Effects of background elastic and permeability anisotropy on dynamic seismic signatures of a fluid-saturated porous rock with aligned fractures

Seismic dispersion, attenuation, and frequency-dependent anisotropy due to wave-induced fluid flow in fluid-saturated porous and fractured rocks have been widely studied. However, most of these studies do not consider the effects of background elastic and permeability anisotropy. In this work, we study such effects by considering a fluid-saturated porous rock with penny-shaped fractures embedded in the isotropic plane of a transversely isotropic (TI) background. Starting with P waves propagating perpendicularly to the fracture plane, we obtain the wavefields in the fluid-saturated porous TI background scattered from a single fracture. This allows for the calculation of the effective P wavenumber through the Foldy approximation and the derivation of a frequency-dependent fracture compliance matrix. The angle-dependent seismic dispersion and attenuation, as well as frequency-dependent anisotropy, can thus be calculated. Using this model, we study a fractured tight sandstone with a TI background. The results indicate that the background elastic anisotropy primarily affects the seismic frequency-dependent anisotropy, whereas the background permeability anisotropy not only affects seismic frequency-dependent anisotropy but also influences seismic dispersion and attenuation. In particular, the background permeability anisotropy alters the rate of change in seismic velocities and velocity anisotropy parameters with frequencies and the peaks of seismic attenuation and attenuation anisotropy parameters. By comparing the theoretical predictions of our model with other theories and with two sets of experimental data, our model is validated. Our model can be applied to characterize the fractured layered earth.