Abstract
For determining anisotropy using acoustic logging data, Stoneley waves are the only wave modes that are sensitive to formation properties transverse to the borehole axis. We derive Stoneley-wave speeds in deviated and horizontal wells penetrating anisotropic formations. We first apply the elastic theory of an anisotropic body to find the radial displacement of a borehole cross section under uniform pressure. We then derive the effective formation modulus based on quasistatic analysis. Finally, we derive a two-dimensional analytical solution for low-frequency Stoneley-wave speed in a horizontal well penetrating a transversely isotropic formation with a vertical symmetry axis. For deviated wells, we derive a 3D analytical solution that is also valid for general anisotropic formations. Our analytic solutions agree with the finite-difference modeling results and are particularly suited for strongly anisotropic formations. With increasing well deviation the sensitivity of Stoneley-wave speed to horizontal shear-wave velocity decreases and the sensitivity to vertical shear-wave velocity increases.
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