Published in Vadose Zone Journal 3:1106-1115 (2004)
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: HYDROGEOPHYSICS
Imaging of Water Content Distributions inside a Lysimeter using GPR Tomography
Jürgen Schmalholza,*,
Heiner Stoffregenb,
Andreas Kemnac and
Ugur Yaramancia
a Department of Applied Geophysics, Technical University of Berlin, Ackerstrasse 76, 13355 Berlin, Germany
b Department of Soil Physics, Technical University of Berlin, Salzufer 11-12, 10587 Berlin, Germany
c Agrosphere Institute, ICG IV, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
* Corresponding author (schmalholz{at}geophysik.tu-berlin.de)
Received 30 January 2004.
 |
ABSTRACT
|
|---|
In a study to investigate water content distributions inside a lysimeter in a noninvasive manner, we used ground penetrating radar (GPR) tomography. Our main objective was to evaluate the temporal changes and spatial distributions of the volumetric water content after a short but intensive irrigation of part of the lysimeter. High frequency GPR antennas of 1-GHz nominal frequency were used because of the small spatial dimensions of the investigated lysimeter (cylinder of 1.5-m height and 1.2-m diameter) and the desired spatial resolution in the range of decimeters. To ensure a relatively steady distribution of water inside the lysimeter for the time-consuming tomographic survey, simple parallel transmission measurements were used to track the water dynamics. Water contents and water content changes were calculated by means of a mixing formula describing the relation between electromagnetic wave propagation velocity and the water content. The transmission measurements indicate a diffusive process following the irrigation for a duration of several hours. The tomographic measurements clearly show the area of increased water content associated with the irrigation.
Abbreviations: CO, constant offset • CMP, common midpoint • CRIM, complex refractive index method • em, electromagnetic • ERT, electrical resistance tomography • GPR, ground penetrating radar • TDR, time domain reflectometry
|
INTRODUCTION
|
|---|
GROUND PENETRATING RADAR has become a widespread geophysical technique for mapping shallow geological structures (e.g., Davis and Annan, 1989) and for detecting buried objects or contaminants (e.g., Lecomte and Mariotti, 1997). The GPR method utilizes electromagnetic (em) waves of limited bandwidth, which are generated and emitted by a transmitter antenna and detected by a receiver antenna. The employed antenna frequencies range from 10 MHz to gigahertz. The most frequently used antenna configurations are the so-called constant offset (CO) configurations, where transmitter and receiver are moved along a profile with a fixed separation, and the common midpoint (CMP), where transmitter and receiver are moved away in opposite directions from a fixed location. Constant offset configurations are mainly used for mapping subsurface structures (e.g., Gross et al., 2002), whereas CMPs are typically used for velocity analysis (e.g., Fisher et al., 1992). Another GPR application is transmission tomography. Mainly applied between boreholes (e.g., Vasco et al., 1997), tomographic measurements can provide valuable structural information about the investigated area. With the increased focus on interdisciplinary research, including the evolving discipline of hydrogeophysics, and development of antennas with higher nominal frequencies, in recent years more efforts have been directed toward investigations of the shallow subsurface (e.g., Stoffregen et al., 2002; Radzevicius et al., 2003).
Because the difference between the dielectric constant of water (
80) and dry soil (3–5) is significant in the typical frequency range of GPR, GPR is now increasingly used for investigations concerning soil water content or water content variations in different media (Greaves et al., 1996; Dannowski and Yaramanci, 1999). Relatively small changes in the soil volumetric water content can substantially change its dielectric properties. The high dielectric constant of water in the radar frequency range is caused by the dipolar character of water molecules and their tendency to build clusters (von Hippel, 1988).
We report on a tomographic transmission-mode GPR survey conducted on a lysimeter to assess its capability to image volumetric water content distributions with high spatial resolution. The cylindrical lysimeter, an undisturbed sandy soil monolith, had a diameter of 1.2 m and a height of 1.5 m, and in contrast to conventional lysimeters, a plastic casing enabling the use of GPR for tomographic purposes. The data presented were gathered before equipping the lysimeter with partially invasive sensors, such as electrodes for electrical resistance tomography (ERT), time domain reflectometry (TDR) probes, or tensiometers. However, in this paper the volumetric water content is derived from the GPR data only. To obtain reliable water content data, all relevant aspects of the parameter determination are carefully considered.
|
METHODS
|
|---|
Ground Penetrating Radar Principles
Commonly used GPR devices are so-called impulse radar systems, where a short em impulse is generated and emitted via the transmitter antenna. This em impulse travels through the area of interest as an em wave and is then recorded with the receiver antenna. With knowledge of the emission time and the initial intensity of the impulse, the travel time and information regarding the attenuation of the em wave can be gathered (e.g., Valle et al., 1999; Holliger et al., 2001). With the respective transmitter and receiver positions, an inversion can be performed to derive the dielectric properties of cells (i.e., small regions according to a regular parameterization of the medium) traversed by several em waves. To perform an amplitude tomography in a heterogeneous environment with strong changes in its dielectric properties in the vicinity of the transmitter and receiver, thorough knowledge of the antenna characteristics in the near-field is required (Lampe et al., 2003).
