Published online 25 February 2008
Published in Vadose Zone J 7:208-214 (2008)
DOI: 10.2136/vzj2007.0132
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: GROUND PENETRATING RADAR IN HYDROGEOPHYSICS
Evaluating Ground Penetrating Radar Use for Water Infiltration Monitoring
Albane Saintenoy*,
Sébastien Schneider and
Piotr Tucholka
UMR 8148 CNRS-UPS, Laboratoire IDES, Université Paris Sud 11, Bâtiment 504, 91405 Orsay cedex, France
* Corresponding author (Albane.Saintenoy{at}u-psud.fr).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 23 July 2007.
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ABSTRACT
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Ground penetrating radar (GPR) was tested to monitor water infiltration in sand. Water was injected down an 81-cm-long tube placed in a hole, with a piezometer recording the depth of water and a tap valve used to adjust it to 15 cm ± 2 cm above the bottom of the tube. During the 20 min of infiltration, a GPR system recorded a trace every second, with its transmitter and receiver antennae at a fixed offset position on the surface. The signal, enhanced by differential correction, allowed tracing of the evolution of the top and bottom limits of the water bulb in space and time. Comparison with hydrodynamic modeling of the infiltration process and simulated radargrams proved that the GPR reflections traced the wetting front and the saturation bulb. A quantified estimation of the evolution of the top border of the wetting zone is provided.
Abbreviations: GPR, ground penetrating radar
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INTRODUCTION
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The accurate description and understanding of near-surface water distribution and dynamics are important for effective cleanup of contaminated sites, agricultural issues, and environmental management of water and land resources (Hopmans and van Genuchten, 2005). In this context, an active area of research concerns the local estimation of the hydraulic functions characterizing the vadose zone behavior.
From the hydrologic point of view, various designs may be used to measure in situ the hydraulic parameters of an unsaturated soil. One of them is the triple-ring infiltrometer at multiple suctions (TRIMS) as conceived by Clothier and White (1981) and Perroux and White (1988). While tension infiltrometer experiments provide relatively quick estimates of hydraulic properties, they can be used only at the soil surface. By comparison, another method based on a modified cone penetrometer, called the cone permeameter (Gribb, 1996; Gribb et al., 1998), was designed to inject water under a known pressure into the soil under the surface, usually at a depth around 1 m; the cumulative inflow volume and pressure heads at two locations above the source are then measured during the water injection. There are several codes for modeling fluid transport in the ground; among them, a finite element modeling code, HYDRUS, has been developed by 
imunek et al. (1996). Using an inverse code based on HYDRUS, imunek and van Genucthen (1996), imunek et al. (1999), and Kodesova et al. (1999) analyzed TRIMS and cone permeameter data via parameter optimization.
From the geophysical point of view, ground penetrating radar (GPR) is a useful method for investigating near-surface water distribution and dynamics. Indeed, GPR data are highly sensitive to variations of the dielectric permittivity (Saintenoy and Tarantola, 2001), the latter being directly related to the water content, e.g., Ledieu et al. (1986) and Topp et al. (1980). The use of GPR for measuring soil water content is now well established, and reviews of the different existing methods were given by Huisman et al. (2003) and Annan (2005).
Monitoring soil water content variations using GPR has also been attempted to study the hydrologic response to an external stimulus such as water infiltration or pumping. In particular, time-lapse GPR surveys allowed mapping of fluid drainage during a pumping test (Tsoflias et al., 2001). Radar transmission measurements between boreholes have also been used to characterize the change in moisture content in unsaturated sandstone due to a controlled water tracer injection (Binley et al., 2001). More recently, joint use of time-lapse cross-borehole transmission GPR travel times and hydrologic information from neutron log and infiltration measurements allowed the determination of field-scale soil hydraulic parameters (Kowalsky et al., 2005).
The main limitation of GPR use is the medium attenuation, which affects the investigation depth. Using borehole antennae, one can characterize the subsurface to a substantial depth but, of course, limited to the space close to the borehole locations. By comparison, off-ground GPR data can be acquired on large areas with a high spatial resolution and, using only the first reflection amplitude variations, the water content variations from the very near surface can be estimated (Lambot et al., 2004a,b, 2006). Also, in a quite electrically resistive medium like sand, with no magnetic properties, surface-based GPR data can have a penetration depth of at least 10 wavelengths of the sounding wave (typically 1.5 m of penetration using an 800-MHz antenna). Many surface-based GPR studies have been reported in the literature in such low attenuating media, including in particular three-dimensional reconstruction of the underground heterogeneities (Heincke et al., 2005). In more conductive media, the ground wave can be used (Grote et al., 2003).
