Stress-induced azimuthal anisotropy in borehole flexural waves

A nonlinear elastic model for acoustic waves in a stressed medium is used to calculate tectonic stress-induced changes in borehole flexural dispersions. Our theoretical analysis shows that a horizontal uniaxial stress in the formation causes a crossover in flexural dispersions for the radial polarization aligned parallel and normal to the stress direction. This crossover in flexural dispersions is caused by stress-induced radial heterogeneities in acoustic wave velocities that are different in the two principal stress directions. Other sources of borehole flexural anisotropy caused by finely layered dipping beds, aligned fractures, or microstructures found in shales, exhibit neither such radial heterogeneities nor flexural dispersion crossovers. Consequently, a crossover in flexural dispersion can be used as an indicator of stress-induced anistropy. In this situation, the fast shear polarization direction coincides with the far-field uniaxial stress direction. The analysis also yields an expression for the largest shear stress parameter in terms of the fast and slow seismic shear-wave velocities with shear polarization parallel and perpendicular to the far-field stress direction.