This study solves the mathematical model for the propagation of harmonic plane waves in a
dissipative double porosity solid saturated by a viscous fluid. The existence of three dilatational
waves is explained through three scalar potentials satisfying wave equations. Velocities of these
waves are obtained from the roots of a cubic equation. Lone shear wave is identified through a
vector potential satisfying a wave equation. The displacements of solid particles are expressed
through these four potentials. The displacements of fluid particles in pores and fractures can
also be expressed in terms of these potentials. A numerical example is solved to calculate the
complex velocities of four waves in a dissipative double porosity solid. Each of the complex
velocities is resolved to define the phase velocity and quality factor of attenuation for the corresponding
wave. Effects of medium properties and wave frequency are analyzed numerically
on the propagation characteristics of four attenuated waves. It seems that P1 and S waves
are not very sensitive to the pore/fluids characteristics, except the fracture porosity. Hence,
the recovery and analysis of slower (P2, P3) waves become more desired to understand the
fluid-rock dynamism in crustal rocks.
Snell's law of elastic waves propagation on moving property interface of time-varying materials
