Reflection and transmission of elastic waves at the interface between a fluid-saturated porous solid and a double porosity solid

The reflection and transmission characteristics of an incidentplane P-1 wave at an interface between a fluid-saturated double porositymedium and a fluid-saturated single porous solid are investigated. Thefluid-saturated single porous solid is modeled with the classic Biot'stheory and the double porosity medium is described by an extended Biot'stheory. In double-porosity media with dual-permeability there exist threecompressional waves and a shear wave. The variation of the phase velocity andattenuation of the four bulk waves in double porosity media with frequencyis studied. It is shown that the peak values of attenuation curves of P-1and S waves emerge at about 1\,kHz, and the decay of P-2 and P-3 waves ismore prominent than other bulk waves in double porosity media. Assumingno relative displacement between the fracture pore fluid and the matrix solid at the interface, the expressions of the reflection andtransmission coefficients are obtained. The effects of incident angle andfrequency on the amplitude ratios of reflected and transmitted waves arediscussed. Numerical calculations show that the amplitudes of the reflectedand transmitted P-1 waves reach the maximum values at a certain incidentangle for a constant frequency, and reach the minimum and maximumvalues, respectively, for a constant incident angle. It is also found that theamplitudes of the reflected P-2, P-3 waves and transmitted P-2 wave are farless than those of the reflected and transmitted P-1, S waves.