Monitoring Unsaturated Flow and Transport Using Cross‐Borehole Geophysical Methods

Improved understanding of unsaturated flow and transport processes is limited by the lack of appropriate in situ measurement techniques. This study was conducted to determine whether two noninvasive cross‐borehole geophysical methods combined could be used to estimate two important unsaturated zone transport parameters, namely the pore water velocity and longitudinal dispersivity. Cross‐borehole electrical resistivity tomography and ground penetrating radar were used to estimate temporal and spatial variation of electrical resistivity and water content, respectively, during a 20‐d forced infiltration experiment. The resulting one‐dimensional profiles and two‐dimensional images of moisture content and electrical resistivity were subsequently combined to estimate solute tracer concentration. The results were used to analyze the downward migration and vertical spreading of water and tracer mass. The two geophysical methods provided independent estimates of soil moisture content and electrical resistivity that were spatially and temporally consistent. The observed changes in moisture content and electrical resistivity were, as a first approximation, used in a one‐dimensional moment analysis. The transport behavior was found to be very susceptible to layering of the subsurface. Even slight reductions in grain size apparently lead to flow barriers and associated lateral flow, resulting in tracer mass loss, reduced vertical pore water velocity, and increased longitudinal dispersivity. Synthetic data showed that the estimated unsaturated transport parameters (i.e., pore water velocity and longitudinal dispersivity) and the mass estimate were influenced by the selected electrical resistivity tomography inversion routine. In effect, an overprediction of all three parameters was observed.

R ecent research has shown that cross-borehole geophysical methods off er promising alternatives to traditional techniques for hydrologic characterization. Th e measurements collected by geophysical methods are on a more appropriate scale, with high spatial resolution and with minimum intrusion of the subsurface. In particular, cross-borehole ground penetrating radar (GPR) and electrical resistivity tomography (ERT) can provide estimates of soil moisture content and electrical conductivity variations in the vadose zone between boreholes located up to ?10 m apart (Hubbard et al., 1997;Daily et al., 1992;Binley et al., 2001;Alumbaugh et al., 2002;Ferré et al., 2003). Such data provide valuable information on fl ow and transport and may be used for identifying or constraining hydraulic and transport parameters of hydrologic models.
A number of studies, aimed at identifying unsaturated hydraulic parameters using GPR and ERT surveys, have been reported. Binley et al. (2002) and Winship et al. (2006) used moisture content changes arising from a point tracer injection experiment, monitored by cross-borehole GPR and ERT, to estimate the fi rst and second spatial moment of the tracer mass. Th ese values were then compared with forward hydrologic simulations of the tracer test to estimate the eff ective hydraulic conductivity of the subsurface of interest (a UK Sherwood Sandstone). Cassiani et al. (2004) identifi ed eff ective hydraulic conductivities using moisture content profi les estimated by GPR in a Monte Carlo inverse approach, while Cassiani and Binley (2005) and Binley and Beven (2003) identifi ed probability distributions of the parameters in functional relationships for the unsaturated hydraulic functions. Kowalsky et al. (2005) performed joint inversion of GPR and neutron probe data collected during a point injection fl ow experiment to estimate hydraulic conductivity and important petrophysical parameters.
Identifying an optimal set of hydraulic parameters using hydrogeophysical methods is often not trivial. Th is is partly due to technical limitations of the geophysical methods associated with resolution and inversion artifacts, but also due to the experimental circumstances and the type of data collected to constrain the hydraulic parameters. In general, hydrogeophysical measurements have been conducted during two experiment types: (i) point injection and trench experiments, where mass balance considerations are limited by assumptions concerning the Fresnel zone of the GPR measurements (Winship et al., 2006); and (ii) natural loading of the subsurface, where moisture content changes are minimal and multiple measurement profi les only provide limited additional information to constrain the hydraulic parameters (Binley and Beven, 2003). A synthetic study by Rucker and Ferré (2004b) stressed the importance of collecting additional data types (in their case pressure head measurements) to further constrain the parameter identifi cation.
