Improvised Explosive Devices or IEDs are responsible for many casualties in asymmetric warfare. A variety of methods can be used to counter their use. These include the use of special protective vehicles, such as the Husky Mine-Resistant Ambush Protected (MRAP) vehicle shown alongside. In this version an interrogation arm is attached and this arm can carry sensors and a digger to disrupt the ordnance at a reasonably safe stand-off distance. MRAPS are designed to deflect the blast from a mine or IED and to absorb damage in a way that can be repaired quickly and inexpensively. The Husky is manufactured by Critical Solutions International. As vehicles become more sophisticated, terrorists develop larger and more effective bombs including those with penetrating shaped charges. Therefore the continuing development of vehicles and sensors to detect mines and IEDs is mandatory.
The IED is the principal tool of the Taliban in Afghanistan. Therefore their detection is very important. In principle the IED itself can be detected by the emission of vapors or, if it contains metal, it may be possible to detect it electromagnetically. To reduce the likelihood of personnel losses, the Taliban would prefer to detonate the IED remotely by radio, for example, by cellular telephone. However, these signals can be jammed to neutralize the threat. Therefore detonation is often by command wire. The IED is connected to a battery using a pair of wires running over a sufficient distance from the IED to minimize risk to the triggerman.
The detection of command wires themselves is an alternative to the detection of the IED. Furthermore command wires constructed of conducting material, usually copper, offer the possibility of electronic detection. There are two main ways of proceeding. Firstly the wire can be excited using a signal generated locally and secondly signals generated remotely can be employed. In the former case the configuration resembles a metal detector in which the source and the receiver are located close together. In the latter case, the signal is generated some distance away. The exciting signal can be transmitted specifically for the detection process or signals of opportunity can be used. In the latter case, these signals might be broadcast by commercial transmitters in the medium frequency band.
Excitation can employ continuous waves or the transmission of short pulses to produce a train of damped harmonic signatures at natural frequencies of oscillation. This resembles a process used in Ground Penetrating Radar (GPR) that is used to classify mines and other ordnance directly. However, in the application to command wires much lower frequencies can be used and the signals are not so strongly absorbed by lossy soils. This renders the method of Complex Natural Resonances (CNRs) quite promising.
While it is possible to design a detection system on a purely empirical basis, reliable estimates of the Electro-Magnetic (EM) fields from excited wires are very desirable. Unfortunately the theory of EM fields from cylindrical conductors located close to or just under conducting ground is quite complicated. Though the basic approach is reasonably straightforward, in that the fields can be expressed as integrals, it is often difficult to evaluate these integrals to obtain useful engineering results in analytic form. The problem is exascerbated by the number of separate cases that must be handled and by the necessity of using saddle point methods, which often leads to functions with complex arguments. These functions may be unfamiliar and in turn require some effort to evaluate.
The presence of the ground can be represented as a conducting half space. The wire acts like an antenna and its properties as a receiver are affected by it. This is a classical problem first addressed by Sommerfeld who showed that propagating radio waves induce currents that are associated with surface waves and extend the range of broadcast stations. Broadcast stations typically transmit vertically polarized waves but the surface waves have a longitudinal component (due to the induced ground currents) that permit a horizontal wire to receive them; the wires act like a Beverage antenna. The excited wire scatters the signal in the presence of the ground, which influences the scattering.
Practical estimates of the signals from broadcast transmitters can be found in the International Telecommunications Union (ITU) documentation. If the propagation constant and the characteristic impedance of the wire can be estimated, this often permits the current in the wire to be estimated. The scattered fields can then be estimated.
Because the ground is conducting and significant currents are induced, the fields in the ground fall off rapidly with distance from the wire. This is the skin effect and at medium frequencies the skin depth is typically some tens of metres. For long horizontal wires this implies that the ground acts as a return conductor.
