Detection of a buried wire with two resistively loaded wire antennas

The use of two identical straight thin-wire antennas for the detection of a buried wire is analyzed with the aid of numerical calculations. The buried wire is located below an interface between two homogeneous half-spaces. The detection setup, which is formed by a transmitting and a receiving wire, is located above the interface. The transmitter is excited by a pulsed voltage in a small gap. A resistance profile according to Wu and King [1965] has been used to suppress the reflections at the end of the wires. This enhances the visibility of properties of the lower half-space directly from the time response of the current along the receiving antenna. The problem is solved in several steps. First, the electric field integral equation for the total current along a single thin-wire antenna in a homogeneous space is formulated. The result is then used to construct a set of coupled integral equations to describe the currents along all three wires without the resistive load. The integral equations contain the transmitted and reflected fields due to the interface. Next, the set of integral equations is adapted for the resistance profile along the wires of the detection setup. The reflected and transmitted fields in both half-spaces are treated as secondary incident fields in the integral equation for the currents along the wires. In these equations, the response from a pulsed dipole source in the same configuration occurs as a Green's function. The inverse spatial Fourier transformation that occurs in the transmitted and reflected fields is carried out with the aid of a frequency independent, composite Gaussian quadrature rule. The set of coupled integral equations is solved by using the continuous-time discretized-space approach, where the space discretization is kept fixed for all frequencies. This results in a linear system of equations with a fixed dimension which is solved by the conjugate gradient-fast Fourier transform (CG-FFT) method. With the aid of a marching-on-in-frequency scheme, the system is solved for a number of frequencies. Time domain results are obtained by applying an inverse Fourier transformation. Representative numerical results are presented and discussed