Apparent Dielectric Permittivity Research Articles

Time domain reflectrometry measurements of water content in coarse waste rock

Methods are presented to calibrate and implement a time domain reflectrometry (TDR) system to estimate the water content of coarse mine waste rock containing high solute concentrations in the pore water. High electrical conductivity of the pore water reduces the quality of TDR waveforms through the loss of signal amplitude. Zegelin-type probes with a resistive coating on the center conductor were used to obtain higher signal-to-noise waveforms. These probes must be calibrated prior to use. The TDR pulse travel-time measured in soils containing pore water with high solute concentrations increases systematically with solute concentration. Empirical calibrations are derived for waste rock with low and high electrical conductivity pore water. An ambient temperature correction is derived from observed diurnal fluctuations in the measured travel time to determine whether or not a detailed laboratory calibration for temperature effects is required. The variation of apparent dielectric permittivity with temperature is positively correlated with temperature at low water content and negatively correlated at high water content. This trend indicates the influence of water bound to mineral surfaces on the variation of apparent dielectric permittivity with temperature. Examination of our field data indicates that the effect of dissolved ions on the TDR calibration was great enough to justify a calibration that accounts for pore-water composition. The effect of ambient temperature was found to be small enough that an intensive laboratory calibration was not required.Key words: time domain reflectrometry, water content, mining.

Evaluation of Uncoated and Coated Time Domain Reflectometry Probes for High Electrical Conductivity Systems

High sample electrical conductivity reduces the quality of a time domain reflectrometry (TDR) waveform by the loss of signal amplitude. Two strategies are examined to obtain higher signal/noise waveforms: (i) waveform differencing by remote diode shorting and (ii) covering probe conductors with resistive coatings. Experiments using electrically conductive water solutions (0–5 dS m−1) and three‐rod Zegelin type probes show conventional dual‐tangent waveform analysis and waveform differencing using manual short circuits can accurately determine travel time but the remote diode shorting method can be systematically biased by the electrical properties of the diodes used. Three‐rod Zegelin‐type probes with a high resistance coating on the central rod permit collection of analyzable waveforms for solutions with electrical conductivities at least as high as 70 dS m−1 Dual‐tangent analysis of the raw waveform is found to be more accurate than the remote diode shorting method within water solutions and within silica sand saturated with an electrically conductive water solution. The probe coating creates a nonlinear relationship between the apparent dielectric permittivity estimated using a coated probe and the actual sample apparent dielectric permittivity. Experimental measurements of this relationship can be fitted using an equation of the form for a coaxial cell. A three‐rod coated probe with a single diode at the probe head is a practical means to collect interpretable waveforms in media with high electrical conductivity. However, measurements of travel time alone may not be sufficient to determine water content in soils with high concentrations of dissolved ions in the soil water solution.

Comparison of travel time analysis and inverse modeling for soil water content determination with time domain reflectometry

Travel time analysis algorithms are used to extract dielectric permittivity (and thereby water content) from time domain reflectometry (TDR) waveforms. A limitation of travel time analysis is the need to define subjective analysis parameters for reproducible measurements. The aim of this paper is to compare three methods to remove subjectivity from the analysis of TDR waveforms: (1) travel time analysis with optimized analysis parameters, (2) fitting a simulated waveform based on a model with frequency‐dependent permittivity, and (3) fitting a waveform based on a model with an apparent dielectric permittivity. We performed an outflow experiment on a sandy soil sample and simultaneously collected soil water content measurements (determined from outflow) and duplicate TDR measurements. After optimizing the travel time analysis parameters by minimizing the difference between duplicate measurements, we found little difference in accuracy and reproducibility between the three methods. However, we showed that small deviations from the optimal travel time analysis parameters have a significant influence on both the accuracy and the reproducibility of travel time analysis. A comparison of the two inverse modeling approaches showed that the inclusion of frequency‐dependent permittivity did not greatly improve the fit between measured and modeled waveforms and that a frequency‐independent (apparent) permittivity adequately describes the TDR measurements made in this sandy soil. We conclude that the removal of subjectivity resulted in similar accuracy and reproducibility for all three methods. Nevertheless, we consider inverse modeling an interesting alternative to travel time analysis because it is a fully automated analysis with high accuracy and reproducibility.

