Reflection of inhomogeneous waves at the surface of a cracked porous solid with penny-shaped inclusions

Abstract

A mathematical model developed by Zhang et al. [Modeling wave propagation in cracked porous media with penny-shaped inclusions. Geophys. 2019;84(4):1–11. doi:10.1190/GEO2018-0487.1] for wave motion in a cracked porous solid with penny-shaped inclusions is solved for the propagation of harmonic plane waves. The solution is obtained in the form of Christoffel equations. The solution of Christoffel equations demonstrates the existence of four (three longitudinal and one transverse) waves in the cracked porous solid. The behavior of the considered medium is dissipative as both host medium and inclusions are filled with the same viscous fluid. So, all the waves are inhomogeneous in nature. A finite non-dimensional parameter is used to represent the inhomogeneity character of an inhomogeneous wave. The phenomenon of reflection is investigated in two situations (i.e. sealed and opened surface pores) at the stress-free plane surface of a cracked porous solid. Further, the partition of incident energy is calculated in the form of an energy matrix. A numerical example is taken to discuss the effects of various properties on the partition of incident energy. The conservation of incident energy at each angle of incidence is prevailed in both situations.