Reflection and transmission of elastic waves at the interface between an elastic solid and a double porosity medium

In this paper, a theoretical analysis has been developed in detail to study the reflection and transmission of elastic waves at an interface between an elastic medium and a double porosity medium. The incident wave is chosen to be a plane harmonic compressional wave and the analytical expressions for the reflection and transmission coefficients have been derived for an impermeable boundary. Numerical calculations have been carried out to discuss the effect of incident angle, frequency, fracture permeability and porosity on the amplitude ratios for the reflected and transmitted waves. It is demonstrated that there are no critical angles for the four transmitted bulk waves in double porosity medium in our discussed cases. It is also shown that the reflection and transmission coefficients depend on the above four parameters greatly. Among the four transmitted waves in double porosity medium, P-1 wave exhibits the fastest phase velocity and P-3 wave exhibits the highest attenuation value. P-1 wave and transmitted S wave show the highest attenuation value at about 1 kHz. Generally the amplitude of P-3 wave is far less than that of the other bulk waves propagating in elastic medium and double porosity medium. © 2006 Elsevier Ltd. All rights reserved.