Attenuation and dispersion of predicted seismic waves in the simplified poroelastic theory

The simplified macro-equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. These assumptions may be reasonable in media with lower porosities and lower permeabilities, i.e. tight oil/gas reservoir. The macro-equations predict two types of compressional waves and two types of shear waves. The expressions of analytical velocity dispersion and attenuation for the predicted waves are derived using plane wave theory. The first types of P and S waves propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types are distinctly dispersive and strongly attenuative thus they behave as diffusive modes. The effects of permeability on the velocity dispersion and attenuation are further studied in brine-saturated shale. The results show that the permeability has a significant impact on the velocity dispersion of P waves but has little effect on the S waves. Moreover, the attenuation for the P and S waves are sensitive to the permeability at lower frequencies, and higher permeabilities make the peaks of attenuation shift to lower frequencies. The second types of waves behave stronger attenuation at lower permeability. This study may have potential applications to seismic interpretation and inversion in tight oil/gas reservoir.