The basis for this project was the belief, on the part of its principal investigators, that there is a better way to make electromagnetic induction (EMI) measurements for unexploded ordnance (UXO) than the conventional method being used industry wide. The method envisioned sensor pairs measuring a spatial difference in dB/dt instead of individual sensors that sense dB/dt fields. Such measurements approximate a gradient (or difference) measurement rather than a whole field measurement. The belief that this method is better is based in part on parallelism with the passive magnetics method wherein gradient measurements are commonly used for certain surveys and in part on the belief that the signal-to-noise ratio (SNR) can be improved, rather than decreased, by the differencing of sensor pairs.

The original objective of this project was to demonstrate that the measurement of both the vector secondary EMI field and the elements of the tensor gradient using three or more transmitter antenna configurations would substantially increase the probability of detection of UXO, improve target characterization, and provide a first attempt to differentiate multiple overlapping signatures from UXO targets.

As the project progressed, the original objective was refined to address the following:

  1. Development of computations and modeling to determine and demonstrate whether measurements made with physical realizable sensors could be used to adequately estimate true gradients and, if so, to demonstrate with numerical models whether the gradient method provides improvements in performance when compared to conventional methods.

Fabricate components and conduct experiments to verify computations, to demonstrate that useful data can be acquired with realizable hardware, and to collect demonstrative data in real-world situations where mitigating factors are often more complex than can be computed and modeled.

Technical Approach

The project was conducted in two phases. Phase 1 was to formulate and perform simple model calculations and to perform simple experiments to test whether physically realizable sensors were capable of estimating the tensor gradient and whether those estimates were useful. Phase 2 was to perform more complex computations and modeling, to fabricate multiple sensors and a complete data acquisition system, and to perform more extensive tests.


Early computations showed that finite difference sampling of whole fields, using pairs of whole-field sensors, was sufficient to estimate gradients as long as the distance to the target was more than 2xB, where B is the baseline distance between the pairs of sensors in the gradiometer. Computations showed that other errors, principally SNR considerations, rotation and positioning errors, and sensitivity errors, could be reasonably met with conventional fabrication and electronics.

Later computations showed that, using the gradient tensor method, multiple targets could not be separated unless the targets are separated by a distance of 4 times their burial depth.

The gradient method was shown to be useful for “dipole mapping,” a method used to track magnetic targets approximated by a magnetic dipole. The method was shown to have significant applicability for surveys where it is necessary to track a target as it passes under a sensing array. It is not useful for static or cued identification (ID) surveys where typically a 20-60 second observation is made over a target and where non-linear computations (inversions) are made to establish the location and characteristics of the target.

Physical experiments showed that a gradient sensor array provides improvement in SNR. Noise is reduced more than signal by the action of subtracting signals from closely spaced sensors, so SNR improves. The experiments amplified the expectation that the characterization of SNR in this case is complex. It is a function of external factors (environmental EM noise), internal factors (balance and thermal noise generated by electronic amplifiers), and finally bandwidth, where bandwidth is itself a function of data acquisition parameters. Importantly, the experiments showed that SNR is usually improved for wideband observations, but they also showed that SNR is usually not improved for narrower band observations such as those made in cued ID observations (long-time, static, in-place measurements, with wide-window gating functions).


The computations and observations showed that the tensor gradiometer methods could be useful for any survey where data acquisition and computation speeds are important, such as dynamic surveys made for target detection and mapping. At the same time, the computations and observations showed that the tensor gradiometer methods are neither superior nor inferior to conventional methods for surveys where data acquisition and computation speed is less important, such as typical static cued ID surveys made for target characterization and classification.