Abstract: Seismic waves exhibit strong attenuation and velocity dispersion when they propagate through porous rocks saturated with a fluid. The main cause of such energy dissipation is fluid flow in the pore space, known as squirt flow. A simple and accurate dual crack analytical model is established for the squirt flow caused by the fluid flow in the microcracks with different aspect ratios commonly found in rocks. The effective compliance matrix of the dry dual crack model is constructed using micromechanics. By analyzing the fluid pressure distribution in the dual crack, crack stiffness relaxation in the wet-skeleton dual crack model is calculated using a one-dimensional fluid pressure diffusion equation, with the diameter of the compliant crack serving as the characteristic length for squirt flow in the dual crack model. The attenuation and dispersion characteristics of the frequency-dependent stiffness component of the dual crack model and the torus stiff pore model are compared, and three-dimensional simulations validate the accuracy of the dual crack model. Parameter analysis shows that as the volume of the stiff crack increases, the attenuation of the stiffness component of the dual crack also increases. The application of the dual crack model in velocity prediction is introduced, and its reliability is validated by comparing it with experimental data and the predictions of the torus stiff pore model.

Key words: squirt flow model, dual crack model, stiff relaxation, dispersion and attenuation, pore structure, velocity prediction