Dielectric permittivity and resistivity mapping using high‐frequency, helicopter‐borne EM data

The interpretation of helicopter‐borne electromagnetic (EM) data is commonly based on the transformation of the data to the apparent resistivity under the assumption that the dielectric permittivity is that of free space and so displacement currents may be ignored. While this is an acceptable approach for many applications, it may not yield a reliable value for the apparent resistivity in resistive areas at the high frequencies now available commercially for some helicopter EM systems.We analyze the feasibility of mapping spatial variations in the dielectric permittivity and resistivity using a high‐frequency helicopter‐borne EM system. The effect of the dielectric permittivity on the EM data is to decrease the in‐phase component and increase the quadrature component. This results in an unwarranted increase in the apparent resistivity (when permittivity is neglected) for the pseudolayer half‐space model, or a decrease in the apparent resistivity for the homogeneous half‐space model. To avoid this problem, we use the in‐phase and quadrature responses at the highest frequency to estimate the apparent dielectric permittivity because this maximizes the response of displacement currents. Having an estimate of the apparent dielectric permittivity then allows the apparent resistivity to be computed for all frequencies. A field example shows that the permittivity can be well resolved in a resistive environment when using high‐frequency helicopter EM data.

Time Domain Reflectometry Measurements of Solute Transport across a Soil Layer Boundary

The mechanisms governing solute transport through layered soil are not fully understood. Solute transport at, above, and beyond the interface between two soil layers during quasi‐steady‐state soil water movement was investigated using time domain reflectometry (TDR). A 0.26‐m sandy loam layer was packed on top of a 1.35‐m fine sand layer in a soil column (0.15‐m i.d.). Soil water content (θ) and bulk soil electrical conductivity (ECb) were measured by 50 horizontal and 2 vertical TDR probes. A new TDR calibration method that gives a detailed relationship between apparent relative dielectric permittivity (Ka) and θ was applied. Two replicate solute transport experiments were conducted adding a conservative tracer (KCl) to the surface as a short pulse. The convective lognormal transfer function model (CLT) was fitted to the TDR‐measured time integral–normalized resident concentration breakthrough curves (BTCs). The BTCs and the average solute‐transport velocities showed preferential flow occurred across the layer boundary. A nonlinear decrease in TDR‐measured θ in the upper soil toward the soil layer boundary suggests the existence of a 0.10‐m zone where water is confined towards fingered flow, creating lateral variations in the area‐averaged water flux above the layer boundary. A comparison of the time integral–normalized flux concentration measured by vertical and horizontal TDR probes at the layer boundary also indicates a nonuniform solute transport. The solute dispersivity remained constant in the upper soil layer, but increased nonlinearly (and further down, linearly) with depth in the lower layer, implying convective‐dispersive solute transport in the upper soil, a transition zone just below the boundary, and stochastic–convective solute transport in the remaining part of the lower soil.

Measurement of relative permittivity in sandy soils using TDR, capacitance and theta probes: comparison, including the effects of bulk soil electrical conductivity

Measurement of the apparent dielectric permittivity of soils (dielectric constant) is becoming a popular way of estimating soil volumetric water content. This paper focuses on the measurement of apparent permittivity in four sandy soils using; time domain reflectometry (TDR), a surface capacitance insertion probe (SCIP) and a Theta probe. Measurement of the apparent permittivity using the SCIP and Theta probe are compared with the apparent permittivity measured using the TDR. Calibration of such instrumentation has remained relatively empirical following the engineering approximation presented by Topp et al. (Topp, G.C., Davies, J.L., Anan, A.P., 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Res. Research 16, 574–582.). The refractive index model proposed by Whalley (Whalley, W.R., 1993. Considerations on the use of time domain reflectometry (TDR) for measuring soil water content. J. Soil Sci. 44(1), 1–9.) based on that of Birchak et al. (Birchak, J.R., Gardner, C.Z.G., Hipp, J.E., Victor, J.M., 1974. High dielectric constant microwave probes for sensing soil moisture. Proc. IEEE 62(1), 93–98.) is investigated as a means of gaining some physical understanding of the relative contributions of the different dielectric components in soils. Predictions made by the model are tested against results using multiple linear regression. The predictions agree well with the observed measurements. Inter-electrode conductivity is found to contribute significantly to the apparent permittivity measured using the SCIP and to a lesser extent the TDR but not the Theta probe. Inclusion of inter-electrode conductivity in regression analysis improved results. The Theta probe was found to overestimate the apparent permittivity of the soil by ∼1.5 when compared with TDR results. It is suggested that this may be the result of compaction of the soil close to the electrodes, coupled with a strong bias in the sensitivity of the probe to the region very close to the central electrode.

