MoM analysis of dipole antennas in crosshole borehole radar and field experiments

Abstract—In this paper, we propose a method-of-moments (MoM) analysis that includes the borehole effects on crosshole borehole radar, and we verify that the MoM represents the crosshole borehole radar data correctly. We derive the far-field approximation of an electric field radiated by an electric point source. In this derivation, we assume that the point source is in a cylindrically layered medium, while the observed electric field is in another cylindrically layered medium. The equations that are derived are used as a transfer function to connect the two impedance matrices—one for the transmitting antenna and the other one for the receiving one. In these matrices, the influence of the scattered field by the borehole is included completely. We conducted field experiments in granite with a controlled borehole medium in order to investigate the influence of the borehole. In this paper, we estimated the relative amplitude and the group delay of the received signals between the water-filled borehole case and the air-filled borehole case. This paper showed that the estimated amplitude and delay depend on the frequency and that the proposed MoM could predict these frequency dependencies. Index Terms—Asymptotic expansion, borehole effects, borehole radar, crosshole, Green’s functions, method of moments (MoM). I