Theoretical estimate of the tube-wave modulus in arbitrarily anisotropic media: Comparisons between semianalytical, FEM, and approximate solutions

Abstract

We revisit an exact, quasi-static, semianalytical solution for the effective tube-wave modulus for any borehole orientation relative to an anisotropic medium of arbitrary symmetry and strength. This exact solution agrees very well with the one computed from a finite-element model (FEM). We compare the exact solution with several analytical approximations for well deviations from vertical to horizontal and for different transversely isotropic media. For elliptic media, we show that the Rice and Chi-Tang approximations are in accordance with the exact solution because they depend only on the horizontal and vertical shear-wave velocity. For anelliptic media, we show that the maximum difference between the exact solution and the Norris-Sinha or Chi-Tang perturbation approximation becomes increasingly significant with increasing degree of anellipticity and shear-wave anisotropy with a maximum error of 5%, 10%, and 18% for Thomsen parameters less than 0.25, 0.4, and 0.6, respectively.