Energy velocity and quality factor of plane harmonic inhomogeneous waves in anisotropic poro-viscoelastic media

Abstract

SUMMARY Energy flux vector and related wavefield quantities are studied for the propagation of harmonic plane waves in an anisotropic viscoelastic porous medium saturated with viscous fluid. In this dissipative medium, Biot's theory is used to define the propagation of four attenuating waves through different complex-valued slowness vectors. The attenuating waves are considered to be propagating as general inhomogeneous waves. The inhomogeneity strength of an attenuating wave is defined by a non-dimensional parameter. A fixed value of this inhomogeneity parameter is used to calculate the complex slowness vector of any attenuated wave in the medium for an arbitrarily chosen propagation direction. The complex slowness vector is then used to calculate the velocity and direction of energy flux for each of the four waves in the medium. Dissipation of energy is explained in terms of quality factors of attenuation such that the contributions from pore-fluid viscosity and anelastic porous-frame are separated. Deviations of the ray (or group velocity) direction from the propagation direction, the attenuation direction and the propagation–attenuation plane are also calculated. A numerical example is studied to analyse the variations in the energy-flux characteristics with propagation direction and inhomogeneity parameter.