Many GPR data modeling codes have been developed (Bergmann et al., 1998; Rejiba et al., 2003; Carcione, 1996; Bourgeois and Smith, 1996; Powers, 1997). In particular, the GprMax suite of programs, based on finite difference time domain modeling, allows the simulation of realistic scenarios encountered in everyday use of GPR (Giannopoulos, 2005).
In this study, we investigated the use of surface-based GPR to detect and monitor the water bulb formation during a water infiltration experiment in sand around 80 cm deep below the surface. We used hydrodynamic numerical modeling to calculate the water content distribution evolution around the injection point in space and in time. As expected, the transition between unsaturated and saturated media is gradual, resulting from capillary action in medium to fine sands. We modeled synthetic GPR data to analyze the GPR response on such a gradual change, and to interpret our field data.
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Field Experiment
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The experiment took place in a sand pit nearby Cernay-la-Ville in France. This site is located in Fontainebleau sands of Stampian age, a marine facies reworked by wind in upper Oligocene with dunes formation (Schneider, 2006). These sands are normally composed of 99% quartz. Nine soil samples of known volume were extracted using a manual auger every 10 cm down to 80 cm. The laboratory analysis of these samples indicated that their average porosity was 0.43 and the initial moisture content was 0.045. Their average particle density was 2.48 ± 0.03. A granulometric analysis showed that 10% of the grains had a diameter less than 0.125 mm and 86% less than 0.16 mm. These values are typical for Fontainebleau sands.
A 4-cm-diameter and 81-cm-deep vertical hole was dug with a manual auger and a polyvinyl chloride tube of the same length and diameter was placed in the hole. The end of a 6-mm hose connected via a tap to a graduated container of 15 L of water was inserted into the hole all the way to the bottom (Fig. 1
). During the water injection, the water level at the bottom of the hole was monitored by a piezometer, and manually maintained by the operator at 15 ± 2 cm, using the tap to control the water flow from the water tank through the hose. The cumulative volume of injected water was manually recorded (Fig. 2
). After a transient phase of infiltration during the first 210 s, a steady-state flow rate was obtained. After 1280 s, the tap was closed; the piezometer indicated that there was no water left in the hole at time t = 1300 s.
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FIG. 1. Experiment setup: water was injected down the 81-cm-long tube inserted in a hole while a pair of transmitter and receiver antennae (S and R, respectively) were recording a trace from the surface at 1-s intervals. The piezometer recorded the depth of the water in the tube. A tap regulated the water flux to keep the water level at 66 cm below the surface.
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All radar measurements were made using a MALÅ RAMAC system (MALÅ Geoscience, Malå, Sweden) centered on 800 MHz in coplanar transverse electric mode. During the infiltration, GPR data were acquired for tracing in time the effects of water injection, using a static setup of one transmitter and one receiver antenna placed on the surface 38 and 52 cm, respectively, away from the injection hole (Fig. 1). The system was set to acquire a trace every 1.3 s. We kept recording static data until t = 1730 s.
To characterize the spatial distribution of radar reflections, surface-based GPR traces were also acquired along 34 parallel lines spaced every 3 cm. On each section, 50 traces were recorded, one every 3 cm. Thus a pseudo-three-dimensional set of radar data was obtained for a 100- by 150-cm rectangle, taking about 20 min to record. This data set was acquired twice: before the injection tube installation, and after the water infiltration experiment, at time t = 1730 s. The difference between the two cubes of data has been used to enhance the variations in GPR data due to the water infiltration.
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Hydrodynamic Modeling
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To get an a priori model of the water distribution in space and time, we simulated the water flow within the geometry of our infiltration experiment. Assuming a homogeneous medium, the system exhibited a radial symmetry around the vertical line centered on the injection hole. Writing the Richards equation using three-dimensional radial coordinates, no variations in the azimuth angle was considered and the computation reduced to a two-dimensional problem that could be simulated efficiently by HYDRUS-2D (imunek et al., 1996), with the axysymmetrical vertical flow option turned on.