PRINTED CIRCUIT BOARD TIME DOMAIN REFLECTOMETRY PROBE: MEASUREMENTS OF SOIL WATER CONTENT

Time domain reflectometry (TDR) is a widely used, nondestructive measurement technique for determining soil-water content (θ) and bulk soil electrical conductivity. Until recently, small scale applications of TDR have been restricted because of the lack of small-scale, high-resolution TDR probes. As a result of the introduction of the TDR coil probe principle (Nissen et al. 1998b) and, in this study, the printed circuit board TDR probe (PCBP), the lower limit of the measurement scale for TDR is changing. The travel time of the electromagnetic waves in the PCBP was prolonged by forcing the electromagnetic waves to travel in a three-rod serpentine waveguide produced in the copper cladding of a circuit laminate (50 mm long, 10 mm width, 0.64 to 1.00 mm thickness). The apparent relative dielectric permittivity (K a ) measured by the PCBP (K a, PCBP ) was calibrated against K a measured by a standard two-rod TDR probe in air and six fluids of various K a . A two-phase dielectric mixing model was used to describe the contributions of the circuit laminate and the surrounding media to K a , PCBP . Eleven PCBPs were produced on four different types of circuit laminate with well known water absorption properties. Minor changes in K a attributable to water absorption could be observed for some of the circuit laminates. However, all four circuit laminates showed equal measurement performance during water infiltration in an initially air-dried soil. None of the circuit laminates was damaged by the soil environment during the water transport experiments. The waveguide of the PCBP is in direct contact with the soil, which should enable the PCBP to also measure electrical conductivity (EC). A calibration experiment was carried out where the load resistance (R 1 ) and the EC were measured in deionized water and six KC1 solutions by the PCBPs and a conductivity meter, respectively. A simple linear relationship was found between RL and EC. Therefore, in contrast to the TDR coil probe, the PCBP seems promising for obtaining simultaneous, small-scale and high-resolution TDR measurements of water and solute transport.

Mesure en laboratoire de la permittivité diélectrique moyenne fréquence de végétaux à 430 kHz à l'aide d'un capacimètre. Relation entre permittivité apparente d'un ensemble d'épis de blé et leur contenu en eau

The laboratory measurements presented here are additional measurements to those performed on a wheat crop by an electrostatic quadrupole at 430 kHz. They give a first calibration for the correlation between water content and apparent dielectric permittivity of ears. These measurements are performed by means of a capacimeter or a plane condenser of which the apparent permittivity is determined. Wheat ears are placed within the condenser and their permittivity is correlated to their water content. A theoretical approach (method of moments) presents the response of the condenser, containing ears similated to a 3D parallelepipedic body in an electromagnetic field.

In situ measurement of medium-frequency apparent permittivity using an electrostatic quadrupole. Application to the determination of the water content of wheat

The objective of this work was to design, to build and to test a new instrument to measure in situ the water content of wheat, 1 or 2 months before harvesting, using a non-destructive and non-intrusive technique. We choose to measure dielectric permittivities, which are known to be correlated to the content of liquid water. Measurement is based on the electrostatic quadrupole principle: two charges of opposite sign are used to polarize the medium, while the resulting voltage between two other poles is measured. The size of the quadrupole is of the order of 40 cm. The static approximation applies in the low- and medium-frequency range. The transfer impedance of the quadrupole is inversely proportional to the apparent permittivity of the medium. Two synthetic models were developed: (i) a 1D model computing the quadrupole response in a stratified medium (air, crop layers and soil) and (ii) a 3D model computing the quadrupole response when a parallelepipedal body or a series of bodies is placed in the vicinity of the quadrupole. After several tests, in the laboratory and outdoors with a parallelepipedal body, the prototype was tested on actual crops. Measurements were performed in an experimental wheat field at the Grignon INRA experimental site. The variations of water content of ears and stems were studied versus space and time. A first law relating the water content and the apparent dielectric permittivity was established. The results show that this technique is relevant and that the water content of plants can be determined in situ, using this new non-destructive approach.

