Hole geometry and anisotropic effects on tube-wave propagation: a quasi-static study

Tube-wave characteristics, namely velocity and polarization, are affected by borehole anomalies related to nonhydrostatic tectonic stress. The anomalies we consider are borehole ellipticity, azimuthal anisotropy as modeled by a rotated transversely isotropic medium, and borehole breakouts as modeled by local heterogeneities in elastic properties. The low-frequency tube-wave velocity is obtained by a variational approach to a plane-strain, static-equilibrium problem. We solve the problem with hole ellipticity analytically and the problem with azimuthal anisotropy numerically by a finite-element method. The results show that weak ellipticity has a negligible effect on the tube-wave velocity: a relative variation of 10 percent in the main diameters of the hole produces a perturbation of only 0.5 percent in the velocity. However, localized damage to the hole can reduce tubewave velocity significantly. -from Authors