P- and SV-wave dispersion and attenuation in saturated microcracked porous rock with aligned penny-shaped fractures

Abstract

P- and SV-wave dispersion and attenuation have been extensively investigated in saturated poroelastic media with aligned fractures. However, there are few existing models that incorporate the multiple wave attenuation mechanisms from the microscopic scale to the macroscopic scale. Hence, in this work, we developed a unified model to incorporate the wave attenuation mechanisms at different scales, which includes the microscopic squirt flow between the microcracks and pores, the mesoscopic wave-induced fluid flow between fractures and background (FB-WIFF), and the macroscopic Biot's global flow and elastic scattering (ES) from the fractures. Using Tang's modified Biot's theory and the mixed-boundary conditions, we derived the exact frequency-dependent solutions of the scattering problem for a single penny-shaped fracture with oblique incident P- and SV- waves. We then developed theoretical models for a set of aligned fractures and randomly oriented fractures using the Foldy approximation. The results indicated that microcrack squirt flow considerably influences the dispersion and attenuation of P- and SV-wave velocities. The coupling effects of microcrack squirt flow with the FB-WIFF and ES of fractures cause much higher velocity dispersion and attenuation for P waves than for SV waves. Randomly oriented fractures substantially reduce the attenuation caused by the FB-WIFF and ES, particularly for the ES attenuation of SV waves. Through a comparison with existing models in the limiting cases and previous experimental measurements, we validated our model.