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 s h and ellipsoid factor R. 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 s h 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 sh 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. Stress field characterization involves the determination of three principal stress directions and magnitudes (s1, s2, s3; s1 > s2 > s3). The relative deviatoric stress tensor sd has the same principal directions as s and the same shape (or ellipsoid) factor R. In practice, the primary objective is to determine the principal stress directions, and the secondary objective is to determine full or partial measures of the magnitudes, that is, any of the possible R, s1, s2 and s3. R is an important quantity that may be estimated more directly than absolute stress magnitudes under certain conditions [1, 2, 3] and helps estimate the remaining stress magnitude (such as maximum horizontal stress sH) when the other two are known (in our example, vertical and minimum horizontal stresses, respectively sV and sh). In this paper, we assume that the vertical direction is a principal stress direction (i.e. sV is a principal stress). One common source of data for stress determination is coming from the analysis of borehole breakouts that are observed on image logs and depend on stresses around the borehole, borehole mud pressure, and rock strength properties. Breakout directions are mostly controlled by the relative deviatoric stress tensor sd for arbitrary well orientations  and, to a first order, do not depend on failure properties and absolute magnitudes of in-situ stress (assuming linear elasticity and instantaneous failure). 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 sH via the fast shear azimuth in vertical wells since the work of Esmersoy et al. [9, 10].