波在双孔隙与单孔隙介质界面上的反射与透射

REFLECTION AND TRANSMISSION OF ELASTIC WAVES AT THE INTERFACE BETWEEN A FLUID-SATURATED POROUS SOLID AND A DOUBLE POROSITY SOLID

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质界面的反射和透射问题,在界面上假定裂缝孔隙流体相对于固体骨架的位移为零,推导了反射系数和透射系数的计算公式,数值讨论了反射系数和透射系数随入射角和频率的变化关系．同时,讨论了双重孔隙介质中3种压缩波 (P-1,P-2和P-3波)和一种剪切波(S波)的频散和衰减特性．

The reflection and transmission characteristics of an incident plane P-1 wave at an interface between a fluid-saturated double porosity medium and a fluid-saturated single porous solid are investigated. The fluid-saturated single porous solid is modeled with the classic Blot＇s theory and the double porosity medium is described by an extended Biot＇s theory. In double-porosity media with dual-permeability there exist three compressional waves and a shear wave. The variation of the phase velocity and attenuation of the four bulk waves in double porosity media with frequency is studied. It is shown that the peak values of attenuation curves of P-1 and S waves emerge at about 1 kHz, and the decay of P-2 and P-3 waves is more prominent than other bulk waves in double porosity media. Assuming no relative displacement between the fracture pore fluid and the matrix solid at the interface, the expressions of the reflection and transmission coefficients are obtained. The effects of incident angle and frequency on the amplitude ratios of reflected and transmitted waves are discussed. Numerical calculations show that the amplitudes of the reflected and transmitted P-1 waves reach the maximum values at a certain incident angle for a constant frequency, and reach the minimum and maximum values, respectively, for a constant incident angle. It is also found that the amplitudes of the reflected P-2, P-3 waves and transmitted P-2 wave are far less than those of the reflected and transmitted P-1, S waves.