Dispersive Propagation of Surface Waves in Patchy Saturated Porous Media

Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low frequency range (0.1 Hz - 1000 Hz). Different patchy saturation models, which the mesoscopic loss mechanism for the interaction of the multiple fluids and solid phases in porous media is considered, are investigated. These models were previously proposed and verified by the compressional wave propagation experiments. In the present work, these formulations are extended to account for the wave propagation along a free surface. The dependence of the frequency-dependent velocity and attenuation coefficient of the surface wave mode on the gas friction is studied. The results show a significant dependence of the velocities and attenuation of the Rayleigh surface wave on the gas friction. More observable correlation of the velocity and attenuation dispersion of the Rayleigh wave mode to the fast compressional wave, but not the shear wave is present at low frequencies. Especially, the significant strong attenuation is observed, and the maximum values of the attenuation coefficient 1/Q for the Rayleigh wave are obtained in the 1-200 Hz range of frequencies, similar to the fast compressional wave. The frequency-dependent attenuation value and the characteristic frequency of this maximum depend on the gas friction. These frequency-response effects present distinctively in the surface-wave dynamical responses in the time domain.