Frequency-dependent velocities and attenuations in fluid-saturated rocks: Fractures aligned in isotropic medium with random pore shape

The modeling of seismic wave velocity and attenuation is crucial for the interpretation of seismic data. In fluid-saturated rocks, the presence of fractures causes dispersion and attenuation of seismic waves due to fluid flow between cracks and pores. Meanwhile, the parallel distribution of cracks is an important reason for the anisotropy of rocks. Combined with poroelasticity theory, we extend Chapman’s model to media with penny-shaped fractures and an isotropic porous matrix, for which no restrictions are placed on the pore shape of the matrix. We conduct simulations at different frequencies to indicate the predicted anisotropy of velocity and attenuation. The variation of velocities and attenuations with orientation angle is consistent with Chapman’s model. Because a typical porous matrix is used in the new model, predicted velocities are lower than those under assumption of spherical matrix pores. Then, we analyze the effect of pore compressibility of the matrix on the velocity and attenuation. We also conduct discussions about the effect of different porosities on velocity and attenuation. The analysis indicates that the predictions of the new model are more closely related to the modulus of the porous matrix than Chapman’s model. The strength of fluid flow in the new model also will change with the matrix pores. The comparison of the new model and Chapman’s model with experimental data indicates that the new model is in better agreement with the experimental results.