Stress and frequency dependence of wave reflection and transmission in patchy-saturated porous media

Partially saturated porous media are frequently encountered in the subsurface. However, the wave reflection and transmission (R/T) characteristics of such media under in situ stress are not fully understood. To address this issue, we derive an exact R/T coefficient equation for an inhomogeneous plane wave incident obliquely at the interface between two dissimilar stressed patchy-saturated porous media, based on our new stress- and frequency-dependent rock physics model. The new model simultaneously incorporates the wave-induced fluid flow (WIFF) mechanisms at macroscopic, mesoscopic, and microscopic scales. Specifically, the nonlinear deformation of cracks is incorporated into the microscopic squirt-flow and mesoscopic patchy-saturated models to modify the solid frame and fluid moduli, while the poro-acoustoelasticity (PAE) theory is incorporated to account for macroscopic global flow and in situ stress effects. The modeling results indicate that P- and S-wave dispersion and attenuation decrease with increasing effective stress, but increase with rising water saturation. The opposite effects can be attributed to the closure of compliant cracks and the increased viscosity of the pore fluid, respectively. By comparing our model with published models and experimental data, we confirm its validity and reliability. Subsequently, the variations of the R/T coefficients with incident angle, effective stress, frequency, inhomogeneity angle, and water saturation are further analyzed. The findings demonstrate that the R/T coefficients exhibit significant dependence on effective stress and water saturation across the entire range of incidence angles, whereas the effect of inhomogeneity angle occurs primarily near the critical angle. With increasing effective stress, the critical angle grows, and at small incidence angles, fast P-wave reflection decreases while transmission increases, these effects diminishing at higher stress. The energy conservation at the interface further illustrates the validity of our R/T coefficient equation.