Inhomogeneous Wave Propagation in Triple-Porosity Medium

The study aims to investigate the propagation of inhomogeneous waves in a material with triple porosity.

The mathematical equations describing the motion of harmonic plane waves in a material with triple porosity have been solved. The solution is derived as Christoffel equations. The propagation of plane harmonic waves may be explained through two equations, which are obtained by solving the Christoffel equations. One of them provides the velocity of longitudinal waves. The other provides a lone shear wave in triple-porosity medium. A general inhomogeneous propagation is considered through a particular specification of complex slowness vector for any of these five attenuated waves. The inhomogeneity of an attenuated wave is represented through a finite non-dimensional parameter. The specification of a wave's slowness vector is utilized to compute its phase velocity and attenuation for an arbitrary value of this inhomogeneity parameter.

The numerical example is considered to compute the propagation characteristics (velocity, attenuation) of each of the five inhomogeneous waves in the triple-porosity medium. The impact of various factors, such as hydrate gas saturation, wave-induced fluid flow, solid Poisson ratio, inhomogeneity parameter, frequency, porosity, critical porosity, depth, and coordination number is investigated on the phase velocities and attenuations of the five waves mentioned above.

The findings reveal that these waves' phase velocities and attenuation coefficients are more sensitive to gas hydrate saturation and frequency than other factors.