The control mechanism of P-wave attenuation in unconsolidated porous media

Unconsolidated porous media are distinct from consolidated porous rocks in the negligible bulk and shear moduli. This paper is motivated by resolving the control mechanism of P-wave attenuation in the media (represented by Toyoura sands and glass beads) saturated with water. The first model is Biot theory in which longitudinal friction (arising from velocity difference between the two phases) is quantified using dynamic permeability as a function of frequency. The first model simulates phase velocity (V-p) and the ultrasonically measured quality factor (Q(p)) well. A second model is the transverse squirt model in which squirt is induced by pressure differential between contact of grains (COG) and the main pore space. The second model outputs unrealistic V-p and Q(p). The results reveal that P-wave attenuation in unconsolidated porous media (saturated with water) is governed by longitudinal friction rather than intrapore squirt. Remarkably, low-frequency dynamic permeability is much smaller than Darcy permeability, indicating that ultrasonic P-wave is surprisingly capable of indirectly detecting the very narrow gap at COG.