Our mesh was created on a 1- by 2-m zone. The infiltration occurred at 81-cm depth through a 2-cm-radius circular surface with a constant potential head of 15 cm for 0 
t 1281 s. The initial conditions were set at pressure head h = –200 cm at ground level with a linear distribution down to h = –100 cm at 1-m depth. A free-drainage boundary limited the bottom and no flux was considered through the ground interface and the sides of our domain. After the end of infiltration, the modeling went on for 1281 t 1791 s to simulate water redistribution.
The main hydraulic properties of a soil are described by the two relations K(h) and 
(h), which are, respectively, the hydraulic conductivity and the water content as a function of the potential head h. The model of Mualem and van Genuchten (1980) was chosen to describe those two relations. It involves six parameters: the residual water content r, the saturated water content s, the saturated hydraulic conductivity Ks, the connectivity parameter l, and the parameters 
and n, which are related to the inverse of the air-entry value and to the width of the pore size distribution, respectively. The exact values of those parameters for the sand in which we were doing our infiltration were not exactly known. We decided to use r = 0.045 and s = 0.43, as estimated from our sample measurements. We took = 0.145 cm–1, n = 2.68, and l = 0.5, which are typical values for a sandy textured soil (Carsel and Parrish, 1988). Schneider (2006) gave Ks = 0.032 cm s–1 as in the range of Ks for Fontainebleau sands. Let us emphasize again that the idea of this simulation was just to obtain a rough qualitative description of the water distribution in the geometry of our infiltration.
Results of the simulation are presented in Fig. 3
and 4
. In Fig. 3, isolines of = 0.05 (plain lines) represent the wetting front at different time steps, whereas isolines of = 0.425 (dotted lines) delimit the water-saturated zone. We observed a wetting bulb with an ellipsoidal shape significantly growing with time while the water-saturated zone stayed confined in the vicinity of the injection hole (< 8 cm). This fact is illustrated in Fig. 4 by superposing water content profiles at three different times along the line A–B–C. The volumetric water content was converted to relative dielectric permittivity 
r using the empirical easy-to-use relation proposed by Ledieu et al. (1986). The calculated r varied in the range from 4 to 30.
Simulations with other sets of hydraulic parameters showed that the shape of the water bulb remained more or less ellipsoidal, depending, as expected, on the capillarity of the medium. Independently from the exact shape of the water bulb, three regions can be defined in Fig. 3 and 4: the water-saturated zone, the undisturbed external zone, and the transition zone between the two. In all our simulations, the simulated saturated zone always stayed very close to the infiltration point when the transition zone width was increasing with the infiltration time.
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GPR Data Simulations
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We used GprMax2D (Giannopoulos, 2005) to compute synthetic radargrams. In this analysis, we assumed the electrical conductivity to be infinitely low, so that the attenuation of the radar signals through ohmic losses was negligible. We also took the relative magnetic permeability to be equal to 1 in all considered media.
Transition-Zone One-Dimensional Modeling
The transition from an unsaturated to a saturated sand presents gradations. Annan et al. (1991) explained that the amplitude of the GPR reflection for such a gradual change depends on the ratio of the transition thickness to the electromagnetic signal wavelength. Looking for the water table is then not always feasible because of the weakness of the reflection, as described by Loeffler and Bano (2004).
We simulated surface-based GPR reflections on one-dimensional models presenting a transition zone between two homogeneous media, as described in Fig. 5
. The mesh was set to 5 mm in a domain of 3 by 1.6 m. The computation time step was 9.435 x 10–12 s. The source waveform was a Ricker centered on 800 MHz. Two cases were considered: in Model 1, the transition zone was composed of 25 layers with a 5-mm thickness and a relative dielectric permittivity increase of 1 from one layer to the other. Given the grid step value, this is equivalent to a continuous model. In Model 2, the transition zone was one homogeneous 12.5-cm-thick layer with a relative dielectric permittivity of 17.2. This value is such that the time needed for the electromagnetic wave to go through this homogeneous layer was the same as the time to go through the 25 layers of Model 1. Other relative dielectric permittivity values were chosen in the range shown in Fig. 4.
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FIG. 5. One-dimensional models created to study the transition zone effect on ground penetrating radar data. In Model 1 (dashed line), the transition zone is made of 25 layers of 5-mm thickness with a relative dielectric permittivity increase from 5 to 31 with a step of 1. In Model 2 (plain line), the transition zone consists of a single homogeneous layer of relative dielectric permittivity 17.2 with a thickness of 12.5 cm.