In this study, attenuation was not analyzed because of the unknown characteristics of the antennas (shielded 1-GHz antennas by MALÅ GeoScience, Sweden; 0.23-m length and 0.14-m width) and the short travel paths of the em waves. A travel-time tomographic analysis was performed only, yielding the distribution of em propagation velocity in the considered region.
Experimental Setup
The investigated lysimeter was located in a special lysimeter facility at the Agrosphere Institute (ICG IV) of the Forschungszentrum Jülich, Germany. The top of the lysimeter was at the soil surface level to ensure natural conditions and to allow evapotranspiration studies. At the time the GPR measurements were performed, no vegetation was present on the top surface of the soil inside the lysimeter. The body of the lysimeter was placed in an opening in the ceiling of the subsurface facility, with 0.4-m space between the lysimeter and the ceiling (Fig. 1)
. This space enabled the GPR operator to place the antennas at any location on the lysimeter walls. This was a necessity for the tomographic surveys since good accessibility was required for good coverage of the region of interest.
The lysimeter was excavated in the field and constituted a nearly undisturbed soil. The extraction was initiated and performed by the ICG IV Jülich at a well-studied site near Kaldenkirchen, Germany. The most important parameters are given in Table 1 (Pütz and Klimsa, 1991). Extracting the lysimeter ensures near natural conditions inside the lysimeter body without, for example, sedimentation effects that inevitably occur in lysimeters with repacked soil. Usually lysimeters with metal casings are used for the extraction of undisturbed soils, since the lysimeter casing has to be pushed into the soil. However, a metal casing would result in disadvantageous conditions for electrical and electromagnetic measurements and, in particular, would make a tomographic GPR survey impossible. Therefore, to offer maximum operability for the geophysical measurements, the lysimeter wall was made of PVC with 0.025-m thickness.
The lysimeter wall itself has several holes and notches designed to accommodate various sensors for additional measurements. This enables the application of different soil physical and/or geophysical methods at the same time. For instance, TDR probes as well as ERT electrodes, in contrast to GPR, require direct contact with the medium under investigation. However, this extra capability was disregarded in the present study since we tried to avoid any disturbance of the soil due to the insertion of additional sensors.
Air-conditioning of the subsurface facility enables full temperature control and, in particular, storage of the excavated soil under near natural conditions. During the GPR survey, the air temperature in the facility was constant at 14°C, with no significant variations in the weeks before the experiment as well. Therefore, any temperature variations should be negligible, and the soil temperature inside the lysimeter can be assumed to be constantly 14°C.
The coordinate system defined for data acquisition and interpretation is displayed in Fig. 1. The origin of the vertical (z) axis is located at the bottom of the lysimeter (and not at the soil surface). This was reasonable because of the presence of a slight topography at the top surface. Because of relatively short transmission distances of the GPR signal, accurate positioning of the GPR antennas was important.
The tomographic measurements were conducted in vertical and horizontal orientations. In the vertical orientation, transmitter and receiver antennas were moved vertically at fixed, diametrically opposed azimuthal positions to image a vertical cross section through the soil monolith. In the horizontal orientation, transmitter and receiver antennas were moved horizontally at fixed vertical positions to image a horizontal plane through the lysimeter. To ensure as much consistency in the transmitted wavelet as possible, the transmitter antenna was mounted at a designated point with a wooden skid, while the receiver antenna was next placed at different receiver positions. The receiver antenna was moved to each designated location by hand. To ensure consistency in the transmitter and receiver locations, the lysimeter was equipped with several measuring tapes in azimuthal and vertical directions. This enabled precise positioning of the GPR antennas with positioning errors <0.01 m. Before and after each transmitter section was recorded, the receiver antenna was placed directly next to the transmitter antenna to obtain the zero time and to estimate possible drifts of the GPR device during signal recording at the different receiver positions. This ensured elimination of small linear drifts of the GPR device, and identification of larger step-like drifts caused by heavy strain at the GPR cables. The different transmitter and receiver positions were separated by 0.08 m in the horizontal and 0.10 m in the vertical directions, respectively.
|
THEORY
|
|---|
Effect of Water Content on the Propagation Velocity of Electromagnetic Waves
The principles of em wave propagation are described by Maxwell's equations in conjunction with constitutive relations involving the macroscopic, material specific em properties (e.g., Jackson, 1962). Assuming a homogeneous, low-loss medium, the em propagation velocity is
 | [1] |
where vs is the velocity inside the medium, c0 is the vacuum propagation velocity of em waves (0.2998 m ns–1), 
r is the dielectric constant, and µr is the magnetic susceptibility. Equation [1] can be simplified for most soils, where µr generally possesses a value of 1. The dielectric constant, although called "constant," is a frequency-dependent, complex parameter, which can be expressed as (Schön, 1996)
 | [2] |
where 
is the angular frequency, i is the square root of –1, ' denotes the real part and '' the imaginary part of the dielectric constant, 
is the electrical conductivity, and 0 is the permittivity of free space [8.854 x 10–12 (A s)/(V m)]. The dielectric constant shows a dependence on the electrical conductivity and is often referred to as the effective dielectric constant eff(). Likewise the electrical conductivity has a frequency dependence, which can be described as a complex parameter. However, we refrain from introducing such an effective parameter because of the difficult distinction between the complex dielectric constant and the complex electrical conductivity with the frequencies used here. Although only travel times were analyzed, the introduction of the complex dielectric constant is necessary since the real and imaginary parts of the dielectric constant affect one another due to the principle of causality.
When the dielectric constant of water is estimated with the formula given by Kaatze (1989), the real part of the dielectric constant will show a significant decrease beyond frequencies >1 GHz. This effect is coupled with a strong increase in the imaginary part. The imaginary part of the effective dielectric constant is crucial for the attenuation of the em waves. Therefore, the effective depth for GPR measurements in moist media decreases vastly with increasing frequency. The same effect of decreasing measurement depths holds for increasing electrical conductivity (Ulaby et al., 1986). Therefore, the 1-GHz antennas we used provide a good compromise, since lower frequencies would not provide the desired spatial resolution in the range of decimeters, and higher frequencies would not guarantee the required penetration depth. Furthermore, because the real part of the dielectric constant of water is decreasing, the effect of the high real part of the dielectric constant of water on the dielectric constant of the soil decreases with increasing frequencies.
The real part of the effective dielectric constant of saline water is only slightly different from that of pure water. Therefore, in our case we ignore the effect caused by the electrical conductivity of pore water for the travel time tomography. On the other hand, an increase of 10°C has a strong impact on the real part of the effective dielectric constant. Although such a drastic increase in temperature does not occur during field surveys beyond the uppermost regions of the subsurface, or in an air-conditioned facility, those temperature effects should be considered when dealing with relatively small-scale objects such as a lysimeter, or locations with exothermic processes, such as waste disposal sites (Oelsner, 1997).
Since the spectra of the recorded traces are broad (Fig. 2)
, we define a dominant frequency d of the recorded wavelet. This frequency was obtained by picking two or more zero-crossings of the wavelet and deriving the average frequency for these wave periods. This is much easier than analyzing the derived trace spectrum and does not need further additional processing of the data. The low-pass filtering effect of the soil leads to lower observed frequencies than the nominal frequency of the antenna would suggest. The dominant frequency decreases even more with higher water contents since the electrical conductivity of a soil is strongly affected by its water content. Using the dominant frequency, no additional work-intensive analysis of the wavelet dispersion is necessary (e.g., Irving and Knight, 2003); neither information on the emission wavelet nor on the electrical properties inside the lysimeter is required. Although this prevents proper interpretation on the attenuation and transformation of the radar signal, it enables a simple evaluation of the registered wavelet.
View larger version (11K):
[in this window]
[in a new window]
|
Fig. 2. (a) Recorded GPR trace before irrigation with normalized amplitude. (b) Spectrum of the trace displayed in Part a.
|
|
The effective dielectric constant of soil as a mixture of solid matrix, air, and water can be expressed by using the Lichtenecker and Rother formula (Shen et al., 1985) with an exponent of 0.5, which leads to
 | [3] |
where the subscripts s, w, m, and a refer to soil, water, solid matrix, and air, respectively. T represents temperature, 
the porosity of the soil, and S the degree of water saturation of the pore space. Equation [3] is often referred to as the complex refractive index method (CRIM).
After simple rearrangement of Eq. [3], the volumetric soil water content 
can be expressed by
 | [4] |
Since all dielectric constants except the one for water do not show significant dependencies on temperature and the frequency in the covered range, those dependencies were eliminated from Eq. [4]. We used this semiempirical mixing model since it can easily be expanded to multicomponent media, a complex dielectric constant can be implemented, and no further structural parameters have to be included. Although structure-dependent mixing formulas such as Hanai–Bruggeman or Maxwell–Garnett (Sihvola and Alanen, 1991) are more appropriate for the exact determination of the water content of a mixture, in the present case the required parameters cannot be provided with the necessary accuracy.
The different grain-size fractions and porosities of the considered soil for various depths are given in Table 1. Since this information was gathered near the extraction location of the lysimeter, the values in Table 1 were used to estimate the degree of homogeneity inside the lysimeter. Although the average porosity derived from Table 1 is 0.44, the average porosity for the region of interest (0.3 to 0.8 m below surface) is 0.43.
For the interpretation of the data presented here, a homogeneous porosity of 0.43, as the mean value in Table 1, and an average dielectric constant of 5 was used for the soil matrix. The estimate of the dielectric constant of the soil is consistent with measurements by Robinson and Friedman (2003) for soils with similar grain-size fractions. This result is in good agreement with the equation given by Peplinski et al. (1995):
 | [5] |
where 
m is the density of the soil matrix (g cm–3). Using the site-specific average density of 2.75 g cm–3 of the soil matrix, Eq. [5] suggests a dielectric constant of the soil matrix of 4.86.
The simplifications for the porosity and the dielectric constant of the soil matrix smear the results for the derived absolute water content values, but the generated errors regarding the temporal changes and spatial distribution of water content are not affected significantly since it is expected that neither the porosity nor the soil matrix change with irrigation.
Although the mixing formula (Eq. [4]) we used is based on simplified theoretical considerations, the correlation between the investigated dielectric constant and the derived volumetric water content with different mixing formulas are similar within the expected water content range. Figure 3
shows the relationship between the determined dielectric constant of the soil and its volumetric water content. Since there are numerous different mixing models, most of them with different model specific parameters, we chose the empirical equation of Topp et al. (1980) as an initial guide, since this equation is well known and often used. From Fig. 3 it is evident that the shape of the empirical Topp equation (black dashed line) is very similar to those of various CRIM derived relations. Here we chose the CRIM equation with the aforementioned porosity and soil matrix dielectric constant values and dielectric constants of water with an estimated value of 81 (black solid line), as well as derived values for a dominant frequency of 750 MHz and temperatures of 14°C (gray solid line) and 24°C (gray dashed line). Using the estimated value of 81 for the dielectric constant of water generally overestimates the water content for a temperature of 14°C, whereas the water content is underestimated for a temperature of 24°C, with this error increasing for increasing water contents.
View larger version (13K):
[in this window]
[in a new window]
|
Fig. 3. Relationship of volumetric water content to determined dielectric constant derived with the empirical Topp equation (black dashed line), the complex refractive index method (CRIM) equation assuming a dielectric constant of 81 for water (black line), and derived by the CRIM equation using dielectric constants of water at 14°C (gray solid line) and 24°C (gray dashed line) for a frequency of 750 MHz.
|
|
Therefore, the derived absolute values may differ slightly for different mixing models. However, using the simple CRIM mixing model is justifiable, since our main focus is detecting changes in the volumetric water content. The temperature dependence of the dielectric constant of water was taken into account, since this is important for measurements designed to investigate the long-term dynamics of the water content. The determined dominant frequency was also taken into account for determining the volumetric water content, although the frequency dependence of the dielectric constant of water is not as distinct in the covered frequency range.
Tomographic Inversion
The tomographic inversion algorithm we used is part of the commercial software tool REFLEX (Sandmeier, 2003). This algorithm uses the simultaneous iterative reconstruction technique introduced by Dines and Lytle (1979) for geophysical tomography and can be written as
 | [6] |
where ui(l+1) is the slowness (i.e., the reciprocal of the determined velocity) of the cell i after (l + 1) iteration steps, 
is a relaxation parameter, m is the amount of source-receiver sets, tok and tdk are the observed and modeled travel times along the ray path k, Dki is the length of the ray path k in cell i, and n is the number of cells. To apply this algorithm, data sets were chosen from the different GPR sections and sorted for the inversion. To minimize the effect of dynamic processes (i.e., dielectric constant changes) during the time span needed for data acquisition, each tomographic plane was measured in one step. Duplicate transmitter–receiver positions used for the inversion of different planes are hence individually collected data sets, and therefore can differ to a certain degree.
|
RESULTS AND DISCUSSION
|
|---|
The measurements were performed in September 2002 as part of the second series after feasibility and data quality tests were performed in April 2002. The tomographic measurements, performed in horizontal and vertical planes, had the purpose of optimizing the measurement layout and to gather additional data sets before the actual irrigation tests took place. To investigate the water content dynamics, a short but intensive irrigation test was performed and tracked using simple parallel transmission measurements. After the irrigation another set of tomographic measurements was performed to check the significance of the gathered data sets and estimate local changes in the water content.