High‐Resolution Time Domain Reflectometry Coil Probe for Measuring Soil Water Content

AbstractTime domain reflectometry (TDR) is becoming a widely used nondestructive method for measuring soil‐water content (θ), but relatively little effort has been put into the development of TDR equipment and especially TDR probes. Therefore, TDR has been used with only limited success for measuring small spatial scale variations in θ. In this study a small‐scale TDR probe (length = 15 mm, diameter = 3.6 mm), applicable with common TDR equipment and easy and inexpensive to produce, was developed. Travel time in the probe is prolonged by forcing the electromagnetic waves to travel in a coil surrounded by four grounded wires. The apparent relative dielectric permittivity (Ka) measured by the coil probe (Ka, coil) was calibrated against Ka measured by a standard two‐rod TDR probe without a balun (Ka, ref) in (i) five soils during transient evaporation, and (ii) air and seven fluids. Calibration in air and fluids was fast and reliable compared with transient‐state calibration in soil. A two‐phase dielectric mixing model was used to describe the contributions of the probe materials and the surrounding media to Ka, coil. Soil volume of influence was found to be approximately 180 mm3, implying that the coil probe measurement can be considered close to a point measurement. By introducing the coil principle, a reduction in probe length of a factor of five was achieved without loss in the sensitivity of the probe to changes in the Ka of the surrounding soil.

Dielectric spectroscopy by inverse modelling of time domain reflectometry wave forms

The travel time analysis of the time domain reflectometry (TDR) wave form gives one single value for the apparent dielectric permittivity, while it is frequency dependent. In this research Fourier Analysis was used to obtain the frequency dependend permittivity from the TDR-signal as measured with a seven rod probe. Inverse modelling of the TDR wave form was used to obtain directly the parameters of the Debye relaxation model, which is used to model the frequency dependence of the permittivity. In the frequency range between 0 and 1.5 GHz the accuracy and reproducibility in different alcohol's and sacharide solutions were examined. The results were compared with standard measurements carried out with a network analyser (NWA) with open end probe, as well as measurements carried out with the NWA following the inverse modelling technique and using the seven rod probe. Without any calibration the inverse modelling method gives good trends for all parameters, while for the static dielectric permittivity the absolute values are accurate within 20%. The results of NWA and TDR compare very well.

The determination of apparent memory functions from dielectric relaxation data for amorphous polymers and glass-forming liquids: Theory and experiment

Interrelationships between time-correlation functions for molecular reorientation, their apparent memory functions and dielectric permittivity for the α relaxation in glass-forming liquids and amorphous polymers are considered briefly and a method is given for the determination of an apparent first-order memory function K̃1(ω) in the frequency domain from dielectric relaxation data. For the Kohlrausch–Williams–Watts (KWW) function and the Cole–Cole function and for experimental data for three amorphous polymers it is shown that the real and imaginary components of K̃1(ω) increase without limit as frequency f(=ω/2π) is increased. The physical significance of such apparent memory functions is considered in view of this behavior and the recent experimental studies of the α relaxation in polymers by Schmidt–Rohr and Spiess and in glass-forming liquids by Cicerone and Ediger, who suggest that a ‘‘dynamic heterogeneity’’ is present that leads to a broad distribution of relaxation times where each elementary process has no proper memory. For such cases it appears that the apparent memory functions are simply related to the parameters characterizing the distribution and may have no physical significance for the α process in glass-forming materials.

Spatial Averaging of Water Content by Time Domain Reflectometry: Implications for Twin Rod Probes with and without Dielectric Coatings

The averaging of apparent relative dielectric permittivities by time domain reflectometry (TDR) is examined for properties varying along TDR waveguides and in the plane perpendicular to a TDR probe. A square root averaging model with uniform weighting factors describes the measured apparent relative dielectric permittivity for axially varying materials; variations in the transverse plane are described by an inverse averaging model with nonuniform spatial weighting. We define the sensitivity of a TDR probe as the change in the measured travel time for a given change in the average soil water content for rods of a fixed length. For rods with dielectric coatings, this sensitivity increases with the dielectric permittivity of the coating and the rod radius and decreases with the soil dielectric permittivity. Due to the dependence of the sensitivity on the soil water content, coated rods will not measure the actual average water content for conditions of axially variable water contents.

Frequency domain analysis of time domain reflectometry waveforms: 1. Measurement of the complex dielectric permittivity of soils

The S11 scatter function of a coaxial probe in the frequency domain is shown to be an accurate model for predicting waveforms of a seven‐wire coaxial probe in the time domain. Reproducibility of discrete Fourier analyses carried out on waveforms measured with the Tektronix 1502b cable tester (Tektronix, Incorporated, Beaverton, Oregon) indicated a frequency band width ranging from 20 kHz to approximately 1.5 GHz. The frequency dependent complex dielectric permittivity can be calculated from measured waveforms by inverting the S11 scatter function. Results indicate that a seven‐wire coaxial probe, connected to a 1‐m RG214 coaxial cable, emulates a coaxial tube for frequencies up to 150 MHz. Application of the frequency domain model to time domain reflectometry waveforms shows that the apparent dielectric permittivity calculated from the travel time in the probe is very dependent on the relaxation frequency of the material in which the probe is embedded. For materials with low relaxation frequencies the apparent dielectric permittivity is much lower than the static permittivity. Inversion of the frequency domain model allows for solving the frequency dependent complex dielectric permittivity of soils from measured waveforms.

Frequency domain analysis of time domain reflectometry waveforms: 2. A four‐component complex dielectric mixing model for soils

Although time domain reflectometry (TDR) is becoming accepted as an important tool for the measurement of soil water content and bulk soil electrical conductivity, a major part of the method is based on empirical relationships. An improved understanding of dielectric measurements on soils may give more insight into soil properties other than soil water content and bulk soil electrical conductivity. Frequency domain analysis of TDR waveforms enables the measurement of the frequency dependent complex dielectric permittivity of soils. The frequency dependent complex dielectric permittivity of soils can be described with a four‐component complex dielectric mixing model based on the volumetric mixing of the refractive indices of the soil components. The four soil components in the model are air, solids, bound water, and free water. Results indicate that the apparent dielectric permittivity obtained from the travel time of the TDR pulse in the soil is the dielectric permittivity at the highest measurement frequency of the cable tester, probe, and soil system. The model based on the volumetric mixing of real permittivities underestimates the measurements in situations with high values of the imaginary part of the dielectric permittivity. Because the model based on the mixing of the complex dielectric permittivities can describe the data, we conclude that the apparent dielectric permittivity is influenced by the imaginary parts in the dielectric, permittivities of the soil components. Combination of the four‐component complex dielectric mixing model with the complex dielectric permittivity obtained from the frequency domain analysis of TDR waveforms gives a tool for modeling the bulk soil electrical conductivity by separating the conductivity of the soil water into a bound water conductivity and a free water conductivity.

Design of Triple‐Wire Time Domain Reflectometry Probes in Practice and Theory

AbstractTime domain reflectometry (TDR) is accepted as a valuable tool for measuring soil water content and bulk soil electrical conductivity. The accuracy of TDR measurements depends on the quality and type of probes, as well as on the length of cable used. The objective of this study was to test the effects of different triple‐wire TDR probe dimensions and cable lengths on the measurements. Additional measurements were done in order to test the performance of small triple‐wire probes in soils with a wide range of water contents. Measurements in air and in water showed that the position of the first reflection from the connection between cable and probe is influenced by the dielectric medium. This problem was solved by using the zero of the cable tester as a time reference, and calibrating the TDR probes before measurements. The major effect of increasing cable lengths is that the rise time of the TDR voltage pulse increases, spreading each reflection across a larger time interval, which influences the accuracy of the wave form analysis and causes a possible underestimation of the apparent dielectric permittivity in dry soils. As a result, it is not possible to use short probes with long cable lengths. Smaller spacing of the wires results in steeper reflections from the end of the probe. Small triple‐wire probes are convenient in laboratory applications. Large triple‐wire probes are convenient for automated field applications in which long lengths of cable are required.

Time domain reflectometry study of fast-ionic-conducting glasses

Dielectric data on model fast-ionic-conducting glasses are reported at various sub-Tg temperatures. A transformer bridge was used from 100 Hz to 200 kHz, while data between 85 MHz and 2 GHz were obtained by time domain reflectometry. Substantial improvements in the sensitivity and equivalent frequency range of the latter correct previous preliminary results reporting the existence and temperature dependence of apparent dielectric permittivity plateaus in the upper MHz spectral region of glasses.