Reflection characteristics of plane-S-wave at the free boundary of unsaturated porothermoelastic media

Abstract

In the present work, the reflection of plane-S-wave at the free boundary of an unsaturated porothermoelastic medium is studied taking into consideration of the theory of porous media and the generalized thermoelasticity model. Based on the wave equations for an unsaturated porous medium considering thermo-fluid-solid coupling and the boundary conditions, the theoretical expressions of the reflection coefficient of five kinds of reflected waves at the free boundary of the unsaturated porothermoelastic medium, i.e., reflected P1 wave, reflected P2 wave, reflected P3 wave, reflected S wave and reflected thermal wave, are derived by using the classical Helmholtz potential function decomposition method. Then the numerical calculations are used to discuss the variation of the reflection coefficients of each reflected wave with the incident angle of plane-S-wave and the thermophysical parameters such as saturation, thermal expansion coefficient, thermal conductivity, medium temperature and phase-lag of heat flux and gradient of temperature. The results show that the reflection coefficient of each reflected wave is affected by not only the incident angle but also the saturation. The change of thermal expansion coefficient has a significant influence on the reflection coefficient of each reflected wave. The change of medium temperature only affects the reflection coefficient of the reflected P2 wave, reflected P3 wave and reflected thermal wave. The change of thermal conductivity, phase-lag of heat flux and phase-lag of gradient of temperature only has a large effect on the reflection coefficient of reflected thermal wave. These conclusions are helpful in the theoretical research and seismic exploration projects.