Borehole flexural modes in transversely isotropic formations: Low-frequency asymptotic velocity

Dipole acoustic logging is widely used for in situ measurement of formation shear velocity. This technique is based on the theoretical result in isotropic formations that the velocity of the dispersive flexural mode approaches the shear velocity at the low-frequency limit. Transversely isotropic (TI) formations frequently are encountered in petroleum engineering, so it is necessary to determine if shear velocity along the borehole can be determined from the low-frequency flexural wave in TI cases. The flexural wave in a borehole parallel to the symmetry axis of a TI formation is investigated. The borehole acoustic field is formulated in the frequency-wavenumber domain as the sum of a direct field from the source and a reflected field from the borehole wall. Poles and branch points of the reflection coefficient are analyzed, and component waves contributed by those singularities are calculated. The dispersion feature of the flexural mode in some TI formations differs from isotropic cases. The low-frequency limit of flexural-mode velocity trends to a value lower than the shear velocity when parameters of the formation satisfy delta>epsilon+c(44)/(2c(33)), where delta and epsilon are Thomsen parameters and c(33) and c(44) are the elastic moduli. That asymptotic value corresponds to a newly found branch point of the reflection function. Numerical results show that the low-frequency flexural wave travels slower than the shear wave in the synthetic full waveforms in Mesaverde clayshale 5501. Extracting the shear velocity from the flexural arrival leads to inaccuracy on the order of 10% in this formation.