The radiation of a loop antenna embedded in a borehole with complicate
d geometry is analyzed by perturbation method and an efficient fast mu
ltiple-integration technique. The perturbation method is not used dire
ctly because there is a drill-stem whose conductivity and magnetic per
meability are very large in the borehole, The prolate ellipsoid equiva
lence of the metal drill-rod is made, then the drill-rod may be remove
d and the perturbation method is valid, Some numerical results indicat
e that the approach is efficient and stable at low frequencies.