THEORETICAL-STUDY OF PERTURBATION METHOD FOR ACOUSTIC MULTIPOLE LOGGING IN ANISOTROPIC FORMATION

A new and effective analytical perturbation method is presented for th e multipole acoustic logging in a transversely isotropic elastic solid whose symmetric principal axis is perpendicular to the borehole axis. The transversely isotropic elastic solid is regarded as a relevant is otropic elastic solid added to the perturbations, and three perturbati on quantities about moduli deviated from the isotropic medium are intr oduced. By selecting a group of displacement potentials and a cylindri cal coordinate system oriented along the borehole axis, the zero- and first-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has i ts symmetric principal axis perpendicular to the borehole axis. The ac oustic fields inside and outside the borehole excited by a multipole s ource are investigated. It is found that not only the nth multipole ac oustic field can be excited by an nth multipole source, but the multip ole fields whose orders are higher and lower than n also can be excite d by an nth multipole source. (C) 1996 Acoustical Society of America.