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Supposing a transmitter and a receiver at the surface with a 14-cm offset, Fig. 6
shows the comparison between the two simulated traces with Models 1 and 2. The gradational transition is creating two reflections, which superpose with the two expected reflections on the two interfaces of the homogeneous transition. The reflection amplitudes for Model 2 are higher than for Model 1, as expected. Anyway, amplitude modeling was not our goal, as we were only interested in a qualitative description of radargrams. Our simulations allowed the use of a single intermediate homogeneous layer as a simple but satisfactory model for a transition with gradations.
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FIG. 6. Simulated traces for Model 1, in which the transition zone is made of 25 layers, and Model 2, in which the transition zone consists of a single homogeneous layer.
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Transition-Zone Two-Dimensional Modeling
We created a two-dimensional model with a cylinder of relative permittivity 28, embedded in another cylinder of relative permittivity 15, both cylinders being centered at 81-cm depth in a medium of relative dielectric permittivity 5 (Fig. 7
). The transmitter and receiver antennae were placed at the surface using the same geometry as presented in Fig. 1. Fifteen synthetic traces corresponding to cylinder radius varying from 2 to 30 cm were simulated (Fig. 8
). The inside cylinder (representing the water-saturated medium) stayed within a radius of 6 cm. Since we were interested only in qualitative results, two-dimensional modeling with estimated parameters was sufficient.
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FIG. 7. Model geometry used for ground penetrating radar data simulations, where S and R are the transmitter and receiver antennae, r are the dielectric permittivities, R is the radius of the external cylinder, and A, B, C, and D are zones of reflection of the electromagnetic wave.
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FIG. 8. Simulated traces corresponding to the model used for ground penetrating radar simulations (Fig. 7). Each trace corresponds to a cylinder radius R in the range 2 to 30 cm. No amplitude gain was applied. The main reflections are named A to E.
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For interpretation needs, we have noted the interesting features of Fig. 8 using the letters from A to E. Corresponding reflecting zones are noted A to D on Fig. 7. Reflection A corresponds to the external cylinder interface toward the antennae position. This reflection arrived earlier and earlier as the cylinder radius R linearly increased. Reflection D corresponds to the outer interface of the external cylinder. It arrived later and later as R increased. Reflections B and C correspond to the internal cylinder interfaces. The time delay between those two reflections was constant as expected, since we were keeping the internal cylinder radius to 6 cm. We interpret Reflection E as multiple reflections.
The polarity of Reflection A is inverse to the polarity of Reflection D, as expected from reflection coefficient study (Straton, 1941). The same inversion of polarity can be observed on Reflections B and C.
Remembering that no gain was applied, Fig. 8 clearly shows that the amplitude of Reflection D is stronger than that of A; similarly, the amplitude of Reflection C is stronger than that of B. This results from the combined effect of focalization due to the concavity of the cylinder and of the surface wave moving along the cylinder's surface (Rheinstein, 1968).
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Field Data and their Interpretation
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Static GPR Measurements
We processed the raw radar data with residual median filtering (Gerlitz et al., 1993) using a window size corresponding to 150 MHz. Then we subtracted the whole radargram median trace from each trace to highlight differences. The processed radargram is displayed in Fig. 9
, using no amplitude gain. The vertical glitch at t = 760 s corresponds to a small sampling shift in the radar acquisition. This small shift is enhanced by the subtraction of the whole median trace. Apart from this artifact, two reflections appear clearly in these data and are underlined in gray. The upper one arrived earlier and earlier with the infiltration time (from t 
14 ns to t 11 ns). Meanwhile, the bottom one arrived later and later (from t 18 ns to t 25 ns). We relate those two reflections to the ones called A and D on Fig. 8, i.e., to the external wetting front evolution.
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FIG. 9. Recorded traces with fixed antennae during the experiment. The water tap was opened at time 0, closed at 1280 s, and there was no more water at the bottom of the hole at 1300 s. The data has been band-passed and the whole median trace has been removed from each trace to show differences. No amplitude gain was applied. Reflections A and D are highlighted by gray lines.