In this study we have used cross-borehole geophysical methods to monitor and analyze a forced water and tracer infi ltration experiment. As opposed to previous investigations, our experiment was designed to approximate one-dimensional conditions by applying water and tracer over an area at the surface. Furthermore, a substantial loading of the system was imposed to produce a considerable dynamic response to enable simple moment analysis for identifying eff ective pore water velocity and longitudinal dispersivity, as well as the possibility of evaluating if the data honored the water and tracer mass balances.
In line with Winship et al. (2006), we have made simultaneous use of high-resolution images based on cross-borehole GPR and ERT. By combining estimates of moisture content (obtained from GPR-determined relative permittivity) with electrical resistivity (through ERT measurements), tracer concentration estimates were obtained. With this approach, two independent data types (moisture content and tracer concentration) were collected to constrain the fl ow and transport parameters.

Field Site
Th e fi eld site was established in Denmark on a 20-to 30-m unit of unsaturated alluvial sand sediments. A schematic of the fi eld site setup is illustrated in Fig. 1. Th e experimental setup consisted of four ERT and four GPR boreholes drilled to a depth of 12 m. Th e eight boreholes formed a cross consisting of two lines. Along each line, the outer two boreholes (7 m apart) were equipped with ERT-instrumented polyvinyl chloride tubes (electrodes every 50 cm), while the inner two boreholes (5 m apart) had access tubes for GPR antennae.
Figures 2b and 2c present well logging results (natural gamma and neutron logging) collected in the GPR access tubes. Apart from a topsoil layer (approximately 1 m thick), the subsurface characteristics appear not to vary substantially with depth; however, the results of a grain size analysis of sediment samples taken at a well located 18 m from the center of the fi eld site indicated that a slight layering exists (Fig. 2a). Th e grain size percentiles show that the top 1 m consists mainly of silt, with just a minor fraction of clay (14%). Below this topsoil, a layered sequence can be observed: coarse sand, followed by fi ner sand, and fi nally coarse sand again. In the sand, the measured clay content was <1%.

Materials and Methods
A forced tracer infi ltration experiment was initiated at the fi eld site in October 2005. Cross-borehole GPR (measuring the relative permittivity) and cross-borehole ERT (measuring electrical resistivity) were used to monitor the downward migration of water and tracer.

Cross-Borehole Ground Penetrating Radar
Measurements were taken using a Sensors and Software PulseEKKO PE100 system (Sensors & Software Inc., Mississauga, ON, Canada) equipped with 100 MHz antennae. Two measurement techniques were conducted: zero-off set profi ling (ZOP) and multiple-off set gather (MOG) (Binley et al., 2001). Zero-off set profi ling enabled an estimation of the one-dimensional electromagnetic wave velocity distribution between two boreholes, while MOG resulted in a two-dimensional tomographic image of the electromagnetic wave velocity distribution. During the ZOP measurements, two antennae were lowered simultaneously into a set of boreholes with measurements taken every 0.25 m. A total of six ZOPs were collected during approximately 30 min. All possible sets of pairs between the four boreholes in Fig. 1 were sampled, i.e., GPR1-2, GPR1-3, GPR1-4, GPR2-3, GPR2-4, and GPR3-4; however, only one MOG was collected using borehole pair GPR1-3. Th is collection routine was more time consuming (1 h, 30 min) due to a larger amount of measurements (1176 measurements in total). Th e measurements were collected by fi xing an antenna at a specifi ed depth in one borehole and lowering the other antenna by 0.25-m increments throughout the depth range of the second borehole. Th e fi xed antenna was then moved to a new position where the procedure was repeated. In each borehole, the antenna was fi xed every 1 m, resulting in 24 fi xed antenna positions. Some of the data collected were later   2. (a) Sediment samples from a well located 18 m from the center of the fi eld site (d10, d50 and d90 are the 10th, 50th and 90th percentile of the grain size distribution; data were provided by Copenhagen Energy); and (b-c) well logs conducted at the fi eld site. GPR1, 2, 3, and 4 refer to the ground penetrating radar boreholes in Fig. 1. disregarded, such as the measurements collected near the surface and traces having an acquisition angle >45°. Attenuation of the signal and wave guiding along the antennae have been observed to deteriorate the quality of the high-angle traces (Peterson, 2001;Irving and Knight, 2005). Th e editing resulted in a data set with just 745 traces.
