Volume of Influence for Magnetic Soils and Electromagnetic Induction Sensors

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 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.