Analytical Perturbation Methods for Studying a Transversely Isotropic Medium in Multipole Acoustic Logging

摘要

A new analytical perturbation method is developed in this study to investigate the general reflection coefficients in the frequency-wavenumber domain of the acoustic field in a fluid-filled borehole surrounded by a transversely isotropic medium (TIM). The transversely isotropic medium with a symmetric axis parallel to the borehole axis, which is usually called a VTI medium, was adopted because its exact solutions exists, and a corresponding isotropic medium was adopted as a reference state of perturbation solution. The general reflection coefficients were originally calculated by using the perturbation method and were compared with the analytical solutions. The zero-, firstand second-order perturbation solutions for the general reflection coefficients excited by monopole, dipole and quadrupole sources were investigated for a transversely isotropic elastic solid. The results showed that the general reflection coefficients obtained by using the perturbation solutions and the analytical solutions were similar for all three sources. In summary, our study demonstrated that the perturbation method is valid and effective in acoustical logging. This work provided a theoretical foundation for extending perturbation analyses to complicated anisotropic acoustical logging applications.