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L.A. Ferré, Dept. of Hydrology and Water Resources, University of Arizona, 1133 E. North Campus Drive, P.O. Box 210011, Tucson, AZ 85721-0011
* Corresponding author (ty{at}hwr.arizona.edu).
Received 3 December 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMETHODSRESULTSCONCLUSIONSREFERENCES |
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Abbreviations: bgs, below ground surface • BPGR, borehole ground penetrating radar • EM, electromagnetic • GPR, ground penetrating radar • TDR, time domain reflectometry • ZOP, zero offset profiling
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMETHODSRESULTSCONCLUSIONSREFERENCES |
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Borehole ground penetrating radar offers a promising new approach to monitoring the water content profile with high spatial and temporal resolution. Typically, each BGPR measurement requires <3 s, including the time required to move the antennae to the next sample depth. As with TDR, BGPR instruments make measurements of the dielectric permittivity of the medium, which do not generally require medium-specific calibration to infer the water content. However, unlike TDR, BGPR measurements are made from within a pair of parallel access tubes, allowing for placement of a single instrument at a series of depths. This leads to high depth resolution of the water content profile (e.g., Binley et al., 2001). Unlike neutron probes, BGPR measures the water content of the medium between two access tubes separated by as much as tens of meters, resulting in a much larger sample volume that extends well past any disturbed region adjacent to the access tubes.
Despite the potential advantages of BGPR, there remains a critical question regarding the maximum spatial resolution that the method can achieve. This question arises due to the length of the BGPR antennae. For example, a typical 100-MHz dipole antenna is approximately 1 m long. These antennae are placed vertically within access tubes. Therefore, each measurement, though centered at a single depth, represents the properties within a relatively large depth interval. It is reasonable to assume that the length of this interval is approximately equal to the length of the antennae. However, a user can choose to lower the antennae any distance between readings, allowing great flexibility in sample locations and, therefore, in the choice of a vertical sampling interval. This ability to lower the antennae with any desired vertical sampling interval offers the possibility of constructing high-resolution water content profiles. However, the construction of water content profiles with depth resolution that is finer than the antennae length requires an understanding of the manner in which measurements average the medium properties within the sample volume of the instrument. As a first step, we examine whether water content profiles collected with a vertical sampling interval smaller than the antenna length can be used to identify water content changes with a depth resolution that is finer than the antenna length. This analysis is based on a series of BGPR water content profiles collected during pumping and recovery of an unconfined aquifer. The maximum depth of drainage is determined from these profiles and is then compared with the water table elevation, which was measured in a shallow piezometer. On the basis of this comparison, we demonstrate the limits on the maximum achievable resolution of the water content profile measured with BGPR. We also identify further work that will be necessary before BGPR can be used for high resolution, quantitative water content profiling.
The specific objectives of this investigation are (i) to demonstrate the repeatability of zero offset profiling (ZOP)–mode BGPR measurements from above the ground surface to below a shallow water table, (ii) to determine whether ZOP profiles show indications of critical refraction near the ground surface or near the water table, and (iii) to determine whether water content changes can be detected with a spatial resolution that is finer than the antenna length using ZOP measurements.
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMETHODSRESULTSCONCLUSIONSREFERENCES |
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 | [1] |
r is the dielectric permittivity relative to that of free space. For most soils, the dielectric permittivity depends strongly on the volumetric water content. A dry, sandy soil will have a dielectric permittivity of approximately 3 to 5, while a water-saturated sandy soil will have a dielectric permittivity of approximately 25 to 30 (Topp et al., 1980). This change in dielectric permittivity results in at least a fivefold decrease in the velocity of propagation of an EM wave from dry to wet soils. In comparison, there is less than a twofold decrease in the velocity of propagation from air to dry soil.
Topp et al. (1980) showed a robust relationship between dielectric permittivity and volumetric water content for a wide range of soils. This correlation allows for the determination of the water content from measurements of dielectric permittivity. Ferré et al. (1996) showed that the polynomial relationship developed by Topp et al. (1980) could be well approximated by a linear relationship between volumetric water content, 
(m3 m-3), and the travel time of an EM wave, t (s), as
 | [2] |
Ground penetrating radar is most commonly operated in reflection mode at the ground surface. Measurements made in this mode can be used to quantify the near surface water content (Davis and Annan, 2002), to determine the average water content above a reflector if a reflector exists at a known depth (Grote et al., 2002) or to approximate the water content profile through common midpoint analysis (Davis and Annan, 2002). However, these surface-based methods do not provide high-resolution, quantitative measurements of the vertical distribution of water content in the subsurface.
Borehole ground penetrating radar offers the possibility of measuring the water content profile with higher spatial resolution than surface GPR. For BGPR applications, the transmitting and receiving antennae are lowered into a pair of vertical access tubes. In the ZOP mode, the antennae are lowered such that their midpoints are always located at the same depth (Fig. 1). At each measurement depth, the time it takes the first-arriving energy to travel from the transmitting antenna (Tx) to the receiving antenna (Rx) is measured. Each of these measurements is related to the velocity of EM wave propagation within a limited depth interval, providing the greatly enhanced spatial resolution of BGPR over surface GPR applications. In practice, multiple measurements are made at each depth and stacked to increase the signal/noise ratio. However, even with tens of stacks, the measurement time at each depth is typically <2 s.
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In general, ZOP BGPR first-arrival travel times that are associated with critically refracted waves are not used for quantitative water content monitoring. Rather, in practice, there is a depth above which ZOP BGPR methods are not used. A first-arriving critically refracted wave can be identified in two ways. First, the measured travel times of these waves increase linearly with increasing depth of the antennae. This is due to the increasing fraction of the total travel path that passes through the soil with increasing antenna depth. Second, the volumetric water content inferred from the measured travel time with the assumption that the length of the travel path is equal to the access tube separation may be unreasonably low. Taking the definition of the capillary fringe as the zone of full saturation above the water table, it is possible that a similar error may arise due to critical refraction of EM waves at the top of the capillary fringe, where lower dielectric permittivity regions overlie wetter regions with higher dielectric permittivities, or at other locations within the subsurface where the water content changes sharply with depth.
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METHODS |
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Four BGPR access tubes were installed between two of the pumping wells (Fig. 2). The access tube boreholes were drilled with a hollow-stem, 15.2-cm (6-inch)–diameter auger to a depth of 11 m. Given that GPR signals cannot propagate through metal well casings, the access tubes were cased with 5-cm (2-inch)–diameter PVC pipe. Each tube was capped at the bottom to prevent water entry. The annulus of each borehole was backfilled with drill cuttings. No measurements were made for at least 1 mo following drilling to allow subsurface hydraulic conditions to re-equilibrate.
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To test the repeatability of the BGPR measurements, a second set of water content profiles was measured in August 2002, almost 1 yr after the initial measurements. Between the times of the two profiles, one of the BGPR access tubes sprang a leak. As a result, there was water in one of the access tubes beneath the water table when measurements were made in August 2002.
A PulseEkko100 radar system (Sensors and Software, Mississauga, ON, Canada) with a 1000-V transmitter was used for all BGPR measurements. Sixteen measurements were stacked for each measurement. The 100-MHz antennae were chosen based on examination of BGPR traces collected with 50-, 100-, and 200-MHz antennae. Specifically, the 200-MHz measurements showed excessive signal loss for some depth ranges while the 50-MHz measurements resulted in a more smoothed travel time profile. Measurements presented here were collected in BGPR access tubes separated by a distance of 2.94 m.
Each BGPR trace is a record of the voltage measured by the receiving antennae as a function of time. A program was written to identify automatically the first arrival of the EM wave from the BGPR traces. Several routines for identifying the arrival time of the first-arriving energy were tested. The most consistent result was found using a routine that first identified the location of the maximum amplitude response on the trace. This is usually associated with the first-arriving energy, but arrives later than the first-arriving energy. Then, the routine searches the trace backward in time from this point to find the earliest time at which the signal is lower than a user-defined noise threshold.
It is standard practice to calibrate GPR instruments using travel times measured in air above the boreholes before each profile is collected. In theory, this approach is advantageous because the velocity is known in air, allowing for determination of absolute travel times. However, applying this calibration gave rise to variations in the measured water contents at depths that were always well below the water table. Examination of the water content profiles showed that there was a near constant offset at all depths below the water table between consecutive profiles. To account for this apparent shift, a constant time offset was determined for each profile based on the average of the five travel times measured between 4.4 and 5.4 m bgs (Fig. 3), a depth range that was located well below the water table for all measurement times, so there was no reason to expect the travel time to change during the survey. The travel time offset was equal to the difference between the average of these five measured travel times for any profile and the average of those measured on the background profile. The offset was added to each travel time profile to form corrected travel time profiles. These offsets ranged from -1.49 to 3.00 ns, with an average offset of 0.55 ns. Although the offset varied sharply between consecutive profiles, the offset does appear to increase with time, suggesting that both operator inconsistency and instrument drift may contribute to these variations. This property of BGPR will require further study to allow for high resolution water content profiling. For this study, the water content was determined using the corrected travel times and Eq. [2].
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RESULTS |
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Repeatability of Travel Time Profiles
Three travel time profiles are shown in Fig. 4. One of the profiles was collected immediately before pumping began in September 2001; two of the profiles were collected approximately 1 yr later, in August 2002. The water table depth measured in the piezometer was 2.06 m bgs at the time of the September 2001 measurements and 1.99 m bgs at the time of the August 2002 measurements. The river had not flooded within 2 mo of either survey. Therefore, it is assumed that the profiles represent hydrostatic, drained conditions. Travel time measurements made at the same depth on the same day differed by no more than 1.6 ns. The greatest difference was observed when the antennae were located between the ground surface and the water table. Above the ground surface and below the water table, travel times measured at any given depth differed by <0.2 ns. The relatively large travel time errors above the water table are likely due to small differences in antennae placement in a region where the travel time varied sharply with depth. For measurements made almost 1 yr apart, the maximum measured travel time difference at any given depth was 2.9 ns. This maximum difference was measured at a depth of 1.3 m, approximately 60 cm above the water table. The maximum travel time difference for measurements made almost 1 yr apart below the water table is 1.2 ns, at a depth of 3.75 m.
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Water Content Profiling across the Ground Surface and across the Water Table
Zero offset profiling BGPR measurements are commonly referenced to the middle of the antennae. For example, the travel time measurements referenced to the 0-m depth (Fig. 4) were made with 50 cm of the 100-MHz BGPR antennae above the ground surface and the other half below ground. The travel time profile shows that measurements made with half, or less, of each antenna below ground surface show little change in travel time compared with measurements made in air. A larger change in travel time is seen when at least three-quarters of each antenna is below ground. As a result, the travel time profile, based on associating each travel time measurement with the center of the antennae, would suggest that the ground surface is deeper than 0 m. That is, associating the measured dielectric permittivity with the center of the antennae may, under some conditions, lead to a misleading dielectric permittivity profile.
As the antennae are lowered below the ground surface, there is a steady increase in the measured travel time from 9.5 ns in air to 44 ns below the water table. This may indicate a progressive increase in water content with depth. Or, this response may be due to the early arrival of critically refracted waves traveling along the ground surface. The low water contents associated with travel times measured above the 1-m depth (<0.05 cm3 cm-3) support the conclusion that critical refractions are arriving before direct arrivals at these depths. The slope of the travel time vs. depth profile is highly linear (R2 = 0.9975) with a slope of 22.12 ns m-1. Following the development of Rucker and Ferré (2002), this slope can be used to determine that the near surface water content is 0.23 cm3 cm-3. The refraction termination depth is then 1.09 m. This suggests that while the shallow subsurface response may be due to critical refractions, the travel times measured deeper in the vadose zone are likely associated with direct arrivals.
The travel time vs. depth does not show a linear increase as the antennae are lowered across the water table (Fig. 4). Rather, there is an initial decrease in travel time with depth. Further travel time changes with depth near the water table are similar to those seen at deeper depths, and are likely due to changes in soil properties. That is, changes in porosity with depth will give rise to changes in travel time with depth that are seen throughout the saturated zone, even in close proximity to the water table. This result suggests that critical refraction along the top of the capillary fringe may not have a significant effect on interpretation of direct wave travel times at or below the water table.
Identifying the Maximum Depth of Drainage Using BGPR Water Content Profiles
Water content profiles collected during the period of pumping differed significantly from those collected under static conditions (Fig. 5). Below 1.5 m depth, there is a region that shows decreasing water content with continued pumping. However, in the shallowest 1.5 m, the profiles show little change in water content with time. This response may be due to slow drainage from a relatively fine-grained layer above 1.5 m depth. Or, it may be an indication that BGPR travel times measured at depths shallower than 1.5 m are associated with first-arriving critically refracted waves that traveled along the ground surface.
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Comparison of Maximum Depth of Drainage Determined Using BGPR and Water Table Elevation Measured in a Piezometer
The maximum depth of drainage determined from BGPR measurements and the water table elevation measured in a nearby piezometer show similar patterns with time (Fig. 6). However, there appears to be a near constant depth offset, with the BGPR measurements consistently showing drainage at a depth below the water table. We propose four possible explanations for this difference: (i) vertical hydraulic gradients, (ii) capillary fringe effects, (iii) refraction above the capillary fringe, and (iv) inappropriate referencing of BGPR measurement depths. These effects are shown schematically on Fig. 7 and discussed below.
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As the water table declines due to pumping, drainage occurs at elevations above the capillary fringe height that is associated with the new water table elevation. By definition, soils within the capillary fringe will have experienced little or no drainage at a given time. As a result, the maximum depth of drainage will be shallower than the water table depth by at least the thickness of the capillary fringe (Fig. 7B).
Some portion of a BGPR signal that is generated below the water table will travel upward to a region of lower water content, refract along its critical path, and travel to the receiving antenna (Fig. 7C). Under some conditions, this travel path will be faster than that of a direct wave through the saturated zone. Then, the measurement at a depth below the water table would show the effects of drainage above the capillary fringe. While there was no direct indication of critical refraction at or near the water table on the drained travel time profiles (Fig. 4), this does not exclude the possibility that critically refracted waves arrive first at some depths. This could help to explain the observed downward offset of the maximum depth of drainage relative to the water table elevation.
The sample volume of BGPR antennae likely extends over the length of the antennae. Therefore, although the measurement depth is attributed to one point at the middle of the antennae, it is likely that water content changes at any point along the antennae will cause changes in the EM wave travel time (Fig. 7D). This offset may account for displacement of the maximum depth of drainage to a depth as much as one-half of the antennae length below the top of the capillary fringe. If half of the antennae length is greater than the capillary fringe thickness, this could help to explain the observed downward offset of the maximum depth of drainage relative to the water table elevation.
It is likely that the observed offset between the maximum depth of drainage and the water table elevation is some combination of capillary fringe effects, refraction along lower water content regions above the capillary fringe, and conventional depth referencing at the middle of the antennae. It is possible that, with further study, the relative magnitudes of these effects can be determined and this offset could be used to identify some useful soil property, such as the air entry pressure (capillary fringe height). For the analysis of the maximum achievable depth resolution of BGPR, we applied a constant upward offset of the BGPR-measured maximum depth of drainage to account for these combined effects. With this offset, there is good agreement between the water table depth measured in a nearby piezometer and the maximum depth of drainage determined from BGPR (Fig. 6). Despite the uncertainty that remains regarding the correct depth referencing of BGPR measurements, necessitating a somewhat arbitrary depth offset, the maximum depth resolution available from the BGPR measurements appears to be constrained primarily by the sampling depth interval chosen, in this case 0.25 m. That is, the resolution of the maximum depth of drainage is finer than the antenna length. Within this selected profiling depth resolution, the timing and magnitude of the aquifer response measured with BGPR show good agreement with those measured in the piezometer through most of the period of pumping and recovery. Further study is required to determine whether measurement with a smaller sampling depth interval would improve the agreement between the BGPR-measured maximum depth of drainage and the water table elevation. The largest differences between the shifted BGPR-determined maximum depth of drainage and the water table elevation are seen in the first 3 h after pumping began. At these early times, the water table appears to have lowered more quickly than the maximum depth of drainage, which is consistent with delayed drainage in response to pumping of an unconfined aquifer (Akindunni and Gillham, 1992; Nwankwor et al., 1992).
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONTHEORYMETHODSRESULTSCONCLUSIONSREFERENCES |
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Repeat water content profiles measured with BGPR during a pumping test and under static conditions 1 yr later are presented. The results show that BGPR measurements are highly repeatable, with maximum changes in volumetric water content of 0.034 cm3 cm-3 for static profiles measured 1 yr apart. Critical refractions obscure the water content profile near the ground surface. But, there is no evidence that refracted waves have deleterious effects on travel time profiles collected across the water table. The high repeatability of BGPR measurements allows for differencing of profiles to construct water content change profiles. However, comparison of the maximum depth of drainage during pumping and recovery with the measured water table depth shows a near constant downward offset of the BGPR measurements. For this study, the observed offset is likely due to the combination of three factors: (i) capillary fringe effects, (ii) refraction above the capillary fringe, and (iv) referencing of BGPR measurements to the middle of the antennae. Determination of the relative contributions of these factors will require further investigation. Once the constant offset between BGPR and piezometer measurements was accounted for, there was very good agreement between the methods for both the timing and magnitude of drawdown. These results suggest that a primary limitation on the achievable resolution of water content monitoring with BGPR is the user-selected measurement sample interval, which can be much smaller than the antenna length. However, the uncertainty regarding the correct depth at which to attribute BGPR-measured water contents must be addressed before ZOP with BGPR can be used independently to profile water content.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONTHEORYMETHODSRESULTSCONCLUSIONSREFERENCES |
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