Anisotropy Inversion in the Frequency Domain for Flexural Waves With Unmatched Sources

Cross-dipole sonic logging is commonly used to obtain the azimuth anisotropy in the horizontal transverse isotropic formation. The current processing method proposed by Tang and Chunduru has been widely used for anisotropy inversion in the time domain. However, that method is based on the assumption that the fast and slow flexural waves are similar in shape and both are not dispersive; this assumption can be removed by processing in the frequency domain. Moreover, it is assumed that the two orthogonal dipole sources are identically the same, which is difficult for tool manufacturers to make the sources match. In this letter, we propose a new method for the anisotropy inversion to avoid these assumptions. Unlike the traditional method, where only the phase information of the flexural wave is used, both the phase and amplitude information are taken into the new objective function. The processing results of synthetic data sets and field data sets validate our method.