Seismic wave attenuation in saturated porous media: A new fractal double-porosity perspective

Abstract

Summary The influence of rock microstructure makes quantifying seismic wave dispersion and attenuation in saturated rock a fundamental challenge. This challenge arises from the multiscale heterogeneity of the pore distribution and the consequent fluid distribution, which gives rise to multiscale fluid flow. To directly incorporate this dual multiscale heterogeneity into wave attenuation, a porosity fractal dimension is first introduced. This parameter provides the quantitative link between rock microstructure and mesoscopic fluid distribution. Integrating this with Biot-Rayleigh theory, a new fractal double-porosity wave equation is derived. While theoretical modeling identifies the pore fractal dimension as the most influential factor, experimental comparisons under controlled confining pressure and constant pore fractal dimension reveal that wave attenuation is instead dominated by the maximum heterogeneity radius, representing the largest mesoscopic fluid-saturated inclusion radius, and the elastic modulus. Crucially, while confining pressure may either increase or decrease the maximum heterogeneity radius, this radius maintains a consistent negative correlation with both the characteristic frequency and the peak attenuation, thereby inducing a positive correlation between them. Thus, peak attenuation and characteristic frequency, the two key characteristics of attenuation, are unified through their common dependence on the maximum heterogeneity radius.