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.
