Response of a current loop antenna in an invaded borehole

Abstract

The problem of the radiation of a current loop antenna in a multicylindrical medium is formulated exactly in terms of an integral. The integrand is calculated using an iterative scheme making the integral more tenable to approximation. This closely approximates the response of a dielectric logging tool such as the deep propagation tool (DPT) or an induction tool in invaded boreholes. To gain more physical insight into the waves, an asymptotic approximation of the integral is derived. The large parameter for the validity of this approximation is the ratio of the transmitter‐receiver separation to the diameter of the invasion around the borehole. An iterative scheme is devised to compute systematically the approximation for an arbitrary number of cylindrical layers. The multicylindrical layer model is a good model of the invasion zone, borehole, and tool housing. The final approximation to the azimuthal electric field contains three terms. The first term resembles the response of a current loop in a homogeneous medium with electrical properties of the outermost medium or the formation. The higher order terms are improvements. The approximation is better at lower frequencies, implying that it is also good for the induction logging tool.