Fracture Related Cross-Over Frequencies of Seismic Attenuation in Porous Rocks

It is well-known that in inhomogeneous porous media the effect of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection to this phenomenon we study the impact of permeability fluctuations on the dynamic behaviour of porous materials. Based on the method of statistical smoothing applied to Biot's equations of poroelasticity we derive a model for a dynamic-equivalent permeability in 1-D and 3-D randomly inhomogeneous media; the low-frequency limit of this permeability corresponds to the hydraulic permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation of P-waves also obtained by the method of smoothing. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. We confirm this through comparison with numerically modelled poroelastic multilayered media. We conclude that estimation of hydraulic permeability from seismic signatures like attenuation is only possible if permeability fluctuations are properly accounted for.