$\hbox{HE}_{11}$ Mode Effect on Direct Wave in Single-Hole Borehole Radar

In this paper, we investigate the influence of radar sonde eccentricity on a direct wave between a transmitting and a receiving antenna in a single-hole borehole radar measurement. We analyze the direct wave using an analytical method with the approximated solution of branch cut integrals and that of residues of poles. According to our calculation, at high frequencies above 200 MHz, guided waves, which are caused by the poles, play a vital role in the direct wave. We found that the most important pole is the HE11 mode one, which is excited only when the antenna is eccentered in the borehole. We show that this causes artificial noise in the moving average subtraction, which is a common signal processing method used to remove the direct wave. In a laboratory experiment with a ground plane, we confirmed the excitation of the guided waves when the antenna was eccentered. In field experiments in granite, we conducted a special experiment, in which the location and rotation of the radar sonde were controlled mechanically. We found the excitation of the HE11 mode at high frequencies when the sonde was noncentered by 1.7 cm in a borehole. These effects are also predicted in a theoretical analysis.