Radar signature of a 2.5-D tunnel

Abstract

The effects of an infinitely long cylindrical void on short‐pulse cross‐borehole radar waveforms are modeled and analyzed. Pulsed electromagnetic sensing system (PEMSS) data are of particular interest. The PEMSS system developed by the Southwest Research Institute uses a vertically oriented electric dipole that emits a short electromagnetic pulse with peak power output centered around 30 MHz, which gives wavelengths of roughly 1.5 cavity diameters. The transmitter and receiver are typically located in boreholes separated by approximately 30 m. The model is based on field solutions for a vertically oriented point‐source electric dipole. A three‐dimensional (3-D) analytical frequency domain derivation of the Green’s function is found using a spatial Fourier transform over the cylinder axis. The resulting wavenumber integral is evaluated by a numerical integration over wavenumber. Time‐domain waveforms are produced by applying a Fourier transform to a 7-80 MHz band of frequencies in the Green’s function spectrum. Model results agree well with PEMSS field data sets. Further modeling examines the effects on waveforms for a wide variety of cases in which the raypath is not orthogonal to the tunnel axis, including the effect of tunnel dip. An air‐filled tunnel with a radius greater than 1.0 m produces a low amplitude shadow zone along its entire length. A low amplitude early arrival is observed in simulations with air‐filled tunnels in which the source to receiver path forms an acute angle larger than 45 degrees with the tunnel axis. This arrival is interpreted as propagation through the tunnel. When this angle is smaller than 45 degree the tunnel is effectively an opaque object and only the energy diffracted around the cylindrical void is observed. Waveform behavior gradually transitions from propagation through the tunnel in the vicinity of 45 degrees.