Th e fi rst arrival time of each electromagnetic (EM) wave was picked individually, from which the velocity distribution was determined. Th e one-dimensional calculation associated with the ZOP data set is straightforward because the distance the EM wave had traveled was equal to the borehole spacing. On the other hand, the velocity distribution resulting from the MOG was achieved through two-dimensional tomographic inversion to account for all the crossing rays passing through each portion of the subsurface. For this procedure, the straight-ray MIGRATOM code (Jackson and Tweeton, 1994) was used. Straight-ray assumptions have been used successfully to analyze data where velocity contrasts are <20% (Peterson, 2001). If velocity contrasts exceed this value, the velocity may be misinterpreted. Th e fi rst arriving ray is, in this case, no longer the direct ray, but instead rays traveling faster across longer distances.
Th e area between the boreholes was discretized by 50-by 50cm uniform pixels, resulting in 25 × 11 model parameters. Th e total amount of cells or model parameters (275) was therefore less than the number of data values (745). Th is criterion was suggested by Jackson and Tweeton (1994) to remain within the resolution capability of the data and to provide robust estimates, even in the presence of noise.
Th e one-and two-dimensional velocity distributions were subsequently converted to relative permittivity and moisture content using and the empirical relationship of Topp et al. (1980): where v is the resulting velocity, c the radar wave velocity in air (?0.3 m ns −1 ), ε r the bulk permittivity, and θ the moisture content at a given depth. Given that the subsurface at the fi eld site was coarse-textured mineral soil with clay contents <1% in the measurement area, the Topp model was expected to give reliable results (Lesmes and Friedman, 2005).

Cross-Borehole Electrical Resistivity Tomography
Before initiating the experiment, 96 electrodes were installed in the fi eld: 84 borehole electrodes and 12 surface electrodes. Th e latter were aligned along the dotted lines on Fig. 1 with 1-m spacing. Four electrodes were used for each resistance measurement. A measurement scheme, consisting of 2315 measurements and 2315 reciprocals, was constructed having only horizontal borehole dipoles (Winship et al., 2006). Horizontal dipoles result in higher values of measured transfer resistances and are therefore more robust toward noise (Binley and Kemna, 2005). Th e noise level was estimated by comparing the original measurements with their corresponding reciprocal measurement. In the reciprocal measurements, the current and potential electrodes used in the original measurements were interchanged. Th is value of noise has been found to represent the true noise level better than using duplicate measurements, which tends to underestimate noise levels (LaBrecque et al., 1996;Slater et al., 2000).
An IRIS SYSCAL Pro Switch 96 10-channel system (IRIS Instruments, Orleans, France) was used to record data during a 2-h, 15-min sampling period. A common data set having reciprocal errors <10% (1767 measurements) was used in the fi nal data inversion, as suggested by French et al. (2002). Th e volume of interest was discretized into a numerical grid of 108 × 52 × 52 cells and solved for 29 × 24 × 24 model parameters. In the area of interest (i.e., the infi ltration area), the cells had a dimension of 50 by 50 by 50 cm, whereas the surrounding area was discretized more coarsely, up to 56 m. Th e fi nite-element-based, Occamtype, three-dimensional electrical resistivity inversion program R3 (Binley, 2007) was used to produce three-dimensional electrical resistivity tomograms. Th is inversion approach has been widely documented and applied in the literature (e.g., for tests of robustness; LaBrecque et al., 1996).
Th e obtained bulk electrical resistivity, ρ b , is by Archie's empirical law (Archie, 1942) related to the pore water electrical resistivity, ρ w , the porosity, Φ, and the saturation degree, where m and n are empirical constants set to 1.3 and 2, respectively. Th e parameter m indicates the cementation of the soil. Unconsolidated sands, as found at the study site, are typically assigned a value of 1.3 (Lesmes and Friedman, 2005), while n is most generally set to 2. Th is parameter accounts for the large increase of apparent electrical resistivity with decreasing soil moisture (Hendrickx et al., 2002). Surface conduction was disregarded as a fi rst approximation since the subsurface below 1 m consisted of coarse-grained sands with a negligible amount of fi ne-grained material (<1%). Th e top 1 m did, however, contain up to 14% fi ne-grained material (<2 μm) and the electrical conductivity may therefore be underpredicted in this area (Lesmes and Friedman, 2005). Th e porosity was assumed constant at 0.41 cm 3 cm −3 . Th is value was obtained from core samples withdrawn from the sand at 1-to 2-m depth. By rearranging Eq.
