Seismic wave propagation in partially saturated fractal porous media

ABSTRACT Wave-induced fluid flow, widely accepted as a dominant loss mechanism of wave attenuation, can lead to significant seismic attenuation due to mesoscopic heterogeneities such as partial saturation. However, dependence of fluid distribution on microstructure in partially saturated porous media remains unclear. To quantify the relationship between microstructure and fluid distribution, a saturation fractal dimension is applied on the assumption of pore fractal distribution and gas patch fractal distribution. By integrating the Biot-Rayleigh theory, a theoretical model of partially saturated fractal porous media is established. The results indicate that the scales of fluid flow and the magnitude of peak attenuation are significantly influenced by the maximum gas patch size and the pore fractal dimension. Our model is further validated by comparing it with laboratory measurements. The findings indicate that the variations in the maximum gas patch size correspond to the variations in fluid distribution, and the peak attenuation will reach its maximum magnitude when the saturation fractal dimension equals the pore fractal dimension. The discrepancies between the measurements and modeling results are discussed, revealing that, in addition to microstructure, factors such as rock properties, boundary conditions, and saturation methods significantly influence the fluid distribution, as well as velocity dispersion and attenuation. Our theory provides a reasonable explanation of dispersion and attenuation in fieldwork, thereby presenting a novel perspective for future endeavors in forward modeling and seismic inversion.