Dynamic permeability of porous rocks and its seismic signatures

In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot's equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for