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The concept of volume of influence (VoI) for electromagnetic induction (EMI) sensors is introduced and accurately defined. It enables one to better understand the response of a magnetic soil to an EMI sensor, as well as the effect of soil inhomogeneity on soil compensation. The VoI is first defined as the volume producing a fraction \alpha of the total response of a homogeneous half-space. As this basic definition is not appropriate for sensor heads with intrinsic soil compensation, a generalized definition is then proposed. These definitions still do not yield a unique VoI, and a constraint must be introduced to reach uniqueness. Two constraints are investigated: one yielding the smallest VoI and the other one the layer of influence. Those two specific volumes of influence have a number of practical applications which are discussed. The smallest VoI is illustrated for typical head geometries, and we prove that, apart from differential heads such as the quad head, the shape of the smallest VoI is independent of the head geometry and can be computed from the far-field approximation. In addition, quantitative head characteristics are provided and show—among others—that double-D heads allow for a good soil compensation, assuming, however, approximate homogeneity over a larger volume of soil. The effect of soil inhomogeneity is further discussed, and a worst case VoI is defined for inhomogeneous soils. [ABSTRACT FROM AUTHOR]

A general model to compute the response of an electromagnetic induction sensor to a magnetic soil, in both time and frequency domains, is developed. The model requires modest computational resources and can be applied to arbitrary soil inhomogeneities and relief, and to arbitrary sensor coil shapes, orientations, and positions. Central to the model is the concept of a head sensitivity map, which can be used to characterize the sensor head as a function of the shape, size, and position of the sensor coils. Two further concepts related to the head sensitivity are presented, which are the zero equisensitivity surface and the volume of influence. We demonstrate that these concepts aid the understanding of the detector behavior. The general model is based on the Born approximation, which is valid if the soil magnetic susceptibility is sufficiently small. A simpler model, which is only valid for homogeneous half-space soils but does not require the Born approximation, is also developed. The responses predicted by both models are shown to be in good agreement with each other and also with available analytic solutions. Comparing the two models also enabled an expression for the error incurred when using the Born approximation to be established. We shown that, for most soils of relevance to mine clearance, the corresponding error is negligible. [ABSTRACT FROM AUTHOR]