Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

Abstract

A mathematical model for mechanical and electrical dynamics in an anisotropic piezo-poroelastic (hereafter referred to as APP) medium is solved for three-dimensional propagation of harmonic plane waves. A system of modified Christoffel equations is derived to explain the existence and propagation of four waves in the medium of arbitrary anisotropy. This system is solved to calculate the phase velocities of four waves in an unbounded APP medium. Directional derivatives of phase velocity are derived analytically and are used to calculate the components of the ray velocity vector. A hypothetical numerical model is considered to compute the phase velocity for given (arbitrary) phase direction and then the ray velocity vector. Surfaces are plotted for the phase velocity and ray velocity of each wave in a saturated poroelastic medium in the absence/presence of piezoelectricity. The contributions of the piezoelectric activeness of the solid frame and pore-fluid to the phase and ray velocities are identified and analysed for each of the four waves in the medium.