Abstract
Normal.dotm 0 0 1 188 1075 INGV BO 8 2 1320 12.0 0 false 14 18 pt 18 pt 0 0 false false false The present study proposes a theoretical modeling of simultaneous and noninvasive measurements of electrical resistivity and dielectric permittivity using a quadrupole probe on a subjacent medium. A mathematical–physical model is applied to the propagation of errors in the measurement of resistivity and permittivity based on a sensitivity functions tool. The findings are also compared with results of the classical method of analysis in the frequency domain, which is useful for determining the behavior of zero and pole frequencies in the linear time invariant circuit of the quadrupole. This study underlines that average values of electrical resistivity and dielectric permittivity can be used to estimate complex impedance over various terrains and concretes, especially when they are characterized by low levels of water saturation (content), and are analyzed within a bandwidth ranging only from low to middle frequencies. To meet the design specifications, that ensure satisfactory performances of the probe (inaccuracies of no more than 10%), the forecasts provided by the sensitivity functions approach are discussed in comparison with those foreseen by the transfer functions method (in terms of both the band of frequency f and the measurable range of resistivity ρ, or permittivity er).
Highlights
This study underlines that average values of electrical resistivity and dielectric permittivity can be used to estimate complex impedance over various terrains and concretes, especially when they are characterized by low levels of water saturation or content [Knight and Nur 1987], and are analyzed within a frequency bandwidth only ranging from LFs to middle frequencies (MFs) [Al-Qadi et al 1995, Myounghak et al 2007]
To meet the design specifications that ensure the satisfactory performance of the probe, the forecasts provided by the theory of error propagation suggested by Vannaroni et al [2004] that apply the sensitivity functions approach, as explicitly developed in the study, are discussed in comparison to those foreseen by analysis in the frequency domain suggested by Grard and Tabbagh [1991]
Average values of electrical resistivity and dielectric permittivity can be used to estimate complex impedance over various terrains and concretes, especially when they are characterized by low water content [Knight and Nur 1987], and are analyzed within a frequency bandwidth ranging from only LFs to MFs [Al-Qadi et al 1995, Myounghak et al 2007]
Summary
To meet the design specifications that ensure the satisfactory performance of the probe (inaccuracies of no more than 10%), the forecasts provided by the theory of error propagation suggested by Vannaroni et al [2004] that apply the sensitivity functions approach, as explicitly developed in the study, are discussed in comparison to those foreseen by analysis in the frequency domain suggested by Grard and Tabbagh [1991] This deepens the transfer functions method to analyze the zero and pole behavior (in terms of both the band of frequency f and the measurable range of resistivity t, or permittivity fr ). According to the following two practical approaches: (a) – (v, fr) as independent variables in order – to establish the class of media with conductivity and permittivity (v, fr) that can be investigated by a quadrupole working in a fixed band B and specified by a known geometry x; (b) – preferential way (v, fr) → (R,C) since – once a subjacent medium with electrical conductivity v and dielectric permittivity fr is selected, the quadrupole probe specifications R and C can be projected both in frequency f and in height/dimension ratio x
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