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

TL;DR

This paper develops a theoretical model to assess the inaccuracy of simultaneous resistivity and permittivity measurements using a quadrupole probe, comparing sensitivity and transfer function approaches for improved accuracy estimation.

Contribution

It introduces a sensitivity functions-based model for error propagation in resistivity and permittivity measurements, enhancing accuracy predictions over classical frequency domain analysis.

Findings

Sensitivity approach provides less stringent accuracy forecasts than transfer function method.

Average values effectively estimate complex impedance in low water saturation terrains.

Model helps design probes with inaccuracy below 10% across specified frequency ranges.

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 the complex impedance over various terrains and concretes, especially when they are characterized by low levels of water saturation (content) and analyzed within a bandwidth ranging only from low (LF) to middle (MF) frequencies. 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 are less stringent than those foreseen by the transfer functions method (in terms of both a larger band of frequency f and a wider measurable range of resistivity or permittivity).