[3], the pore water electrical resistivity, ρ w , can be found using the bulk electrical resistivity determined by cross-borehole ERT, the moisture content estimated from crossborehole GPR, and porosity: Changes in soil water electrical conductivity were converted to meq L −1 assuming that 100 μS cm −1 = 1 meq L −1 (Appelo and Postma, 1999).

Infi ltration Experiment
Th e forced infi ltration tracer experiment lasted 20 d from 18 Oct. to 7 Nov. 2005. Th e infi ltration experiment was designed to mimic one-dimensional water and solute infi ltration within the measurement area to enable a one-dimensional analysis of the results. During 20 d, clean water (electrical conductivity = 760 μS cm −1 ) was applied at a rate of 88.4 mm d −1 over a 7.33-by 7.33-m area using drippers spaced every 33 cm over the entire surface (484 drippers). Each dripper consisted of 85-cm-long, 1-mm tubing having enough resistance to ensure constant fl ow in all drippers. Tap water supplied from a nearby tap was used as irrigation water. Th e water was supplied to a water tank in which it was maintained at a constant level and from which it was distributed to the drippers. An independent water meter was connected to the system to verify that a constant fl ow rate was imposed. Furthermore, fl ow measurements were made at the individual drippers to ensure that water was uniformly applied to the fi eld site. Th e fi eld site was covered by a tent to avoid precipitation and to minimize evapotranspiration. Th e potential evapotranspiration was estimated to 0.8 mm d −1 using the Penman-Monteith equation (Dingman, 1994) and data from a nearby weather station. Th e estimated evapotransporation constituted <1% of the applied infi ltration.
Geophysical measurements were taken on a daily basis at the start of the experiment and reduced to every 2 to 3 d toward the end. Th e entire measurement routine, comprised of MOG, ZOP, and ERT, was completed in 4½ to 5 h. During this time frame, a water front migrating with a vertical velocity of 1 m d −1 will move up to 21 cm, a distance comparable with the vertical discretization of the ZOP, but half that of the MOG and ERT results. As a result, moisture content estimates can appear slightly smeared at the water front, but this eff ect should be negligible compared with the spatial smoothing of the geophysical methods.
After 4 d of infi ltration, a saline tracer, 890 L containing 75 kg NaCl with an electrical conductivity of 105.4 mS cm −1 , was added during 150 min through the drippers. Th e applied tracer corresponded to 16.5 mm of water. Density fl ow was assumed to be insignifi cant, considering the high dilution of the tracer during the downward migration and the already dominant vertical gravitational fl ow. Figure 3 shows the background (pretracer and preinfi ltration) cross-borehole GPR-and ERT-derived moisture content profi les. Th e six collected ZOP (Fig. 3a) and six similar crosssections withdrawn from the three-dimensional ERT parameter volume (Fig. 3b) exhibit some variability with depth. Th e overall trends, however, such as increased moisture content around 8 m followed by a drier sequence, are easily recognizable in each profi le. Th e average variability of the moisture contents at each depth are 0.026 and 0.015 cm 3 cm −3 for the six GPR and six ERT profi les, respectively.

Results and Discussion
Th e GPR data from 0.00 to 1.50 m is not included in Fig. 3. In this region, the fi rst arriving electromagnetic signal may be a refracted wave traveling at the air-soil interface and not the direct wave passing through the subsurface. It can be diffi cult to distinguish between the diff erent waveforms, rendering estimation of the moisture content at these depths problematic. To calculate moisture content from ERT, the soil water electrical conductivity and porosity were assumed to be constant throughout the measurement volume. Th e groundwater electrical conductivity (=760 μS cm −1 ) sampled below the fi eld site was assumed to be representative of the soil water electrical conductivity, while the porosity was set to 0.41 (the porosity determined for the sand layer at 1-to 2-m depth). Local-scale variations in porosity and soil water electrical conductivity may contribute to "noisy" results, while a general bias of the soil water electrical conductivity will bias the soil moisture content.