The theory has been developed by a number of authors. Researchers such as Sommerfeld and Banos described the basic concepts in their books and, more recently much progress has been made by the two groups headed by James Wait and Ronold King. These workers have also published books on the subject. However, some of the basic conceptual details can only be found in the early work. This is summarized in J.K.E. Tunaley, "A Summary of EM Theory for Dipole Fields near a Conducting Half-Space", January 2012.
Simulation code has been developed to estimate the fields near a buried conducting wire as a result of continuous wave excitation. It is assumed that the wire comprises straight sections and the exciting field induces currents in these sections that re-radiate a signal that can be detected. This code is based on a transmission line model and it is assumed that the parameters lie within practical ranges. One key ingredient in the code is the estimation of the wire propagation constants (the wave number and the characteristic impedance) that vary with wire distance from the ground. (As a function of height, they do not exhibit a discrete jump at the ground.) It is important to take into consideration both the inductive components introduced by ground currents and capacitive components, which are associated with electric fields and are often neglected by other researchers.
The current excited by magnetic or electric exciters in a horizontal wire can be calculated by the Method of Moments (MoM) and this is the approach used by the proprietary program "FEKO"; the calculations also involve the Sommerfeld theory and are based on the inversion of a large matrix. When models are used as a part of wire detection algorithms, it is important that they can be implemented very rapidly and this favours transmission line models. A comparison between the transmission line software results and FEKO output demonstrates that the transmission line approach is viable for wires in free space, in full spaces (equivalent to deep wires) and half spaces. The physical theory is presented in a report J.K.E. Tunaley, "Transmission Line Models of Wire Scattering", May 2015. See also P. Sooryadavan, J.K.E. Tunaley and S.E. Irvine, "Parametric Modeling of the Current Induced in Linear conductors", DRDC Report 2015-R108, July 2015. A more recent example of a comparison between FEKO (black) and the program (red) results are shown in the accompanying plot for a bare wire buried 1cm in very wet ground; it is excited by a magnetic dipole at 5 MHz.
The program also estimates the current excited in insulated wires. An insulated cylindrical sheath affects the propagation constants and thereby shifts resonances.
In the case of CNRs, it is worth noting that the natural resonant frequencies generally differ from those frequencies that would result in a maximum scattered response for a continuous wave excitation. This is because the CNR frequencies depend on the dissipation in the system. For buried wires this depends on the ground conductivity. This can be understood by considering a tuned circuit consisting of a lossy inductor and an ideal capacitor. When a voltage is applied, there is a transient response at the CNRs, which dies away after some cycles depending on the losses. If the excitation is a continuous wave, the response is a maximum when the reactance is zero and this only depends on the purely inductive and capacitive components.
Calculation of the CNRs of a buried wire is not straightforward in part because the imaginary part of the ground permittivity varies significantly with frequency. For bare wires Baum’s transformation can be used. A calculation for insulated wires has been implemented and this demonstrates some interesting effects. An important parameter is the soil type especially with regard to soil moisture. Wet ground can cause high dissipation in some circumstances but, when the wire is sheathed with insulation, wet ground can result in less dissipation and longer-lasting resonances.
The present theory for the propagation of electromagnetic waves in the presence of lossy ground is based on the Sommerfeld model, which has been exploited notably by the Wait group in the US. Here the model is used to estimate the electric field produced by a CW transmitter near a horizontal insulated wire of finite length buried a short distance below the ground and to estimate the fields scattered in the neighbourhood of sensors above ground. The adjacent figure shows the scattered response in the vertical component of the magnetic field for a 100 m wire sheathed in PVC when the stand-off distance is 10 m and the ground is very dry (using the International Telecommunications Union (ITU) definitions). Various resonances are visible; the fundamental is at about 0.9 MHz. The scattered magnetic field is usually much smaller than the direct field (including the component due to the ground) but, when the transmitter is a vertical electric dipole and under ideal circumstances, the direct z-component is zero.
As the ground moisture increases, the resonances tend to be suppressed due to greater damping of the signals in the earth. The scattered fields also decrease.
Estimates of scattered field magnitudes as a result of short pulses suggest that CNRs have great promise for command wire detection.
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