Inaccuracy Assessment for Simultaneous Measurements of Resistivity and Permittivity applying Sensitivity and Transfer Function Approaches

Abstract

This paper proposes a theoretical modelling of the simultaneous and non invasive measurement of electrical resistivity and dielectric permittivity, using a quadrupole probe on a subjacent medium. A mathematical-physical model is applied on propagation of errors in the measurement of resistivity and permittivity based on the sensitivity functions tool. The findings are also compared to the results of the classical method of analysis in the frequency domain, which is useful for determining the behaviour of zero and pole frequencies in the linear time invariant (LTI) circuit of the quadrupole. The paper underlines that average values of electrical resistivity and dielectric permittivity may be used to estimate wave signal strength over some concretes, especially if characterized by high resistivities over the band straddling from LF to MF. In order to meet the design specifications which ensure satisfactory performances of the probe (inaccuracy no more than 10%), the forecasts provided by the sensitivity functions approach, proposed in this paper, are less stringent than those foreseen by the transfer functions method, adopted in some other papers (in terms of both larger band of frequency f and measurable range of resistivity ρ or permittivity εr).