Wave dispersion and attenuation in fractured rocks: a spherical squirt model with the Biot effect

Abstract Wave-induced fluid flow plays a dominant role in the attenuation and velocity dispersion of seismic waves in porous media, especially through mechanisms such as squirt flow at a microscopic level. This study delves into the fluid squirt mechanisms at the pore-to-fracture scale, with a specific focus on spherical squirt flow across both rigid intergranular pores and deformable fractures. By establishing dynamic equations for rocks with compliant porosity under fluid pressure excitation, we develop an enhanced spherical squirt flow model that incorporates the Biot effect. This model builds upon the macroscopic Biot flow theory and the spherical squirt flow model, without relying on assumptions about porous space geometries (e.g. elliptical cracks) and unknown parameters (e.g. aspect ratio). The proposed model corrects the low-frequency velocity limitations of the spherical squirt flow model to align with Gassmann’s equation. Through numerical examples, we examine the effect of various parameters on wave propagation. Moreover, we demonstrate a practical application of the model using Guang’an sandstones. Simulation results show that the present model effectively captures the seismic wave dispersion and attenuation observed in experiments. In summary, the present model offers a rational explanation for wave-induced fluid flow mechanisms, enabling accurate prediction of seismic wave dispersion and dissipation caused by both squirt flow and macroscopic fluid flow.