As expected, the ERT and GPR methods resulted in moisture profi les having similar trends and magnitudes (Fig. 3c). Th e ERT profi le, however, indicates slightly higher moisture contents near the surface and lower moisture contents below approximately 8 m.
To illustrate how well the ERT method, as applied in this study, can reproduce vertical resistivity variations of the subsurface, a synthetic ERT test is presented in Fig. 4. Th e ERT profi le in Fig.  4 was obtained by constructing a synthetic resistivity model and using the ERT inversion algorithm to solve the forward problem for a selected measurement scheme. Th e synthetic measurements were then used as input for an ERT inversion. Th e synthetic resistivity model was constructed to represent the background GPR moisture content profi le in Fig. 3c, having slightly larger moisture content values at selected depths (i.e., 6, 8, and 10 m) where thin layers of fi ner sand appeared likely. Th e top 1.5 m was also assigned a high moisture content (?0.35 cm 3 cm −3 ) to mimic the higher retention of the topsoil indicated by the background ERT profi les in Fig. 3b.
Th e synthetic analysis of the electrical resistivity profi le shows that the magnitudes of thick, low-resistance layers tended to be overpredicted by the selected ERT inversion algorithm. Furthermore, Fig. 4 illustrates that the ERT method, used in this study, suff ered in prediction capability near the bottom of the profi le due to fewer measurements that resulted in a low resolution. At this depth, the estimated resistivities, corresponding to the moisture content in Fig. 3b, are >1000 Ω m. High resistivity values, caused by low moisture contents, are intrinsically prone to higher measurement errors since the electrical contact resistance between the electrode and the surrounding subsurface may be very high. The cross-borehole ERT-derived moisture content values are therefore quite uncertain at this depth.
Th e vertical resolution of the ERT method is also lower than the GPR ZOP data, due to the larger vertical spacing of the electrodes (50 cm) compared with the vertical measurement spacing of the GPR (25 cm), and slight variations in moisture caused by layering will not, as a result, be as pronounced.
Th e vertical variations of the drained profi les in Fig. 3 are consistent with the layered changes in grain size distribution (see Fig. 2a). Th e top 1 m diff ers from the rest of the profi le, having higher moisture content, and thereby indicating fi ner material with high retention. Below the topsoil the moisture content does not vary much, but slight changes exist. Most evident are the higher moisture content around 8-m depth and the low moisture content below this depth. Th is confi rms the observed smaller grain sizes in Fig. 2a at 8 m and the underlying coarser material. But also the coarse material observed around 2-to 4-m depth in Fig. 2a can be recognized in Fig. 3. At this depth, low moisture contents down to 0.08 are observed.

Soil Moisture Content
Th e GPR-derived moisture content profi les (Fig. 5) and moisture content tomographic images (Fig. 6) collected throughout the infi ltration experiment elucidate the downward water movement. During the fi rst 7 d of infi ltration, the water front migrated 0.50 to 1.50 m d −1 . After approximately 7 d, the infi ltrating water reached 8 m, where further migration was temporarily halted. For the next 6 d, an increase in moisture content above the 8-m boundary is observed instead. At some time between Day 13 and Day 15, however, the water continued the downward movement. Th e tomographic images in Fig.  6 furthermore suggest that initially preferential flow took place and fl ow was not entirely one-dimensional, as would be expected due to the applied infi ltration mode. Water fl owed from the top 1.5 m through the left portion of the subsurface (at 2-5-m depth), bypassing almost completely a 2-by 2-m area at the very right of the image (near borehole GPR3). Below 4 m, the water moved laterally toward the right side of the image, whereafter the infi ltration became laterally more uniform.
