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

Abstract

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.

Effects of Coupling Between Wave‐Induced Fluid Flow and Elastic Scattering on P‐Wave Dispersion and Attenuation in Rocks With Aligned Fractures

“…Note that apart from FB‐WIFF, the fluid pressure gradient between the peak and trough of the incident P wave will also result in the fluid flow, which is known as the Biot macroscopic fluid flow. Since this fluid flow often occurs at very high frequencies and its effects are usually much smaller than FB‐WIFF and elastic scattering (e.g., Caspari et al, ), we ignore the effects of this fluid flow in this work. This means that all of the derivations are carried out under the assumption that the frequency is small compared with Biot's crossover frequency: where ω B = ϕb /( τρ f ) is called the Biot's crossover frequency, with τ being the tortuosity of the background pores and the other parameters defined in Appendix A.…”

“…On the numerical aspect, Gurevich et al (1997) investigated the influence of the coupling between fluid flow and elastic scattering on attenuation numerically and proposed that such combined effects can be estimated by superposing their separate effects. Recently, Caspari et al (2019) employed the low-frequency Biot dynamic equations to study the interplay between FB-WIFF and elastic scattering through the finite difference approach. On the theoretical aspect, Gurevich et al (1998) studied the scattering of a P wave in a poroelastic medium by an ellipsoidal inclusion.…”

Azimuth-, angle- and frequency-dependent seismic velocities of cracked rocks due to squirt flow

“…One can define fractures as discontinuities at the mesoscopic scale and cracks as discontinuities at the pore scale. There are several analytical and numerical studies on the effect of wave-induced fluid flow between mesoscopic fractures and a porous rock background and between interconnected fractures using Biot's equations (Brajanovski et al, 2005;Rubino et al, 2013;Quintal et al, 2014;Masson and Pride, 2014;Grab et al, 2017;Hunziker et al, 2018;Caspari et al, 2019) as well as on the comparison between the numerical and analytical results (Guo et al, 2017(Guo et al, , 2018. Experimental studies of synthetic rock samples showed the impact of fluid-saturated fractures on seismic velocities (Amalokwu et al, 2016;Tillotson et al, 2012Tillotson et al, , 2014.…”

Supplementary material to "Seismic attenuation and dispersion in poroelastic media with fractures of variable aperture distributions"

“…Several authors have studied fracture-related FPD effects on seismic attenuation and velocity dispersion (Chapman, 2003;Brajanovski et al, 2005;Carcione et al, 2013;Rubino et al, 2013;Quintal et al, 2014;Caspari et al, 2016Caspari et al, , 2019, as well as on the effective anisotropy (Maultzsch et al, 2003;Masson and Pride, 2014;Tillotson et al, 2014;Amalokwu et al, 2015;Rubino et al, 2016Rubino et al, , 2017 and scattering (Nakagawa and Barbosa et al, 2016;Caspari et al, 2019), based on experimental or theoretical works. A common approach to study seismic attenuation and velocity dispersion in fluid-saturated fractured media consists of numerically solving Biot's (Biot, 1941(Biot, , 1962 poroelasticity equations (Masson and Pride, 2007;Quintal et al, 2011Quintal et al, , 2014Rubino et al, 2013).…”