Potential function for Acoustic Multipole Logging on guided waves in Transversely Isotropic Medium

摘要

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.