Flexural dispersion curves of acoustoelastic borehole waves by the perturbation method in a triaxially stressed transversely isotropic formation with vertical symmetry

Abstract Cross-dipole acoustic logging is widely used to determine the maximum horizontal stress azimuth and stress imbalance in vertical boreholes within isotropic formations. However, theoretical analysis of dipole flexural dispersion under imbalanced stresses in transversely isotropic formations with a vertical symmetry axis (VTI) remains limited. This study integrates borehole stress effects into an acoustoelastic model, deriving flexural dispersion curves via the perturbation method (PM). We identify four distinct dispersion signatures related to the fast and slow dispersion curves. Analysis of 33 rock samples from cited references reveals that flexural dispersion crossovers reliably indicate stress imbalance in isotropic formations for most rock samples. Furthermore, alignment between the fast shear-wave azimuth and the maximum horizontal stress azimuth is consistent for most rock samples. Given that radial variations in axial-shear velocities are related to flexural dispersion curves, we find that the elastic constants (c11, c44, c66, c144, and c155) critically influence these four types. We demonstrate that for intersecting flexural dispersion curves, the fast and slow dispersion curves typically exhibit a single crossover at sonic frequencies. Synthetic examples confirm that the PM results are consistent with finite-difference time-domain (FDTD) simulations. Consequently, we propose a classification method utilizing c11, c44, c66, c144, and c155