptote with slope 1, so that the attenuation factor at low frequencies is proportional to the frequency ω. However, for slit cracks, the asymptotic low‐frequency solution contains a logarithmic function of ω, and no such asymptote exists. At the same time, similarly to the penny‐shaped crack case, the solution for compressional velocity in the low‐frequency limit is consistent with the anisotropic Gassmann theory.

show abstract

Section: Discussionsupporting

confidence: 87%

mentioning

confidence: 91%

Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

Guo

et al. 2018

JGR Solid Earth

View full text Add to dashboard Cite

show abstract

“…Additionally, the larger crack volume makes the 2.5D model more compressible as evidenced by a generally lower real-valued P-wave modulus, which also contributes to the increase in attenuation. The comparison between numerical results from a 3D cubic model with those of a 2D model points to the importance of 3D effects that are neglected in studies based on 2D models, as shown by Hunziker et al (2018). An important aspect is that 2D models overestimate attenuation.…”

Section: O M P a R I S O N W I T H A N A L Y T I C A L S O L U T I O Nmentioning

confidence: 84%

“…The comparison between numerical results from a 3D cubic model with those of a 2D model points to the importance of 3D effects that are neglected in studies based on 2D models, as shown by Hunziker et al . (). An important aspect is that 2D models overestimate attenuation.…”

Section: Comparison With Analytical Solutionmentioning

confidence: 99%

Numerically quantifying energy loss caused by squirt flow

Quintal

Caspari

Holliger

et al. 2019

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.

show abstract

“…In a poroelastic framework, pressure diffusion phenomena, such as wave-induced fluid flow and squirt flow, have been studied numerically (e.g. Rubino et al 2013Rubino et al , 2014Rubino et al , 2017Quintal et al 2014;Vinci, Renner and Steeb 2014;Hunziker et al 2018) and analytically (e.g. Chapman 2003;Gurevich et al 2009;Guo et al 2016), whereas scattering in fractured media is commonly studied in an elastic context (e.g.…”

mentioning

confidence: 99%

Attenuation mechanisms in fractured fluid‐saturated porous rocks: a numerical modelling study

Caspari

Новиков

Lisitsa

et al. 2018

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

Seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid‐saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot's so‐called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set‐up based on Biot's low‐frequency dynamic equations and numerical upscaling based on Biot's consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot's intrinsic mechanism are rather small for the models considered in this study.

show abstract

Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

Cited by 52 publications

References 37 publications

Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

Numerically quantifying energy loss caused by squirt flow

Attenuation mechanisms in fractured fluid‐saturated porous rocks: a numerical modelling study

Contact Info

Product

Resources

About