Three-dimensional wave propagation in a general anisotropic poroelastic medium: phase velocity, group velocity and polarization

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This is an attempt to study 3-D wave propagation in a general anisotropic poroelastic medium. Biot's theory is used to derive a modified Christoffel equation for the propagation of plane harmonic waves in an anisotropic fluid-saturated porous solid. This equation is solved further to obtain a biquadratic equation, the roots of which represent the phase velocities of all the four quasi-waves that may propagate in such a medium. These phase velocities vary with the direction of phase propagation. Expressions are derived to calculate the group velocities of all the four quasi-waves without using numerical differentiation. The eigensystem of modified Christoffel equation is used to calculate the polarizations of all the quasi-waves. The particle motion of each wave is a function of the direction of phase propagation. Some fundamental differences between wave propagation in anisotropic poroelastic medium and anisotropic elastic medium are suggested, an interesting one is that in an anisotropic poroelastic medium, the polarizations of different quasi-waves need not be mutually orthogonal. In the anisotropic poroelastic medium, the motion of fluid particles deviates from solid particles and this deviation varies, also, with the matrix porosity. Propagation regimes for an isotropic medium, giving velocities and polarizations of both compressional and shear waves, are obtained as special cases. The variations of phase velocity, group velocity, ray direction with phase direction (in 3-D space), are plotted for a numerical model of general anisotropic poroelastic solid. The same numerical model is used to plot the deviations of polarizations from phase direction and ray direction. The deviations among the motion in fluid of the particles and solid parts of porous aggregate are also plotted.