We compare two stress models, "subsidiary" and "borehole," as mechanisms responsible for, respectively, the sonic fast-shear azimuth (FSA) and breakout directions for arbitrary well orientations. We show that the sonic FSA coincides with the "maximum subsidiary principal stress" as the dipole shear is unaffected by borehole stress concentrations, and is, therefore, directly related to the relative deviatoric stress tensor described by the orientation of σh and ellipsoid factorR. In contrast, the breakout orientation, controlled by borehole stresses, occurs at a location where the compressive principal stress in the borehole tangential plane is maximum. We show that, to a first-order approximation, the breakout directions are also related to the orientation of σh and R as for normally pressured to slightly overpressured conditions, the breakout orientation is not very sensitive to the borehole mud pressure. Results indicate that, for arbitrary well orientations, sonic FSA and breakout direction are not necessarily at 90° of each other. This analysis implies that the sonic FSA, from stress-induced origin, is theoretically a better measurement to estimate the relative deviatoric stress tensor, and FSA observations from wells with at least two different orientations can be used to estimate the orientation of σh and R. To a first-order approximation, the same can be done using breakout orientations.
Knowledge of the stress field is important for all subsurface rock mechanics applications. Another common source of data is coming from dipole shear sonic anisotropy from a stress-induced origin. It has been frequently used to measure the direction of σH via the fast shear azimuth in vertical wells since the work of Esmersoy et al. [9,10]. The fast shear azimuth (FSA) is defined as the polarization direction of the fast dipole shear wave propagating along the borehole direction.