We explore the impact of roughness in crack walls on the P-wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P-wave modulus dispersion and attenuation: the arithmetic mean, minimum and hydraulic apertures. We show that the arithmetic mean of the crack apertures controls the effective P-wave modulus at the low- and high-frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process, and consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model and, in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in presence of contact areas, the hydraulic aperture tends to control de characteristic frequency. Analysing the local energy dissipation, we can more specifically visualise that a different aperture controls the energy dissipation process at each frequency, which means that a frequency-dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls.

Understanding the properties of cracked rocks is of great importance in scenarios involving CO 2 geological sequestration, nuclear waste disposal, geothermal energy , and hydrocarbon exploration and production. Developing noninvasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle-and frequency-dependent behavior for specific geometries, appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid-solid deformation at the pore scale based on coupled Lamé-Navier and Navier-Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle-and frequency-dependent behavior due to squirt flow between interconnected cracks. Furthermore, the overall anisotropy of a medium mainly increases due to squirt flow, but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface.