Construction and calibration of a field TDR monitoring station

Transcription

1 Near Surface Geophysics, 2012, 10, doi: / Construction and calibration of a field TDR monitoring station G. Curioni 1*, D.N. Chapman 1, N. Metje 1, K.Y. Foo 2 and J.D. Cross 2 1 School of Civil Engineering, College of Engineering and Physical Sciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK 2 School of Electronic, Electrical and Computer Engineering, College of Engineering and Physical Sciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Received November 2011, revision accepted December 2011 ABSTRACT Time-Domain Reflectometry (TDR) has been used extensively in the past thirty years in order to measure soil water content and bulk electrical conductivity (EC b ), both in the laboratory and in the field. TDR can be effectively used in combination with geophysical techniques such as Ground Penetrating Radar (GPR) in order to provide information on relative dielectric permittivity and EC b. As part of the Mapping the Underworld project, a TDR monitoring station was constructed with the aim of monitoring the geophysical parameters of the soil in a field case study. A rigorous methodology, utilizing the latest knowledge for calibration and analysis was followed and is thoroughly elucidated in this paper. The reasons behind the choice of the equipment setup are described, with the intention of providing a reference for similar TDR field installations. The precision and accuracy of TDR and the validation of the calibration procedures were assessed with laboratory and field tests. The standard deviation of several TDR measurements in the laboratory was on average smaller than 2% for both apparent permittivity and EC b. The accuracy, expressed as the mean difference to reference values, was on average smaller than 2% and 3% of apparent permittivity and EC b respectively, although higher errors, up to 5% and 7.5% respectively, were measured in media with very low apparent permittivity (i.e., air) and at EC b values smaller than S/m. These results demonstrate that with the chosen methodology and setup, TDR can provide reliable data and can be used for long-term geophysical monitoring. The data provided by TDR monitoring stations could contribute to a data base of geophysical properties for soils. This information may eventually be used to assist the fine tuning of shallow geophysical techniques such as GPR. INTRODUCTION The research described in this paper is part of the Mapping the Underworld project, ( which aims to improve the detection of underground utilities in all types of soil conditions by deploying different shallow geophysical techniques (Metje et al. 2007). One of these techniques is Ground Penetrating Radar (GPR), which is strongly affected by the soil type and conditions. For example, it is well-known that the reliability of a GPR survey is limited in conductive soils such as wet clays (Cassidy 2008). In order to identify the suitability of GPR in specific field applications and potentially improve its employment, it is desirable to have prior information of the ground properties and in particular its geophysical properties, such as relative dielectric permittivity and bulk electrical conductivity (EC b ), in addition to its geotechnical properties. The geotechnical properties of the soil are known to be related to the geophysical ones and * g.curioni@bham.ac.uk thus could be used to estimate the geophysical soil parameters when no direct information is available (Thomas et al. 2010a,b). In order to improve our understanding of these properties it is necessary to gather field data. Relative dielectric permittivity and EC b are dynamic parameters mainly affected by the soil water content, which varies with time and is dependent on the soil type. In order to account for seasonal variability it is necessary to obtain information over long time periods by developing field monitoring stations. Time-Domain Reflectometry (TDR) can provide information on such properties and can be employed in field monitoring (Robinson et al. 2003a). The application of TDR in soil science increased after the seminal work by Topp et al. (1980), who developed an empirical model that enabled the volumetric water content of the soil to be estimated from the apparent permittivity measured by TDR. Dalton et al. (1984) advanced the potential applications of TDR by simultaneously measuring the apparent permittivity and the EC b of soil. Since then, further research has been carried out concerning 2012 European Association of Geoscientists & Engineers 249

2 250 G. Curioni et al. TDR and in recent years a robust methodology for apparent permittivity and EC b measurements has been defined. Robinson et al. (2003b) presented a calibration methodology for apparent permittivity and its validity is described in detail. Huisman et al. (2008) and Bechtold et al. (2010) clarified a methodology for EC b calibration. A strength of the TDR technique is that it has a relatively low cost, while capable of accurately measuring both the apparent permittivity and EC b with minimal disturbance to the soil. A TDR can also be easily multiplexed to multiple probes and can be automated for field monitoring (Jones et al. 2002; Robinson et al. 2003a). The use of TDR in field monitoring became possible after some important technological advances. Baker and Allmaras (1990) and Zegelin et al. (1989) demonstrated the possibility of deploying multiple probes in the field with the aid of multiplexers. Heimovaara and Bouten (1990) developed an algorithm to automatically analyse the waveforms collected by TDR, which allowed numerous measurements to be taken over long periods of time. Despite the large amount of research, the literature focuses mainly on the measurement and monitoring of soil water content. For specific geophysical applications, such as underground utility surveying, it is important to have direct knowledge of the geophysical parameters of the soil, their natural variability with depth and over time and their relationship with the geotechnical soil properties. The aim of the current research was to demonstrate a methodology for using TDR in long-term geophysical monitoring in the field. In this paper the methodology and the reasons for the chosen experimental setup are described in detail. This work defines a rigorous procedure for the development of similar TDR field monitoring stations and demonstrates the potential and also the limitations associated with the TDR technique for the purpose of geophysical monitoring. PRINCIPLES OF TIME-DOMAIN REFLECTOMETRY TDR injects a short electromagnetic pulse into a coaxial transmission line consisting in a coaxial cable and a probe (coaxial, multi-rod) filled with or embedded in the material under test and measures the reflected signals from the start and the end of the probe (Fig. 1a). The frequency dependent propagation velocity, v(f), of the electromagnetic signals is described by equation (1) (Huisman et al. 2003). where c is the speed of light in free space ( m/s), f is the frequency of the electromagnetic wave, ε (f) is the real part of the relative dielectric permittivity, µ r is the relative magnetic permeability and tan δ (equation (2)) is the loss tangent representing the ratio of the imaginary to the real part of the complex dielectric permittivity. where ε p (f) accounts for the dipolar losses due to relaxation, σ dc is the static electrical conductivity and ε 0 is the absolute permittivity of free space ( F m 1 ). The relative dielectric permittivity (hereafter simply referred to as permittivity) is a unitless quantity representing the ratio between the absolute permittivity of the material (F/m) and the absolute permittivity of free space (F/m). With the exception of some igneous rocks and soils rich in ferromagnetic materials (Cassidy 2008), the relative magnetic permeability is assumed to be equal to 1 (Huisman et al. 2003). In low conductive soils with modest clay content, the loss tangent becomes negligible at the higher frequencies ( GHz) used by TDR and equation (1) can be simplified to equation (3). where ε a is the apparent permittivity measured by TDR. The term apparent is used to identify the TDR-measured permittivity, which is approximated to the real part for practical applications but also comprises the losses due to conductivity and the dipolar (1) (2) (3) FIGURE 1 a) Example of a TDR waveform used to measure permittivity with the tangent method. b) Example of a waveform used to measure ECb, exploiting the reflection coefficient at long distances.

3 Construction and calibration of a field TDR monitoring station 251 losses caused by the bound water present in the soil (Topp et al. 2000). The speed of the signal propagation along the probe rods is v(f) = 2L cal /t, where L cal is the calibrated length of the rods in metres and t is the two way traveltime. L cal is obtained after measurements in reference materials with known permittivity and is very similar to the physical length of the TDR probe. Equation (3) can therefore be rearranged into equation (4). The distance between the two points corresponding to the reflections occurring at the start and at the end of the rods (ct 1 /2 ct 2 /2), is called apparent distance, L app (Fig. 1a), because a propagation velocity factor (ratio between the actual signal velocity and the speed of light in free space) is assumed equal to 1 for convenience in the analysis. Equation (5) is thus used to determine the apparent permittivity measured by TDR. The signal attenuation caused by the conductivity of the material being tested is a potential problem for apparent permittivity measurements because it can cause the end reflection to be nondetectable. This attenuation of the reflection coefficient at long apparent distances can be exploited to measure the soil EC b. It is important to note that TDR measures EC b (bulk electrical conductivity), which in the case of soils comprises the electrical conductivity of both the solid particles and the pore fluid. According to the method proposed by Giese and Tiemann (1975), the resistance of the sample, load resistance R L (Ω), can be determined using equation (6). where Z out is the output impedance of the TDR device ( 50 Ω) and ρ is the reflection coefficient at long distances, where the multiple reflections have vanished and the high frequencies have been attenuated (Fig. 1b). Lin et al. (2008) demonstrated the necessity of correcting the reflection coefficient at long distances using equation (7) to account for deviations from optimal opencircuit measurements (known to vary between for the TDR100 device). where ρ open is the reflection coefficient of an open-circuit measurement, ρ meas is the measured reflection coefficient at long distances and ρ corr is the corrected reflection coefficient to be used in equation (6). Heimovaara et al. (1995) proposed a series resistor model, which included additional resistance parameters due to cables, connectors and multiplexers in the calculation of the sample EC b. (4) (5) (6) (7) According to this model, recently revived by other authors (Lin et al. 2007; Lin et al. 2008; Huisman et al. 2008; Bechtold et al. 2010), the soil EC b is calculated using equation (8). where D is the cable length (m), R c is the cable resistance per unit length (Ω/m), R 0 is the extra resistance (Ω) caused by the TDR device, connectors, multiplexers and probe head and K p is the probe constant (1/m) defined by equation (9). where Z 0 is the characteristic impedance of the probe (Ω) and L is the physical length of the probe rods (m). MATERIALS AND METHODS Experimental development A total of 16 probes were installed in the field, in two vertical arrays of 8 probes. The probes were connected to a Campbell Scientific (Logan, UT) TDR100 unit using two levels of SDMX50 multiplexers and 0.5 m RG58, 50 Ω, coaxial cables (Fig. 2). Three-rod commercial probes (CS645, manufactured by Campbell Scientific, rod length: 75 mm) were connected to the multiplexers with low-loss cables (LMR200DB) approximately 3 m long. Eight probes were connected to one multiplexer and then the two multiplexers were attached to a third multiplexer, thus representing two levels of multiplexers. A netbook was used for the data collection in the field. Three 110 Ah deep cycling batteries were connected in parallel and to the netbook; an extra battery (70 Ah) was used for the TDR100 in order to avoid short circuits in the system. With this setup the equipment had an operating time of 8 days in the field therefore the batteries had to be changed regularly (although this time could have been extended using solar panels). Three USB thermocouples manufactured by Omega Engineering (accuracy ± 1 C) were also connected to the netbook for soil temperature measurements. All the instrumentation was placed in a sealed aluminium container (900 long 640 wide 450 deep, dimensions in mm). The cables were additionally insulated using polyolefin heat shrinkable tubes and run through holes drilled in the walls of the container. The holes were waterproofed with IP68 cable glands and silicon. In order to obtain the measurements Matlab scripts were developed to collect the waveforms automatically in the field. The parameters to be specified were: 1) velocity propagation factor, for simplicity set to unity in order to use apparent distances instead of actual distances. 2) number of averages, set to 50 as a compromise between smooth waveforms and the time necessary to take one measurement. 3) number of data points in each waveform, set to 2048, the maximum allowed by the TDR100, in order to obtain more detailed waveforms. (8) (9)

4 252 G. Curioni et al. FIGURE 2 a) TDR monitoring station installed in the field. b) Schematic of the installation. c) TDR probe with plastic guides used to keep the rods parallel during insertion into the ground. 4) start and length of the waveform plot, identifying the apparent distance from the TDR unit to where the displayed waveform begins and the length of the display window from the start distance, respectively. These values were empirically determined in order to visualize all the elements of interest in the waveform (i.e., to determine the apparent permittivity, the reflection in the probe head (i.e., reference point) and the end reflection need to be visualized (Fig. 1a), while the steady state reflection coefficient at a long apparent distance must be visible in order to determine EC b (Fig. 1b). This results in different start and length values for the two parameters). For apparent permittivity measurements with two levels of multiplexers the start and length were set to 6.4 m and 1.2 m of apparent length respectively. The EC b measurements used a start of 0 and a length of 200 m of apparent length, in accordance with Huisman et al. (2008) and Bechtold et al. (2010). 5) channel of multiplexer/probe. The sampling rate in the field was set to one measurement per probe every hour, both for apparent permittivity and EC b. This sampling rate was shown to be sufficient to detect daily variations of these properties. Calibration for apparent permittivity Every probe was numbered and calibrated in air and distilled water following the procedure reported in Robinson et al. (2003b). Four measurements in air and water were carried out and then averaged in a temperature controlled room at 20 ± 1 C. The water measurements were carried out in a beaker; the temperature of the water was checked before each measurement with a thermometer and was adjusted by leaving the beaker in an incubator for the time necessary to equilibrate at exactly 20 C. The combined use of two levels of multiplexers and short probes did not permit the identification of the end reflection point (Fig. 3). As an alternative, shorted measurements were carried out in air by shorting the rods with aluminium foil. The waveform analysis was performed using the tangent method (Robinson et al. 2003b). An easily recognizable reference point within the probe head was found by crossing a base line and a line tangent to the subsequent rising part of the waveform (Fig. 1a). The position of this reference point does not vary across different measurements because the geometric and dielectric properties inside the probe head are fixed. The end reflection point was identified by crossing a base line and a line tangent to the subsequent portion of the waveform. The apparent distance L t (in Fig. 1a, L t = L 0 + L app ) between the reference point and the end reflection point was calculated from the average of 4 measurements in air (shorted) and water. By setting ε a to 1.00 for air and to for distilled water at 20 C (Chemical Rubber Company 1972) it was possible to calculate the offset distance within the probe head from the reference point and the start of the rods, L 0 (Fig. 1a) and the calibrated length of the rods, L cal according to equation (10). (10) Calibration for bulk electrical conductivity (EC b ) The EC b calibration followed the two-step procedure reported in Huisman et al. (2008) and in Bechtold et al. (2010). The reflection coefficient of an open-circuit measurement, ρ open, to be used in equation (7) according to Lin et al. (2008), was calculated as the average of 96 measurements in air, corresponding to 6 repetitions for each probe with all the multiplexers attached. Eight reference solutions with known EC b were prepared by repeatedly diluting potassium chloride solutions, starting from a 0.15 M solution prepared by adding g potassium chloride to 1 L of distilled water. Each solution was tested three times with both

5 Construction and calibration of a field TDR monitoring station 253 the TDR and a conventional conductivity meter (HI 9033, Hannah Instruments, manufacturer claimed accuracy ± 1%) to obtain the average reference EC b. The measurements were taken at a constant temperature of 21 C, carefully measured and adjusted with the use of an incubator. The start and length parameters defining the dimension of the waveform plot were set to 0 and 200 m of apparent length respectively. The reflection coefficient at long distances was determined by averaging the last portion of the waveform between m of apparent length (Huisman et al and Bechtold et al. 2010) corresponding to the 75 data points between data points 1973 and To achieve more accurate calibrations the number of data points was kept to its maximum of 2048, with 50 averages per waveform (Bechtold et al. 2010). In the first step of the calibration, four low-conductivity solutions with EC b ranging from approximately S/m were used to determine the probe constant, K p, by setting R c equal to zero in equation (8). The reflection coefficient corresponding to these low conductivities ranged between making it possible to neglect the cable and extra resistance parameters (Huisman et al. 2008). The inverse of the probe constant, 1/K p, was resolved from the plot of the TDR sample conductance (i.e., the inverse of the load resistance, 1/R L ) against the EC b of the low conductivity solutions (Fig. 5a). In the second step, the calculated K p was fixed in equation (8) and the additional resistance parameters R c were estimated by using all eight reference solutions with known EC b, with the higher-conductivity ranging from approximately S/m. The extra resistance parameters were estimated by minimizing the sum of the squared residuals between the measured and modelled EC b using the simplex optimization algorithm (Nelder and Mead 1965). The function optim implemented in the stats package in the software environment R was used (Venables et al. 2010). For each probe, optimization was performed on a range of initial R c values and the initial pair that provided the best minimization of the error was selected. As reported in previous studies (Lin et al. 2007; Huisman et al. 2008), R c were both expected to be small positive values therefore the evaluated initial values were between 0 0.5, with increments of 0.01 (Fig. 5b). Waveform analysis The analysis of the waveforms was carried out using scripts specifically developed in the software environment R. For EC b measurements the script automatically evaluated equations (6) (8). The load resistance was computed by averaging the last 75 data points of the waveform as explained above. Apparent permittivity was calculated by identifying the points corresponding to crossing tangents (Fig. 1a) and applying equation (5). The script written performed the following steps: 1) compute the first derivative of a waveform and perform a smoothing average over 100 data points in order to reduce its roughness and improve the identification of the maxima and minima. 2) find the points of inflection in the original waveform located after the reference reflection point and end reflection point (Fig. 1a). This step was achieved by splitting the derivative in two sections and finding the maximum in each section corresponding to the respective point of inflection. 3) empirically identify a suitable range of points before and after the points of inflection and perform a linear fitting across these points to draw tangents. 4) find the minima located before the reference point and the end reflection point in the original waveform and plot horizontal tangent lines. 5) identify the crossing points between tangents, as shown in Fig. 1(a) and calculate their separation, L t. Subtract L 0 from L t to find L app. 6) evaluate equation (5) to obtain the apparent permittivity by using L app calculated above and L cal derived after the air-water calibration (equation (10)). FIGURE 3 Measurements in air with different levels of multiplexers. The shorted measurement in air was used to find the end reflection with two levels of multiplexers attached.

6 254 G. Curioni et al. Laboratory experiments to test equipment A number of tests were carried out in order to quantify the precision and accuracy of the equipment setup and the selected method of analysis. The results of these analyses are discussed later in the paper, in the section called Laboratory tests. The measurements were carried out in a temperature controlled room on the final equipment setup, with two levels of multiplexers and the probes connected to the corresponding channel. A selected probe was also tested with and without multiplexers and both manually, by drawing tangents in Matlab and automatically, using the R scripts. The apparent permittivity measurements were taken in air (shorted), water at different temperatures and acetone. The accuracy of the EC b measurements obtained with the TDR was tested in 11 solutions with different electrical conductivities, measured with a HI 9033 (Hannah Instruments) conventional conductivity meter. Five of these solutions were potassium chloride solutions, the remaining were soil solutions, diluted to a ratio of 5:1, with different electrical conductivities obtained from samples of topsoil, sandy subsoil (from the field trial site) and English china clay treated with different amounts of calcium. The EC b of the fluids ranged from S/m and from S/m for the soil solutions. The precision was tested in air, Leighton Buzzard dry sand, English china clay and in an unclassified clay-based soil in the field. Study site and field installation The TDR monitoring station was installed in the field on the University of Birmingham campus (UK) at the beginning of July 2010, after a warm and dry period (Fig. 4). The soil consists of approximately 0.2 m of topsoil overlying sandy subsoil (> 90% sand and gravel). A 3 m 2 m trench was dug with a small excavator after manually removing the topsoil. The different layers of material were kept separated and were later backfilled in their original order. The TDR probes were pushed horizontally into the ground at 8 different depths up to a maximum depth of 1.08 m. In a few cases, due to the very dry conditions during the installation and due to the presence of gravel that hampered their insertion, the probes were partially pushed into the side of the trench and then buried during backfilling. A second set of 8 probes was installed approximately one metre away on the same side of the trench in order to provide cross-validation of the results and act as a backup in case of equipment failure (Fig. 2b). The probes were inserted with the aid of a small plastic guide that helped to keep the rods parallel (Fig. 2c). The three temperature sensors were buried at different depths close to the second array of probes. Before backfilling each probe was tested with a few sets of measurements. RESULTS AND DISCUSSION Laboratory tests Table 1 reports the results of a series of tests carried out to verify the accuracy of the calibration for apparent permittivity on the monitoring station setup. The variability between probes, expressed as a standard deviation, is caused by inaccuracies during the calibration procedure, experimental error during the test (for instance caused by small temperature variations between measurements), errors in the waveform analysis and systematic errors intrinsic in the TDR measurement. A comprehensive FIGURE 4 Location of the TDR monitoring station.

7 Construction and calibration of a field TDR monitoring station 255 TABLE 1 Variability and accuracy of apparent permittivity measurements for the 16 probes used in the monitoring setup Material Std. dev. on the 16 probes mean difference between measurements and reference (error) Std. dev. of the error acetone (25 C) 0.29 (1.38%) 0.28 (1.35%) 0.18 (0.90%) water (10 C) 0.30 (0.37%) 0.38 (0.46%) 0.29 (0.35%) water (25 C) 0.43 (0.55%) 0.33 (0.42%) 0.26 (0.34%) air (shorted) 0.06 (6.17%) 0.05 (5.10%) 0.03 (3.33%) Mean 0.27 (2.12%) 0.26 (1.83%) 0.19 (1.23%) TABLE 2 Precision and accuracy of apparent permittivity measurements carried out in 10 repetitions with a single probe, with no multiplexers (mux0) and with two levels of multiplexers (mux2), with manual and automatic analysis of the waveforms Material Std. dev. on 10 repetitions (precision) mean difference to reference (accuracy) mux0 manual Acetone (25 C) 0.10 (0.46%) Water (10 C) 0.35 (0.42%) Water (25 C) 0.20 (0.25%) Air (shorted) 0.03 (3.31%) Mean 0.17 (1.11%) mux0 script 0.10 (0.46%) 0.38 (0.46%) 0.11 (0.14%) 0.01 (1.30%) 0.15 (0.59%) mux2 manual 0.20 (0.98%) 0.48 (0.58%) 0.40 (0.52%) 0.03 (3.39%) 0.28 (1.37%) mux2 script 0.11 (0.54%) 0.28 (0.34%) 0.27 (0.34%) 0.02 (2.23%) 0.17 (0.86%) mux0 manual 0.13 (0.61%) 0.83 (0.99%) 0.20 (0.25%) 0.03 (2.73%) 0.30 (1.15%) mux0 s cript 0.32 (1.54%) 0.49 (0.58%) 0.58 (0.73%) 0.04 (3.91%) 0.36 (1.69%) mux2 manual 0.20 (0.99%) 0.67 (0.80%) 0.41 (0.52%) 0.03 (2.66%) 0.33 (1.24%) mux2 s cript 0.12 (0.58%) 0.25 (0.30%) 0.22 (0.29%) 0.05 (5.04%) 0.16 (1.55%) investigation of these sources of error was beyond the scope of this study. The experimental errors during calibration and measurements were reduced by using a rigorous laboratory procedure and by averaging at least three measurements every time. The random systematic error associated with the device was minimized by taking the average of 50 measurements for each waveform. Overall, all the TDR probes performed similarly with a mean standard deviation for all the probes of 0.27 (2.12%). The mean accuracy, which comprises all the sources of errors described earlier, was expressed as the absolute difference between the measured apparent permittivity and reference permittivity values reported in Chemical Rubber Company (1972) (acetone at 25 C: 20.70, water at 10 C: 83.83, water at 25 C: 78.54, air: 1.00). The results show that this difference is below 0.38, or in other words 5.10% for all materials, which is regarded as an acceptable accuracy for practical applications, demonstrating that TDR can provide a high level of accuracy for soil permittivity measurements. It is important to note that a rigorous and direct comparison between the reference values and the measured permittivity is not possible because TDR measures an apparent permittivity, while the reference permittivity refers to the real component only, at a specific frequency. Acetone and water were chosen as reference values because they are not dispersive and their imaginary permittivity component is negligible in the TDR frequency range (Robinson et al. 2003b). As can be seen in Table 2, which shows the performance of an arbitrarily selected probe, the standard deviation of measurements taken in repetitions is generally low, demonstrating a good consistency in the TDR measurements. Similar standard deviation values, of the order of 0.10, were obtained from measurements (not shown) in dry Leighton Buzzard sand, wet English china clay and in an unclassified clay-based soil in the field. When compared to reference values, the absolute error is confirmed on average to be lower than 0.36 (1.69%). The higher inaccuracy in air (up to 5%) is due to the very low permittivity of air, which corresponds to a short apparent length along the rods (L app ). A small error in the identification of the start and end reflection points will have a greater impact in the calculation of apparent permittivity compared to materials with a longer apparent length. In other words the percentage accuracy of the TDR equipment used is reduced in materials with low permittivity. Despite the attenuation caused by the two levels of multiplexers, clearly shown in Fig. 3, the use of multiplexers does not have a substantial impact in the precision and accuracy of the measurements (Table 2). As expected, the automatic analysis of the waveforms shows an improvement in precision, since it eliminates the error introduced by human interpretation but does not always give better accuracy when compared to manual interpretation. The script is empirically adjusted to draw tangents in the right position

8 256 G. Curioni et al. by selecting a suitable range of data points around the inflection points. If the shape of the waveform changes, the range of points used in the linear fitting might become less adequate, leading to slightly inaccurate results. However, an automatic analysis of the waveforms is necessary in field monitoring, when large amounts of data are collected. Regular visual checks of the waveforms and tangents can indicate when it is necessary to adjust the range of data points to be fitted in the script. This allows flexibility and improves the accuracy of the measurements. The mean reflection coefficient at a long distance from 96 open measurements carried out in air with all the probes was with a standard deviation of This value was used as ρ open in equation (7). The standard deviation on a number of EC b measurements carried out in air, sand and clay was S/m, which is an indication of the TDR resolution for EC b measurements. Figure 5(a) shows the sample conductance (1/R L ) measured by a selected TDR probe as a function of the known EC b of all the reference solutions. The simplex model (grey line in Fig. 5a) agrees well with the measured sample conductance demonstrating it to be appropriate in the two-step calibration procedure. Compared to the information reported in Huisman et al. (2008) for similar cable lengths, the deviation from linearity at higher conductivities is more pronounced here because of the extra resistance caused by the two levels of multiplexers. Figure 5(b) shows combinations of initial R c values for one probe to be used as inputs in the simplex algorithm, noting that an arbitrary selection of these initial parameters can lead to suboptimal minimizations. For this reason it is important to test multiple initial R c values to find the global minimum, which can then be used in the simplex optimization. The global minimum was always found at small initial values (< 0.50) of R c for each probe. When approaching larger initial values of R c, from (not shown), R 0 became negative. For this reason, only the initial values between were evaluated. Table 3 summarizes the probe constant and the initial and FIGURE 5 a) Measured (dots) and modelled (lines) TDR sample conductance (1/RL) as a function of reference ECb; the slope of the linear fitting to the low EC b solutions (solid line) corresponds to 1/Kp (first calibration step); the grey line corresponds to the simplex optimization carried out on all 8 reference solutions (second calibration step). b) Minimization performed with the simplex method on a range of combinations of initial Rc and R0 parameters.

9 Construction and calibration of a field TDR monitoring station 257 optimized resistance parameters for the 16 probes of the monitoring setup. Both R 0 and R c showed a strong variability with a standard deviation greater than 50% and R c rarely matched the values reported by other authors (Reece 1998; Huisman et al. 2008; Bechtold et al. 2010), usually found to be greater than the direct measurements reported by earlier works. These results show that the optimized R c do not represent the actual physical resistance of the cables and attachments. Huisman et al. (2008) suggested treating R 0 as an empirical fitting parameter. From the data collected in this study it appears that both R c must be treated as empirical fitting parameters. R c are the result of a fitting procedure and therefore their high variability is caused by the uncertainty associated with the fitting (linear fitting for the estimation of K p and non-linear fitting in the case of the simplex). The experimental error associated with the measurement of R L (equation (6)) by the TDR and reference EC b (equation (8)) by a standard conductivity meter, are both affecting the quality of the fitting. In addition, as shown in Fig. 5(b), there are several pairs of initial resistance parameters that could lead to similar minimizations but the selection of the initial pair will affect the estimated parameters. However, since the function minimum is similar for a range of initial parameters, the quality of the fitting remains comparable for several combinations of R c that produce similar minimizations and will not depend on their absolute values. Thus, the reliability of the results is not necessarily influenced by the variability of R c. The two-step calibration procedure used for the estimation of EC b provides a high level of accuracy, as shown by the low error values in Table 4. The accuracy is expressed as the difference from the TDR measurements and the reference values obtained with a conventional conductivity meter. Deviation from the reference values increases substantially with increasing EC b. However, the overall accuracy expressed as a percentage remains similar for the whole range of electrical conductivities (Table 4), with a mean value of 3.16% and a standard deviation of 1.41%. Only at very low EC b, smaller than S/m, does the error increase substantially to more than 7%. This could be related to the sensitivity of the TDR instrument. However, at this low electrical conductivity range, it is possible that the reference values measured by the standard conductivity meter are less accurate and therefore, the error measured by TDR could be overestimated. It is worth noting that at electrical conductivities higher than 0.5 S/m the TDR is unreliable for apparent permittivity measurements because the end reflection point becomes indistinguishable. In such cases the TDR loses its ability to accurately measure the apparent permittivity but can still provide measurements of the EC b with a reasonable accuracy ( 3%). Field data from the monitoring station This section presents some data from the field monitoring station to demonstrate the quality of the data being obtained. Figure 6 shows an example of the data obtained from the field monitoring TABLE 3 Probe constant, Kp (1/m), initial and optimized resistance parameters, Rc (Ω/m) and R0 (Ω), with their mean and standard deviation for the 16 probes of the monitoring setup Probe K p (1/m) Initial R c (Ω/m) Initial R 0 (Ω) Optimized R c (Ω/m) Optimized R 0 (Ω) average st.dev (58.13%) 0.13 (68.73%)

10 258 G. Curioni et al. TABLE 4 TDR ECb accuracy calculated from the average of the measurements carried out with the 16 probes of the monitoring station. A range of potassium chloride and soil solutions (dilution 1:5) were tested with a conventional conductivity meter (HI 9033, Hannah Instruments) to provide these reference values. The samples represent natural soil (subsoil and topsoil), pure English China Clay (ECC) and potassium chloride solutions (KCl) Sample mean HI mean TDR mean error: mean difference Std. dev (S/m) (S/m) ρ corr to reference (S/m) of the error ECC (7.58%) (2.49%) subsoil (7.48%) (3.99%) subsoil (2.51%) (1.35%) topsoil (1.46%) (0.96%) topsoil (1.80%) (1.27%) ECC (1.15%) (0.52%) ECC (2.83%) (1.21%) KCl sol (2.40%) (0.86%) KCl sol (1.57%) (0.68%) KCl sol (2.85%) (0.60%) KCl sol (3.13%) (1.55%) mean 3.16% 1.41% During this period two main rainfall events occurred and were measured by a nearby weather station. The first rainfall event lasted 17 hours, starting from 00:50 on 1 st October, with a cumulative rainfall of 25.8 mm. The second lasted approximately 10 hours and occurred between 04:35 14:00 on 3 rd October, with a cumulative precipitation of 16.6 mm. Figure 7 shows the sudden increase in apparent permittivity for the shallower probes following the rainfall. Also evident is a smaller increase in apparent permittivity measured by the deeper probes. This occurs several hours after the rainfall event and this delay can be seen to increase with increasing depth. In addition, it can be seen in Fig. 7 that the EC b at different depths does not increase uniformly and there seems to be a more conductive layer between m depth. This layer was not visually obvious during the probe installation and due to the coarse nature of the material, although samples were taken, these were disturbed and so the fabric could not be preserved. This meant that laboratory testing could not be conducted to prove this. Such information can be useful for GPR applications, since weather events can affect the performance of GPR caused by the changes in permittivity and EC b in the soil, the extent on which depends on the composition of the soil. A sampling rate of one measurement per hour allows these changes to be tracked with sufficient detail. Figure 7 also shows the need for two vertical arrays of probes to cross-validate the results. Since the probes measure small volumes of soil, they are sensitive to the small-scale spatial variability of the soil properties. Two arrays do not provide enough information to study the spatial distribution of these properties but can demonstrate the existence of similar trends in the data. Figure 7 seems to indicate the presence of different trends of apparent permitstation corresponding to specific depths, for a period of one week where no rain occurred. To test the consistency of apparent permittivity measurements in the field, a linear regression was performed on the data (solid lines in Fig. 6a). The standard error of the residuals is , and for the probes at 0.07 m, 0.60 m and 1.08 m depth, respectively. These values agree well with the standard errors reported by Heimovaara and Bouten (1990) and Menziani et al. (1996) and demonstrate the high precision that may be obtained using TDR. Figure 6(b) shows irregular EC b data for the same period for one set of probes. This is caused by daily temperature variations as shown by the sinusoidal behaviour of both the shallower TDR probe (0.07 m) and the temperature sensor (0.16 m). The influence of temperature reduces with depth as the temperature variability decreases, hence the consistent sinusoidal pattern evident for shallower depths becomes less pronounced, making it more difficult to interpret the relationship between EC b and temperature. As a consequence, the EC b measurements at higher depths become noisier, resulting in a decrease of accuracy. The decrease in accuracy with increasing depth is not thought to be related to the sensitivity of the instrument because similar results were obtained for other probes at greater depth but with higher EC b. The standard error of the linear regression performed on the probes at 0.42 m and 1.06 m depth is and respectively. However, this is still considered a good level of accuracy. In practical terms, it is reasonable to say that the equipment in use is able to detect changes of 0.3 units of apparent permittivity and of 0.5 ms/m of EC b. Figure 7 shows the profile of apparent permittivity and EC b with depth of the two arrays installed in the ground. The data refer to a period of 4 days starting from 00:00 on 1 st October

11 Construction and calibration of a field TDR monitoring station 259 tivity and EC b. However, a detailed look shows that these parameters are linked, both increasing with rainfall events. Due to the sandy and gravelly nature of the soil, the absolute EC b values are very low and their response to precipitation events remains small. However, apparent permittivity and EC b show similar trends in a deeper and more conductive layer. The use of multiple probes allows the detection of variations with depth. The wetter and more conductive horizon (Fig. 7) present between m of depth might not have been detected if a smaller number of probes were used. Installing horizontal probes has the disadvantage of being laborious and disruptive but allows more flexibility in the choice of the position of the sensors compared to measurement systems inserted from the ground surface. In addition, horizontal probes are less affected by possible preferential water paths occurring down the side of vertical probes (Topp et al. 2003). CONCLUSIONS The potential of using TDR for geophysical monitoring was evaluated in a field case study. Despite the wide use of TDR to FIGURE 6 a) Apparent permittivity and b) ECb and temperature measurements from selected probes at specific depths in the field over a period of one week with no rainfall. Linear regression (solid lines) was used to determine the standard error of the residuals in order to know the precision of the TDR measurements in the field. FIGURE 7 Apparent permittivity and ECb vertical profiles obtained from both arrays installed in the field, for a period of 4 days starting from 1st October 2010.

