THE FIELDS FROM A FINITE ELECTRICAL DIPOLE - A NEW COMPUTATIONAL APPROACH

Controlled-source, frequency-domain, and time-domain electromagnetic m ethods require accurate, fast, and reliable methods of computing the e lectric and magnetic fields from the source configurations used. Excep t for small magnetic dipole sources, all electric and magnetic sources are composed of lengths of straight wire, which may be grounded. If t he source-receiver separation is large enough, the composite electrica l dipoles may be considered to be infinitely small, and in a 1-D earth model the fields are expressed as Hankel transforms of an input funct ion, which depends only on the model parameters. The Hankel transforms can be evaluated using the digital filter theory of fast Hankel trans forms. However, the approximation of the infinitely small dipole is no t always valid, and fields from a finite electrical dipole must be cal culated. Traditionally, this is done by numerical integration of the f ields from an infinitesimal dipole, thus increasing computation time c onsiderably. The fields from the finite electrical dipole are expresse d as Hankel transforms and as integrals of Hankel transforms. The theo ry of fast Hankel transforms is extended to include integrals of Hanke l transforms, and a method is devised for calculating the filter coeff icients. Unlike the fast Hankel transform, the computation involved in the integrated Hankel transforms is not a true convolution, and so a set of filter coefficients must be calculated for each source-receiver configuration. Furthermore, the method is extended to include the cal culation of potential differences where one more integration is involv ed, which is what is actually measured in the field. The computation o f filter coefficients is very fast, and for standard configurations, t he coefficients need be computed only once. The method is as fast, acc urate, and reliable as the fast Hankel transforms method, and is up to an order of magnitude faster than the usual numerical integration.