Th e estimated one-dimensional GPR moisture data can be used to evaluate the amount of water accumulated within the measurement volume (see Fig. 7). Th e mean moisture content profi le is, for this estimation, assumed to be representative of the entire infi ltration area. In order for this assumption to be valid, water infi ltration should be uniform within the infi ltration area. Th e tomographic results in Fig. 6 as well as the six background ZOP in Fig. 3a did, however, show that this assumption is not valid. To illustrate the variance present in the infi ltration area, the water accumulation estimated from the individual ZOPs are also plotted in Fig. 7 (gray curves). Th e individual profi les do exhibit some variance. In particular, ZOP34 and ZOP23 (indicated with arrows) have substantially lower water accumulation than the remaining four ZOPs, perhaps caused by the area bypassed by the water infi ltration at 2-to 4-m depth, as discussed above. All curves show consistency in the accumulation trends, however, having high and fairly linear water accumulation during the fi rst period of the infi ltration experiment, after which the accumulation rate decreased during the last 10 d of measurement. It is especially evident from the average ZOP curve in Fig. 7 that the increase in infi ltrated water was nearly constant during the fi rst 6 to 7 d. After 7 d, the water accumulation stagnated, coinciding with the time the water front reached 8 m. Th e sediment at 8-m depth has small grain sizes and overlies coarser material (see Fig. 2a). A capillary barrier was most likely created at this depth. Th e water built up above the capillary barrier and at the same time lateral transport out of the infi ltration area took place. Th is continued until the moisture content became great enough (or suction low enough) for the water to penetrate into the underlying coarser sand. After 13 d, the water broke through the capillary barrier and the water accumulated in the measurement volume increased again. Th e accumulation rate was, however, diminished compared with the fi rst 7 to 8 d, indicating continued lateral fl ow. Figure 7 also suggests that the average water accumulation rate in the measurement volume during the fi rst 8 d of 2.16 m 3 d −1 diff ers by more than a factor 2 compared with the rate at which water was infi ltrated through the drippers of 4.75 m 3 d −1 (as measured by the water meter at injection). Th e diff erence between these two infi ltration rates is substantial. Several plausible causes were examined to determine the reason for this diff erence. Among others, the moisture content estimates could be erroneous due to refraction, as suggested by Rucker and Ferré (2004a). Th ey found water balance errors up to 41% when conducting synthetic tests of layered sediments without accounting for refracted arrivals of the EM wave. Th e proposed methodology was applied to the ZOPs collected at our fi eld site but refraction could not explain the large water balance error. It only led to small corrections in moisture content near the surface (top 2 m) and at the water front.
Inadequate petrophysical relationships could perhaps also explain the disagreement. Binley et al. (2001) and West et al. (2003) discussed the necessity of determining site-specifi c relationships to convert relative permittivity values to soil moisture; however, using diff erent petrophysical models did not improve the water balance result. Furthermore, it has been shown that changes in volumetric moisture content, when using the complex refractive index method, are only dependent on the background permittivity value, the permittivity at time t, and the permittivity of air and water  and are therefore not dependent on the permittivity of the soil in question.
Furthermore, as shown in Fig. 3c, the moisture content profi les derived from GPR and ERT are in good agreement, suggesting that the large quantities of missing water are not due to fl aws in the measurement or conversion procedures, but were more likely caused by uncontrolled subsurface diversion of the infi ltrated water. In fact, the particle size data suggests that a sequence of fi ne sand overlying coarser sand is present at 1-to 2-m depth, which can create a hydraulic barrier and associated lateral diversion of the infi ltrated water. Th is eff ect is observed at the 8-m depth where the contrast in grain size distribution, according to Fig. 2a, is smaller than at the 1-to 2-m depth.
Unfortunately, the design of the infi ltration experiment does not allow a quantifi cation or identifi cation of lateral fl ow since the geophysical measurements were constrained within the infi ltration area. Th e three-dimensional electrical resistivity parameter volume does extend beyond the infi ltration area. Th e electrical resistivity estimates in this area are highly uncertain, however, and detection of small-scale lateral fl ow mechanisms is not possible. FIG. 7. Accumulated difference in water volume estimated from the individual zero-offset profi les (ZOPs) (gray curves) and an average value (black curve).
FIG. 8. Average electrical resistivity profi les measured using electrical resistivity tomography at various days. The gray curve is the background electrical resistivity profi le, i.e., Day 0. Figures 8 and 9 illustrate the changes in bulk electrical resistivity values determined by the ERT method. In Fig. 8, the electrical resistivity is averaged at each depth from the threedimensional tomograms to represent a one-dimensional profi le, while the two-dimensional electrical resistivity images (Fig. 9) were extracted from the three-dimensional inversion results. Th e tomographic images represent the same area (between Boreholes 1 and 3) sampled with the GPR method in Fig. 6. Th e water infi ltration during the fi rst 4 d only lowered the electrical resistivity slightly near the surface. Th ere is a clear reduction in electrical resistivity (an increase in electrical conductivity) after 5 d, however, corresponding to the time the tracer was added. Th e subsequent nine profi les and images indicate the tracer's downward movement and vertical spreading.