12 260 G. Curioni et al. monitor soil water content, its capability can be exploited for the direct monitoring of the geophysical properties of the soil. At present, geospatial geophysical records are sparse and inconsistent. There is a need to collect direct geophysical data in the field in order to improve the understanding of the geophysical properties of soils and their relationships to geotechnical soil parameters. This can eventually facilitate the application of shallow geophysical techniques such as GPR. The ability to gather precise and accurate TDR data was evaluated. Good reliability was achieved both in laboratory tests and in the field after careful calibration for both apparent permittivity and EC b, based upon the most recent methodologies. Due to the attenuation caused by two levels of multiplexers, the airwater calibration for apparent permittivity was performed with shorted measurements in air. The low standard deviations measured in the laboratory (on average < 2% for both apparent permittivity and EC b ) and the low standard error of the linear regressions conducted on the field measurements ( 0.1 for apparent permittivity, 0.2 for EC b ) demonstrated a high consistency in measurement. The mean errors compared to the reference values were smaller than 2% and 3% for the apparent permittivity and EC b measurements, respectively. However, higher errors of up to 5% were measured in media with very low apparent permittivity (i.e., air, with a permittivity of 1.00) and up to 7.5% in low EC b solutions (< S/m). In addition, at EC b higher than approximately 0.5 S/m, the ability of TDR to measure apparent permittivity is compromised since the waveforms attenuate to the point that the end reflection becomes undistinguishable. This level of EC b can be considered as a constraint of the experimental setup used in this study. The paper has also shown that the addition of two levels of multiplexers combined with short cable lengths ( 4 m) does not seem to have an impact on the accuracy and precision of the TDR measurements. An automatic script for waveform analysis is necessary in field monitoring and the procedure followed was shown to be more precise and at least as accurate when compared to manual analysis. The method for EC b calibration recently developed by Huisman et al. (2008) was evaluated and proved suitable for obtaining accurate EC b measurements with TDR. It was found that both the series resistance parameters R c used in the EC b measurements have to be treated as empirical fitting parameters and do not represent the actual physical resistance of the cables, connectors and multiplexers. A small subset of the field data has been reported to demonstrate the capability of TDR to detect changes corresponding to rainfall events. A sampling rate of one measurement per probe per hour was enough to detect these variations. The use of two arrays consisting in 8 TDR probes installed horizontally allows the definition of detailed vertical trends in the soil. Due to the small volume of soil measured by the TDR probes used in this work, two arrays were considered necessary to confirm the existence of such trends and provide confidence in the measurements. ACKNOWLEDGEMENTS The authors acknowledge the financial support provided by the UK s Engineering and Physical Sciences Research Council (EPSRC). The authors also acknowledge the research team associated with the Mapping the Underworld project for their helpful support and advice. REFERENCES Baker J.M. and Allmaras R.R System for automating and multiplexing soil moisture measurement by time-domain reflectometry. Soil Science Society of America Journal 54, 1 6. Bechtold M., Huisman J.A., Weihermüller L. and Vereecken H Accurate Determination of the Bulk Electrical Conductivity with the TDR100 Cable Tester. Soil Science Society of America Journal 74, Cassidy N.J Electrical and magnetic properties of rocks, soils and fluids. In: Ground Penetrating Radar Theory and Applications (ed. H.M. Jol.), pp Elsevier Science. Chemical Rubber Company Handbook of Chemistry and Physics. 53rd edition Dalton F.N., Herkelrath W.N., Rawlins D.S. and Rhoades J.D Time-domain reflectometry: Simultaneous measurement of soil water content and electrical conductivity with a single probe. Science 224, Giese K. and Tiemann R Determination of the complex permittivity from thin-sample time domain reflectometry improved analysis of the step waveform. Advances in molecular relaxation and interaction processes 7, Heimovaara T.J. and Bouten W A computer-controlled 36-channel time domain reflectometry system for monitoring soil water contents. Water Resources Research 26, Heimovaara T.J., Focke A.G., Bouten W. and Verstraten J.M Assessing temporal variation in soil water composition with time domain reflectometry. Soil Science Society of America Journal 59, Huisman J.A., Hubbard S.S., Redman J.D. and Annan A.P Measuring soil water content with ground penetrating radar: A review. Vadose Zone Journal 2, Huisman J.A., Lin C.P., Weihermüller L. and Vereecken H Accuracy of bulk electrical conductivity measurements with time domain reflectometry. Vadose Zone Journal 7, Jones S.B., Wraith J.M. and Or D Time domain reflectometry measurement principles and applications. Hydrological Processes 16, Lin C.P., Chung C.C., Huisman J.A. and Tang S.H Clarification and calibration of reflection coefficient for electrical conductivity measurement by time domain reflectometry. Soil Science Society of America Journal 72, Lin C.P., Chung C.C. and Tang S.H Accurate time domain reflectometry measurement of electrical conductivity accounting for cable resistance and recording times. Soil Science Society of America Journal 71, Menziani M., Rivasi M.R., Pugnaghi S., Santagnelo R. and Vincenzi S Soil volumetric water content measurements using TDR technique. Annuali di geofisica (Annals of geophysics) 39, Metje N., Atkins P.R., Brennan M.J., Chapman D.N., Lim H.M., Machell J. et al Mapping the underworld State-of-the-art review. Tunnelling and Underground Space Technology 22, Nelder J.A. and Mead R A simplex method for function minimisation. Computer Journal 7, Reece C.F Simple method for determining cable length resistance in time domain reflectometry systems. Soil Science Society of America Journal 62,