Acoustic wave propagation in a fluid‐filled borehole surrounded by a formation with stress‐relief‐induced anisotropy

The stress relief associated with the drilling of a borehole may lead to an anisotropic formation in the vicinity of the borehole, where the properties in the radial direction differ from those in the axial and tangential directions. Thus, axial and radial compressional acoustic velocities are different, and similarly, the velocity of an axial shear‐wave depends on whether the polarization is radial or tangential. A model was developed to describe acoustic wave propagation in a borehole surrounded by a formation with stress‐relief‐induced radial transverse isotropy (RTI). Acoustic full waveforms due to a monopole source are computed using the real‐axis integration method, and dispersion relations are found by tracing poles in the [Formula: see text] plane. An analytic expression for the low‐frequency Stoneley wave is developed. The numerical results confirm the expectations that the compressional refraction is mainly given by the axial compressional velocity, while the shear refraction arrival is due to the shear wave with radial polarization. As a result, acoustic logging in an RTI formation, will indicate a higher [Formula: see text] ratio than that existing in the virgin formation. It also follows that the shear velocity may be a better indicator of a mechanically damaged zone near the borehole than the compressional velocity. The Stoneley‐wave velocity was found to decrease with the increasing degree of RTI.