In this study no automatic picking routine could be applied, since the first arriving wavelets generally were those traveling through air around the lysimeter. Figure 4a
shows a horizontal GPR section measurement. Notice that the geometry of the lysimeter is recognizable. At a circumference of 1.88 m the receiver is opposite of the transmitter such that the em wave travels through the entire diameter of the lysimeter. At lower or higher circumference values, the receiver antenna becomes closer to the transmitter, resulting in earlier arrival times of the transmitted wave. The less intensive wavelets at earlier arrival times are those traveling through air around the lysimeter body. At high circumference values in Fig. 4a the interfering superposition effects of the air waves can be seen. To ensure that the picked phases of the em waves are actually those that traveled through the lysimeter body, transmitter–receiver separations smaller than 0.5 m were not included. Figure 4b is an example of a vertical section, indicating a relatively wet region in the uppermost part of the lysimeter, since the shortest travel path (transmitter and receiver at same height on opposite sites) does not feature the earliest arrival time of the transmitted em wave. The em waves traveling through air are visible again in Fig. 4b, although interference with the transmitted signal is not as distinct as in the horizontal sections since the receiver transmitter distance is at least 1.2 m. Data sets of the uppermost region of the lysimeter could not be included because of strong interferences caused by GPR waves traveling through air.
View larger version (94K):
[in this window]
[in a new window]
|
Fig. 4. (a) Typical GPR data for a horizontal section (transmitter at approximately sector 9 o'clock or circumference 0 m) and (b) a vertical section (transmitter at z = 1.02 m).
|
|
Tomographic Measurements of the Initial State of the Lysimeter
The resulting straight beams of the horizontal tomograms are shown in Fig. 5
. A raster of 0.051-m side length produced a sufficient coverage of each point of the plane. Using this raster the water content distributions at two depths were calculated (Fig. 6)
. Focusing on the center body of the lysimeter with a radius of 0.4 m, one can see that the water content varies between approximately 0.11 and 0.13 m3 m–3. Although porosity variations and structural changes in the soil matrix cannot be excluded, the differences in the resulting propagation velocities are correlated to changes in the water content in this interpretation. Since soil water retention is related to its porosity, a lower porosity can also lead to higher volumetric water contents. While the relatively dry zones close to the lysimeter walls could be caused by desiccation through cut-outs in the lysimeter walls, we believe that they probably result from artifacts of the tomographic inversion algorithm. The derived high water contents at about x = –0.2 m and y = –0.5 m (or sector 7 o'clock) may be due to poor beam coverage. There are two other anomalies that may indicate heterogeneous conditions inside the lysimeter. One between sectors 9 and 12 o'clock originated during the first GPR tomography test in April 2002 when we added a small point-injection of tap water. The other anomaly is clearly visible in both displayed depth sections between 2 and 5 o'clock. While the cause of this anomaly was not immediately clear, it is probably due to incomplete top-cover of this part of the lysimeter, which may have allowed water to infiltrate during intensive rain events.
View larger version (31K):
[in this window]
[in a new window]
|
Fig. 6. Derived horizontal planes of the volumetric water content distribution inside the lysimeter. The two planes are situated approximately 0.45 m (z = 0.82 m) and 0.70 m (z = 0.57 m) below the surface.
|
|
For vertical tomograms, beam coverage (Fig. 7a)
comparable to horizontal tomograms is difficult to realize. We made measurements with the receiver placed at the top of the soil surface and the transmitter at the lysimeter wall. However, due to the strong interferences between em waves traveling through air and through the lysimeter body, plus additional occurrence of refracted em waves, those transmitter–receiver layouts provided travel times too erroneous to be useful for the inversion. Especially regions close to the lysimeter walls and the top and bottom boundaries were poorly covered and could not be used in our analysis.
