Research on dispersion and attenuation of P wave in periodic layered-model with patchy saturation

In this paper poroelasticity is used to study the P wave propagation in periodic layered-model with patchy saturation at mesoscopic scale. Compared with the White's method, the deduction by the proposed method is more rigorous from mathematical view, without the assumption that the fluid pressures are not equal at the boundaries of different mediums as White has done. The proposed method solves the poroelastic equations in more directly perceived way than Dutta's mathematic techniques to make the equations uncoupled for solutions. When a P wave passes through the periodic layered-model with patchy saturation, the results of dispersion and attenuation by the method in this paper are consistent with those by White. Because of its periodic structure the patchy model becomes a phononic crystal with several passbands and stopbands in high frequency band. So the velocity of the P wave won't increase monotonously while the frequency increases, and there are several peaks of attenuation. As for seismic band, the attenuation peak of the patchy model moves to the low frequency as the permeability decreases, in accordance with the factual observation, but contrary to the results by Biot s theory before. When the gas volume rises in the model, the value of the attenuation peak increases at first, then decreases, and the maximum of the attenuation appears when the fraction of gas is nearly 0.1. The numerical results are in line with those by the related experiments. Researches show that the periodic layered-model with patchy saturation can qualitatively account for the observed seismic attenuation.