Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dual-permeability material. The incidence of two main waves (i.e., P₁ and SV) is considered. As a result of the incident waves, four reflected (three longitudinal and one shear) waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the 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 the reflection process, conservation of incident energy is obtained at each angle of incidence.