View larger version (40K):
[in this window]
[in a new window]
|
Fig. 7. (a) Straight beams obtained with a vertical tomographic measurement and (b) derived vertical plane of the volumetric water content distribution inside the lysimeter before sector irrigation started.
|
|
As expected, the dome-like structure at the bottom of the evaluated vertical section (Fig. 7b) is an artifact of the tomographic inversion because of poor beam coverage. Even with the spatial limitations used for the vertical plane, the beam distribution provided insufficient coverage to prevent such an artifact. The volumetric water content distribution displayed in Fig. 7b indicates a distinct increase in soil water at x > 0 m. This one-sided distribution can be followed over the entire vertical plane, and widens for lower z values. The geometry of the anomaly correlates well with the derived horizontal water distributions in Fig. 6, whereas the calculated water contents diverge up to 0.02 m3 m–3 near their maximum values. Considering the different beam coverage of the particular measured areas, this aberration is acceptable, with the vertical plane providing sufficient accuracy to cross-check the horizontal planes as an independent data set.
Sector Irrigation
Following the first tomographic measurements, we irrigated the lysimeter at one particular section. During this experiment approximately 30 L of tap water was applied to an area between sectors 9 and 11 o'clock. However, because of surface topography the main infiltration occurred between sectors 11 and 12 o'clock. The water was applied within a time period of nearly 3 h, and was accompanied by several vertical-plane parallel transmission measurements to follow the irrigation event. Those parallel transmission measurements were performed by positioning the transmitter and receiver antenna at the same z position on opposite sites of the lysimeter and lifting the antennas gradually. These measurements hence provided an integral volumetric water content of the entire diameter of the lysimeter along a vertical plane over the lysimeter height. The parallel transmission data at various depth levels in Fig. 8
show that the volumetric water content gradually increased with time after irrigation started. The evaluated GPR waves did not travel through the bulk of the applied water because of particular location of the measurement plane (y = 0 m). After the water was applied, a clear increase in the volumetric water content of the uppermost region is visible (black dashed line in Fig. 8). No increase in the volumetric water content was visible at heights z < 0.35 m. The difference between the initial volumetric water content at z = 0.05 m and the water content immediately after irrigation may indicate rapid flow through macropores, but could also be caused by erroneous data picking.
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 8. Vertical integral volumetric water content distributions before (solid black line) and after (dashed black line) the irrigation. The measurements were taken at the plane y = 0 m. Several other measured distributions after the irrigation (various gray lines) are also shown.
|
|
A comparison of water contents directly after the irrigation (black dashed line in Fig. 8) and those made when the tomographic measurements started (gray solid line) indicates considerable horizontal water flow. Notice that the integral volumetric water content increased significantly over the entire height of the lysimeter. Horizontal flow is caused by horizontal pressure head gradients in the soil. Furthermore, the transmission data show noticeable downward flow of water with time since the day after the irrigation. The integral volumetric water content increased in deeper regions of the lysimeter, whereas the uppermost region of the lysimeter featured decreasing volumetric water contents (gray solid, dashed, and dotted lines in Fig. 8).
Tomographic Measurements after Irrigation and Changes of Water Content
The horizontal planes of the tomographic measurements show a strong increase in the water content between sectors 9 and 1 o'clock after the irrigation (Fig. 9)
. As expected, the upper horizontal plane featured higher water contents than the lower plane. The location of the maximum derived water content correlated well with the aforementioned topographical minimum at the soil surface. The applied water flowed here first over the soil surface before infiltrating. Subtracting the derived water contents before the irrigation from those after the irrigation clearly shows the areas where the water content changed most (Fig. 10)
. Although the utilized tomographic inversion algorithm implemented a strong regularization, part of the interpreted gradual transition from marginal (<0.02 m3 m–3) to significant (>0.08 m3 m–3) water content changes must be attributed to inaccuracy in the location of infiltration at the soil surface and horizontal flow caused by the pressure head gradients in the soil. Again, the region with poor beam coverage of the data sets gathered before irrigation, at approximately sector 7 o'clock, and the regions close to the lysimeter walls must be evaluated carefully.
View larger version (32K):
[in this window]
[in a new window]
|
Fig. 9. Derived volumetric water content distribution approximately 14 h after the irrigation. Figure 8 indicates that the distributions changed only minimally during data acquisition.
|
|
The vertical tomographic measurements (Fig. 11a)
feature a corresponding effect caused by the irrigation as observed in the horizontal planes. In the upper part of the lysimeter the derived volumetric water content shows a significant increase in the area of the irrigation. The changes in the derived volumetric water contents in Fig. 11b show that the bulk of the added water is concentrated in the upper part of the lysimeter at x < 0 m. Although the water contents increased almost everywhere in the observed vertical plane, they increased especially in the lower part of the profile (x > 0 m). A minor decrease can be observed in the vicinity of the lysimeter wall at x > 0.3 m and z > 0.6 m. This area again correlates well to the same region in the horizontal plane shown in Fig. 10. Comparing the two resulting intersections by combining the vertical (Fig. 11b) and horizontal (Fig. 10) planes, the derived water content changes are similar for z = 0.82 m. For z = 0.57 m, the horizontal plane indicates a region with minor changes in the center of the lysimeter, while the vertical plane features the same trend, although not as distinct.
