Abstract
Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and double-porosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves (i.e., incident and reflected) in an elastic medium are considered as homogeneous (i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous (i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.
Highlights
The process of reflection/refraction is of great importance in various scientific fields, such as hydrogeology, engineering geology, seismology and petroleum geophysics
The mathematical model developed by Berryman and Wang (1995, 2000), Pride and Berryman (2003a, b) and Pride et al (2004) is employed to study the wave propagation in DP2 media
The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure
Summary
The process of reflection/refraction is of great importance (practically as well as theoretically) in various scientific fields, such as hydrogeology, engineering geology, seismology and petroleum geophysics. Sharma (2017a) studied the effects of wave frequency, wave inhomogeneity, pore-fluid viscosity and skeletal permeability on the propagation and attenuation of waves in double-porosity dual-permeability (DP2) materials. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in the pore fluid. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure It has been confirmed from the numerical interpretation that during reflection/refraction processes, conservation of incident energy is obtained at each angle of incidence.
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