Acoustic Logging Guided Waves in Transversely Isotropic Formations

We have studied the velocity dispersion of guided waves in transversely isotropic formations. Theoretical velocity dispersion curves were calculated with elastic constants based on laboratory and field measurements and compared to dispersion curves for isotropic formations having the same vertical po and S-wave velocities. The symmetry axis for the transverse isotropy was parallel to the borehole. The differences between the phase velocities for the transversely isotropic and isotropic formations depend on the type of wave, its frequency, and the amount of anisotropy, and can be as high as 7 to 10 percent. The changes in the phase velocity due to changes in the elastic constants of the formation (cn, C13, C33, C44, and C66) and the bulk modulus of the borehole fluid (A) vary with frequency. In a hard formation, the tube wave's velocity is sensitive to C66 at low frequencies, to C44 at high frequencies, and to A at all frequencies. The pseudoRayleigh wave is affected by C44 near its cutoff frequency and by A at high frequencies. The flexural wave, which is generated by a shear wave logging tool, is similarly affected by C44 at low frequencies and by A at high frequencies. As the formation becomes soft, the effect of the elastic constants upon the phase velocity gradually changes. Like a hard formation, the tube wave's velocities in a moderately soft formation are primarily affected by C66 and A at low frequencies, but the influence of C44 is much greater at high frequencies. Since array processing methods can accurately estimate the velocity dispersion of the guided waves over a wide range of frequencies, some elastic constants can be estimated. In a hard formation, the refracted Pand S-wave velocities uniquely determine C33 and C44, and an inversion can be used to estimate C66 and A. In a moderately soft formation, the refracted P-wave velocity determines C33, the flexural wave from the 1 Now at Etudes et Productions Schlumberger, 26 Rue de la Cavee, 92142 Clamart, France