Electrical Resistivity
Th e large range of electrical resistivity values of the subsurface, from tens to several thousands of ohm meters, and the coarser vertical discretization mask the details of the infi ltration dynamics somewhat. It is possible to distinguish the water front movement ceasing at approximately 8-m depth at Day 7 to 8, however, and the following buildup of water above this depth. Th e electrical resistivity results also indicate a breakthrough of water below the 8-m boundary around Day 13 and thereby corroborate the infi ltration dynamics observed using GPR.

Electrical Resistivity Tomography and Ground Penetrating Radar Image Comparison
Th e two-dimensional images of the moisture content and electrical resistivity shown in Fig. 6 and 9 clearly show some structural dif-ferences. Th is is to be expected, as the two methods have very diff erent resolution and sensitivity patterns within the plotted area. Ground penetrating radar has a higher resolution in areas with many crossing ray paths (i.e., in the central part of the interwell region) and ERT has the highest resolution around the electrodes (located in the boreholes and at the surface; see, among others, Day-Lewis et al., 2005). Furthermore, changes in electrical resistivity occurred due to changes in moisture content as well as changes in soil water electrical conductivity (Eq. [3]).
Nonetheless, the infi ltration patterns are quite consistent. Th e tomographic images of the two methods both visualize an initial infi ltration slightly skewed toward the left of the image (Borehole 1). Th is becomes especially evident when changes in moisture content for the fi rst 4 d are plotted (see Fig. 10).

Tracer Mass
When the cross-borehole ERT and GPR results are combined to estimate the tracer concentration, following Eq.
[4], the tracer movement and spreading is better visualized. Figure 11 and Fig. 12 show the one-dimensional tracer profi les and the two-dimensional tracer images, respectively. Since GPR moisture content estimates were not available for the top 1.50 m, the ERT moisture content data from the day before the tracer application (Day 4) were used as an approximation. Electrical resistivity data in Fig. 8 and 9 illustrate that this approximation is not too rough, as there does not appear to be further electrical resistivity changes in the top 1.50 m after 4 d. Instead the resistivity changes are observed deeper, around 2-to 4-m depth, indicating that the water front had passed the top layer and steady-state conditions could be expected to be present.  Figure 11 illustrates how the shape of the tracer pulse became more dispersed as it migrated downward in the profi le. At Day 13, only a little spatial variation in concentration remains, and after 15 d the pulse is not recognizable any more. A better understanding of the tracer movement can be achieved from examining the two-dimensional images in Fig. 12. Th e tracer infi ltration behaves fairly one-dimensionally the fi rst 2 d, i.e., Days 5 and 6. In the following images, however, some of the tracer appears to move laterally out of the area of measurement toward the left of the image. Th is observation may be caused by the temporary standstill of water at 8-m depth, but it could also be an artifact as the ERT method is more sensitive toward low values of electrical resistivity near the edges of the images. After Day 10, the tracer migrates downward again, but has by this time become so diluted that it is diffi cult to distinguish the tracer plume from background noise.
Th ese results illustrate that the cross-borehole geophysical methods enable a nondestructive mapping of the migration and spreading of an applied tracer, and the methods provide data on a refi ned spatial scale comparable to the scale of traditional water sampling from suction probes. Th e varying spatial resolution of the computed images resulting from cross-borehole ERT and GPR, as mentioned above, is, however, still an issue that needs to be dealt with.
In an attempt to overcome these shortcomings, transfer functions (e.g., random field averaging [Day-Lewis et al., 2005]), apparent petrophysical relations (Singha and Gorelick, 2006;Singha and Moysey, 2006), and full-inverse statistical calibration (Moysey et al., 2005 have been applied to cross-borehole geophysical data. Joint inversion of multiple data types can also be used to produce more reliable geophysical models (Kowalsky et al., 2005;Linde et al., 2006).

