Borehole flexural waves in the presence of uniaxial stresses

The presence of a horizontal uniaxial stress in the formation causes azimuthal anisotropy in the flexural wave propagation along a vertical borehole. Due to the effects of stress concentration around the borehole; the stress induced azimuthal anisotropy in formations is significantly different from the other sources of anisotropy, such as those associated with formations with finely layered dipping beds or aligned microstructures found in shales. The azimuthal flexural anisotropy refers to the differences in the velocity dispersions associated with the two principal radial polarizations. Theoretical predictions show that at low frequencies, the higher flexural wave velocity corresponds to the radial polarization aligned parallel to the far-field stress direction. On the other hand, at high frequencies the higher flexural wave velocity corresponds to the radial polarization aligned perpendicular to the far-field stress direction. This reversal in the relative magnitudes of the flexural wave velocities between low and high frequencies results in a crossover phenomenon in the two flexural wave velocity dispersions. Since this cross-over phenomenon is not predicted for formations with intrinsic anisotropy, it provides a technique for distinguishing stress induced anisotropy from the other sources. The low frequency asymptotes of the two flexural wave velocities (with radial polarizations parallel and perpendicular to the far-field stress direction) together with the formation mass density yield an estimate of the largest formation shear stress parameter from a derived expression