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A closeup of the first 66 s of the static measurements is displayed in Fig. 10
. On this closeup, we changed the data processing. Instead of subtracting the whole median trace from each trace, we subtracted the median trace computed on a moving window of 30 traces. This processing better highlights the two interesting reflections at the beginning of the static radargram while their travel times are changing significantly. When the variations in travel time become too weak, this processing removes the reflections in which we are interested.
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FIG. 10. Closeup of the recorded traces shown in Fig. 9 with different data processing. The mean of a running 30-trace window was removed from each trace.
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We computed the distance d from the injection point to the reflector responsible for Reflection A, using the picked travel time (upper gray curve of Fig. 9). Lacking a precise zero time measurement, we estimated the crossing point of Reflections A and B at the beginning of the infiltration at 14.8 ± 0.5 ns (Fig. 10). Considering a depth of 81 cm, an apparent velocity was calculated and used to compute d vs. the infiltration time (Fig. 11
). The gap from t = 131 s to t = 262 s is due to the difficulty of picking Reflection A across this interval. Sand layering interfaces could be responsible for interferences. Figure 11 shows a wetting front displacement of 23.5 ± 2 cm during the infiltration experiment.
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FIG. 11. Distance from the injection point to the wetting front in the antennae direction, with its uncertainty as a function of time, retrieved from picked two-way travel times on Reflection A measured in Fig. 9.
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It is more difficult to interpret distance values from Reflection D in Fig. 9. Indeed, the two-way travel time changes during the infiltration are due to two combined effects: (i) the wetting bulb size is increasing, and (ii) the wave velocity inside the wetting bulb is decreasing with increasing water content. More information on the behavior of the electromagnetic wave velocity in relation to the differentiated water content is needed for further interpretation.
In Fig. 9, between Reflections A and D, two reflections could be interpreted as the ones coming from the internal saturated zone, called B and C in Fig. 8.
The GPR Data Cube
The 100- by 150-cm differential data cube is displayed in Fig. 12
. This data set confirms the presence of the reflections on the wetting front upper and lower interfaces (underlined with gray dots). They correspond to Reflections A and D, underlined in gray in Fig. 9, after t = 1300 s. Fitting the upper points with a hyperbolic surface gives a velocity estimation of 0.130 m/ns, with an asymptotic standard error of 0.0014 m/ns. The hyperbolic surface fitting with latter points gives 0.11 ± 0.01 m/ns. This value is less than the above one, as expected if we consider a wet zone between the two reflectors (the wave velocity decreases as the water content increases).
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FIG. 12. Cube of surface ground penetrating radar data obtained by difference between the data sets acquired before and after the water injection. Gray dotted surfaces correspond to the two reflections underlined in gray in Fig. 9 after 1300 s.
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On Fig. 12, traces from the internal saturated zone reflections are not clear. This could be due to the fact that we have acquired the three-dimensional data set too long after the end of the infiltration experiment. We also note that the injection access tube does not appear in two-dimensional sections or on static measurements.
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Conclusions
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We have presented a set of static GPR data acquired during a water infiltration experiment. Repeated recording of one trace from antennae at fixed positions shows two main reflections. From numerical GPR data and hydrodynamic modeling, we interpreted those two reflections as coming from the upper and lower interfaces of the wetting front. The static GPR data also display two weaker reflections that we interpret as coming from the upper and lower interfaces of the water-saturated zone.
At any time we can compute the distance from the injection point to the wetting front toward the antennae. From this computation, we can monitor the displacement of the wetting front as it moves up 23.5 cm between t = 0 s and t = 1450 s, with an estimated accuracy of ±2 cm.
Therefore, surface-based GPR data contain valuable information on the water bulb evolution that could be brought into an inverse hydraulic parameter estimation.
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ACKNOWLEDGMENTS
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We are thankful to A. Zennaki, who participated in the acquisition of the data. We would like to acknowledge as well the contribution from A. Giannopoulos of the 2D FDTD code. A free version of the software GprMax2D may be downloaded from www.see.ed.ac.uk/agianno/GprMax/ (verified 5 Oct. 2007). We are also thankful to the OpenDtect developers for their three-dimensional data visualization tool from www.opendtect.org (verified 5 Oct. 2007), and finally, to J. Stockwell for maintaining the Seismic Unix package, which may be downloaded from www.cwp.mines.edu/cwpcodes/ (verified 5 Oct. 2007).
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TOP
ABSTRACT
INTRODUCTION