View larger version (27K):
[in this window]
[in a new window]
|
Fig. 11. (a) Derived vertical volumetric water content distribution approximately 13 h after the irrigation. (b) Calculated volumetric water content changes due to the irrigation.
|
|
|
CONCLUSION
|
|---|
Using a lysimeter with PVC (i.e., electrically nonconducting) walls, we show that GPR tomography can be used to investigate the water content inside the lysimeter. During quasi-steady-state conditions (without major changes in the water contents) GPR tomography provides high spatial resolutions in the range of a few decimeters. The derived volumetric water contents provide reasonable estimates of water distribution in the lysimeter caused by a short and intensive irrigation experiment. With GPR the near-surface flow regime can be investigated without the use of invasive sensors. For short-term processes simple parallel transmission measurements offer useful data for interpreting infiltration and soil water flow processes, although no distinct spatial information is acquired. By comparing intersections of independent tomographic planes, information concerning the reliability of the derived water contents can be gathered.
Changes in the soil dielectric properties during the measurements can be correlated directly to changes in the water content. Even small changes in the volumetric water content can be resolved because of the comparatively high dielectric constant of water. Conducting the lysimeter experiments in a temperature-controlled area avoids the need to eliminate temperature effects, since the dielectric constant of water is a function of temperature.
Because of the small dimensions of the lysimeter, em waves traveling through air will affect the accuracy of the collected data. The uppermost region of the lysimeter hence could not be adequately included in the tomographic inversion. A similar problem pertained to the bottom of the lysimeter, which was placed on a foundation.
To gather more specific information about the soil, a combination of several methods may be needed in a joint inversion. New algorithms for tomographic inversion recently have been developed for optimizing the combined results of several uncorrelated geophysical methods (Musil et al., 2003). Utilizing only one geophysical method sometimes provides ambiguous interpretations, which may be improved considerably by combining them with different but complementary methods.
|
ACKNOWLEDGMENTS
|
|---|
The authors thank Dr. Thomas Pütz (Agrosphere Institute, Forschungszentrum Jülich) for his efforts concerning lysimeter extraction and preparation and Stephan Strehl (Dep. of Applied Geophysics, Technical University of Berlin) for his support during data acquisition and processing.
|
REFERENCES
|
|---|
- Dannowski, G., and U. Yaramanci. 1999. Estimation of water content and porosity using combined radar and geoelectrical measurements. Eur. J. Environ. Eng. Geophys. 4:71–85.
- Davis, J.L., and A.P. Annan. 1989. Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy. Geophys. Prospecting 37:531–551.
- Dines, K.A., and R.J. Lytle. 1979. Computerized geophysical tomography. Proc. IEEE 67:1065–1073.
- Fisher, E., G. McMechan, and A.P. Annan. 1992. Acquisition and processing of wide-aperture ground-penetrating radar data. Geophysics 57:495–504.[Web of Science]
- Greaves, R.J., D.P. Lesmes, J.M. Lee, and M.N. Toksöz. 1996. Velocity variations and water content estimated from multi-offset, ground-penetrating radar. Geophysics 61:683–695.[Web of Science]
- Gross, R., A. Green, K. Holliger, H. Horstmeyer, and J. Baldwin. 2002. Shallow geometry and displacements on the San Andreas Fault near Point Arena based on trenching and 3-D georadar surveying. Geophys. Res. Lett. 29(20):1973. doi:10.1029/2002GL015534
- Holliger, K., M. Musil, and H.R. Maurer. 2001. Ray-based amplitude tomography for crosshole georadar data: A numerical assessment. J. Appl. Geophys. 47:285–298.
- Irving, J.D., and R.J. Knight. 2003. Removal of wavelet dispersion from ground-penetrating radar data. Geophysics 68:969–970.
- Jackson, J.D. 1962. Classical electrodynamics. John Wiley and Sons, New York.
- Kaatze, U. 1989. Complex permittivity of water as a function of frequency and temperature. J. Chem. Eng. Data 34:371–374.
- Lampe, B., K. Holliger, and A.G. Green. 2003. A finite-difference time-domain simulation tool for ground-penetrating radar antennas. Geophysics 68:971–987.[Web of Science]
- Lecomte, P., and C. Mariotti. 1997. Handbook of diagnostic procedures for petroleum-contaminated sites. RESCOPP Project, EU813. John Wiley and Sons, New York.
