Seismic attenuation and dispersion in poroelastic media with fractures of variable aperture distributions

Abstract

Abstract. Considering poroelastic media containing aligned periodic fractures, we numerically quantify the effects that fractures with variable aperture distributions have on seismic wave attenuation and velocity dispersion due to fluid pressure diffusion (FPD). To achieve this, realistic models of fractures are generated with a stratified percolation algorithm which provides statistical control over geometrical fracture properties such as density and distribution of contact areas. The results are sensitive to both geometrical properties, showing that an increase in the density of contact areas as well as a decrease in their correlation length, reduce the effective seismic attenuation and the corresponding velocity dispersion. Moreover, no FPD effects are observed in addition to the one occurring between the fractures and the background, in the analysed frequency range, by considering realistic fracture models. We demonstrated that if appropriate equivalent physical properties accounting for the effects of contact areas are employed, a simple planar fracture can be used to emulate the seismic response of fractures with realistic aperture distributions. The excellent agreement between their seismic responses is demonstrated for all incidence angles and wave modes.

Frequency‐Dependent P Wave Anisotropy Due to Wave‐Induced Fluid Flow and Elastic Scattering in a Fluid‐Saturated Porous Medium With Aligned Fractures

“…This may have some influence on the frequency‐dependent P wave anisotropy. However, a recent study of Lissa et al (2019) showed that the seismic response of fractures with realistic thickness (aperture) distributions (including multiple contacts) can be emulated by fractures of constant thickness with equivalent poroelastic infills accounting for effects of thickness variations. Such fractures with poroelastic infills can be approximated by void fractures with equivalent fracture compliances (Guo, Rubino, et al, 2018a, 2018b).…”

Fluid Pressure Diffusion in Fractured Media: The Role Played by the Geometry of Real Fractures

“…The seismic response of a fractured Berea sandstone is numerically modeled considering a poroelastic upscaling approach (Lissa et al., 2019; Masson & Pride, 2007; Quintal et al., 2011). For that, we solve the quasi‐static Biot's equations (Biot, 1941) in the frequency domain, which are where is the total stress tensor, w is the relative fluid displacement vector, p is the fluid pressure, is the angular frequency and i is the complex unity.…”

“…That is, a medium containing a periodic repetition in the vertical z ‐direction of semihorizontal fractures having infinite length in the x ‐direction and y ‐direction. In addition, the applied boundary conditions account for the strain and stress field interactions of consecutive fractures (Lissa et al., 2019; Milani et al., 2016). The mathematical description of the applied boundary conditions is given in Appendix A.…”

Squirt Flow in Cracks with Rough Walls

“…In order to study the role played by the roughness of the cracks on the squirt flow mechanism, the aperture distribution of the cracks has been generated following the approach introduced by Nolte and Pyrak‐Nolte (). The full workflow for the model generation is described by Lissa et al ().…”