Effects of anisotropy upon the normal modes in a borehole

Elastic anisotropy affects the modes generated during acoustic logging. To study these effects, the wave equation was solved using a variational method for a model consisting of a fluid-filled borehole through a solid whose anisotropy is defined in the Cartesian coordinate system. The solution for each normal mode includes its phase velocity, group velocity, pressures in the fluid, and displacements in the solid. The most significant findings are: (1) two quasiflexural waves exist and have different phase and group velocities; (2) for the slow quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the slow, planar qS wave whose wave-number vector is parallel to the borehole; and (3) for the fast quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the fast, planar qS wave whose wave-number vector is parallel to the borehole.