- Musil, M., H.R. Maurer, and A.G. Green. 2003. Discrete tomography and joint inversion for loosely connected or unconnected physical properties: Application to crosshole seismic and georadar data sets. Geophys. J. Int. 153:389–402.
- Oelsner, C. 1997. Geothermik. In K. Knödel et al. (ed.) Handbuch zur Erkundung des Untergrundes von Deponien und Altlasten Band 3. Springer Verlag, Berlin.
- Peplinski, N.R., F.T. Ulaby, and M.C. Dobson. 1995. Corrections to Dielectric Properties of Soils in the 0.3–1.3–GHz Range. IEEE Trans. Geosci. Remote Sens. 3:1340.
- Pütz, Th., and K. Klimsa. 1991. Profilbeschreibung und Analyseergebnisse des Standortes Kaldenkirchen–Hülst. Internal Rep. IRA 6/91. Forschungszentrum Jülich, Germany.
- Radzevicius, S.J., C.-C. Chen, L. Peters Jr., and J.J. Daniels. 2003. Near-field dipole radiation dynamics through FDTD modeling. J. Appl. Geophys. 52:75–91.
- Robinson, D.A., and S.P. Friedman. 2003. A method for measuring the solid particle permittivity or electrical conductivity of rocks, sediments, and granular materials. J. Geophys. Res. 108(B2):2076. doi:10.1029/2001JB000691
- Sandmeier, K.-J. 2003. Reflexw 3.0: Windows 9x/NT-program for the processing of seismic, acoustic or electromagnetic reflection, refraction and transmission data. Available at www.sandmeier-geo.de (verified 21 Sept. 2004). Sandmeier Software, Karlsruhe, Germany.
- Schön, J.H. 1996. Physical properties of rocks: Fundamentals and principles of petrophysics. Pergamon Press, New York.
- Shen, L.C., W.C. Savre, J.M. Price, and K. Athavale. 1985. Dielectric properties of reservoir rocks at ultra-high frequencies. Geophysics 50:692–704.
- Sihvola, A.H., and E. Alanen. 1991. Studies of mixing formulae in the complex plane. IEEE Trans. Geosci. Remote Sens. 29:679–687.
- Stoffregen, H., U. Yaramanci, T. Zenker, and G. Wessolek. 2002. Accuracy of soil water content measurements using ground penetrating radar: Comparison of ground penetrating radar and lysimeter data. J. Hydrol. (Amsterdam) 267:201–206.
- Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: Measurement in coaxial transmission lines. Water Resour. Res. 16:574–582.
- Ulaby, F.T., R.K. Moore, and A.K. Fung. 1986. Microwave remote sensing: Active and passive. Vol. III. From theory to applications. Artech House, Norwood, MA.
- Valle, S., L. Zanzi, and F. Rocca. 1999. Radar tomography for NDT: Comparisons of techniques. J. Appl. Geophys. 41:259–269.
- Vasco, D.W., J.E. Peterson Jr., and K.H. Lee. 1997. Ground-penetrating radar velocity tomography in heterogeneous and anisotropic media. Geophysics 62:1758–1773.[Web of Science]
- von Hippel, A. 1988. The dielectric relaxation spectra of water, ice and aqueous solutions, and their interpretation. IEEE Trans. Electr. Insul. 23:801–816.
This article has been cited by other articles:
|
|
|
|
 
R. Deiana, G. Cassiani, A. Villa, A. Bagliani, and V. Bruno
Calibration of a Vadose Zone Model Using Water Injection Monitored by GPR and Electrical Resistance Tomography
Vadose Zone J.,
February 25, 2008;
7(1):
215 - 226.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. B. Farmani, H. Keers, and N.-O. Kitterod
Time-Lapse GPR Tomography of Unsaturated Water Flow in an Ice-Contact Delta
Vadose Zone J.,
February 25, 2008;
7(1):
272 - 283.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
L. Weihermuller, J. Siemens, M. Deurer, S. Knoblauch, H. Rupp, A. Gottlein, and T. Putz
In Situ Soil Water Extraction: A Review
J. Environ. Qual.,
October 24, 2007;
36(6):
1735 - 1748.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. Attia al Hagrey
Geophysical imaging of root-zone, trunk, and moisture heterogeneity
J. Exp. Bot.,
March 1, 2007;
58(4):
839 - 854.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Vereecken, S. Hubbard, A. Binley, and T. Ferre
Hydrogeophysics: An Introduction from the Guest Editors
Vadose Zone J.,
November 1, 2004;
3(4):
1060 - 1062.
[Full Text]
[PDF]
|
|
|
TOP
ABSTRACT
INTRODUCTION
