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Abstract
Using a set of surface integral equations together with the moment method, we develop a numerical algorithm so that one can calculate the response of the induction logging tool in an arbitrarily shaped borehole. The integral equations are derived whereby the small formation signal can be calculated in the presence of a large direct signal. The results of a circular borehole with an eccentered tool are presented and compared with the results from other approaches. The responses of a horizontal magnetic dipole in an elliptical invasion zone and an elliptical borehole are obtained. The results show that horizontal magnetic dipoles can be used to detect asymmetry in an invasion profile and a borehole.