Stoneley-wave speed modeling in general anisotropic formations

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.