Acoustic Logging Guided Waves In Transversely Isotropic Formations

摘要

We have studied the velocity dispersion of guided waves in transversely isotropic formations. Theoretical velocity dispersion curves were calculated with elastic constantsbased on laboratory and field measurements and compared to dispersion curves forisotropic formations having the same vertical po and S-wave velocities. The symmetryaxis for the transverse isotropy was parallel to the borehole. The differences betweenthe phase velocities for the transversely isotropic and isotropic formations depend onthe type of wave, its frequency, and the amount of anisotropy, and can be as high as7 to 10 percent.The changes in the phase velocity due to changes in the elastic constants of theformation (c[subscript 11], C[subscript 1]3, C[subscript 33], C[subscript 44], and C[subscript 66]) and the bulk modulus of the borehole fluid (⋋) vary with frequency. In a hard formation, the tube wave's velocity is sensitive to C[subscript 66] at low frequencies, to C[subscript 44] at high frequencies, and to ⋋ at all frequencies. The pseudo-Rayleigh wave is affected by C[subscript 44] near its cutoff frequency and by ⋋ at high frequencies. The flexural wave, which is generated by a shear wave logging tool, is similarly affected by C[subscript 44] at low frequencies and by ⋋ 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 C[subscript 66] and ⋋ at low frequencies, but the influence of C[subscript 44] is much greater at high frequencies.Since array processing methods can accurately estimate the velocity dispersion ofthe guided waves over a wide range of frequencies, some elastic constants can be estimated. In a hard formation, the refracted P- and S-wave velocities uniquely determineC[subscript 33] and C[subscript 44], and an inversion can be used to estimate C[subscript 66] and ⋋. In a moderately soft formation, the refracted P-wave velocity determines C[subscript 33], the flexural wave from the shear wave logging tool determines C[subscript 44], and the tube wave's velocity dispersion can beused to estimate C[subscript 66] and ⋋.