Moment Analysis
Th e one-dimensional mass profi les in Fig. 11 were used for a one-dimensional moment analysis. In moment analysis, the location of the center of mass and how the tracer pulse disperses at consecutive times is quantifi ed. By computing the zeroth, fi rst, and second moments for the profi les, it is possible to estimate how mass balance, pore water velocity, and dispersivity develop with time.
(For a description of moment analysis, see, e.g., Singha and Gorelick [2005].) Th e results of this analysis are plotted in Fig. 13a to 13c. Th e results clearly reveal a temporal development of both mass balance and transport parameters. Th e pore water velocity of the tracer declines throughout the measurement period, decreasing most substantially during the fi rst 4 to 5 d. After 5 d, the pore water velocity stabilizes at approximately 0.3 m d −1 . Th e dispersivity value is around 0.2 m for the fi rst 5 d and then increases to 0.5 m during the last period of the infi ltration experiment. Th e changes in both pore water velocity and dispersivity coincide with the standstill of the water front at approximately 8 m. At the same time, the tracer mass begins to decrease, which complicates the interpretation of the results in a one-dimensional framework, as water and tracer are diverted laterally out of the infi ltration area.
Th e amount of mass distributed over the area was 17.3 meq m −2 . Th is amount is double the amount of mass estimated using the cross-borehole geophysical techniques. Th e lack of mass is in accordance with the previously discussed error in water balance, and again confi rms the speculation that tracer and water moved laterally out of the measurement area in the top 1.0 to 1.5 m.
It is important to note that, since the basic assumption behind the one-dimensional moment analysis is violated due to the occurrence of lateral fl ow, the temporal development of the transport parameters cannot be considered to represent the true physical properties of the subsurface. Th e observed reduced vertical velocity cannot therefore be directly associated with the observed increased vertical longitudinal dispersivity.
A two-dimensional moment analysis was used to determine the center of mass of the tomographic images in Fig. 12. Th e location of the fi rst moment is illustrated with a red circle in Fig.  12. Th e tracer is observed to move slightly toward the left of the image from Day 8 to Day 13. After Day 13, the center of mass moves back toward the middle of the image. Th e changes in the zeroth moment (not shown here but identical to the results of the one-dimensional moment analysis in Fig. 13a) show substantial mass loss after Day 8. As the majority of the mass is no longer contained within the images in Fig. 12 after Day 8, the moment analysis results cannot therefore be assumed to represent the complete transport regimes.

Synthetic Test
A synthetic numerical experiment was performed to examine whether the ERT inversion method would inherently alter the shape and magnitude of the estimated tracer plume and thereby infl uence the resulting transport parameters. A forward onedimensional hydrologic simulation of fl ow and transport was performed using the code HYDRUS-1D (Šimůnek et al., 1998) for the soil and transport parameters listed in Table 1 (i.e., typical values for sand in HYDRUS-1D). Th e development of tracer concentration and moisture content profi les in a 12-m profi le were calculated for a 16-d-long forced tracer infi ltration experiment with constant loading. Th e electrical resistivity profi les were calculated using Eq.
[3] and used as input for a forward model calculation using the R3 ERT inversion program (assuming the petrophysical relationships as discussed above). Resistance data for the same measurement confi guration as used in the fi eld were thereby obtained and subsequently used as input for inversion. Finally, the electrical resistivity profi les were combined with the simulated moisture content profi les to compute tracer concentration (Eq. [4]) and these profi les were then used in a moment analysis.
Th e purpose of the synthetic test was not to represent reality; it was designed only as a means to identify errors associated with the ERT method. Random errors were not added to the synthetic data and one-dimensional fl ow through a homogeneous medium was assumed. Th e synthetic test cannot, as a result, be compared with the moment analysis results conducted on the real data, where lateral fl ow and loss of tracer mass greatly infl uenced the results.
Th e true and estimated values of mass, pore water velocity, and dispersivity based on the one-dimensional model are shown in Fig. 13d to 13f, where the true values are represented by a gray horizontal line. Figure 13d illustrates that the tracer mass is poorly determined by the ERT method. Apart from Days 1 and 2, the mass was generally overpredicted by 30%. Th is systematic overprediction of tracer mass can be explained by the results of the synthetic analysis presented in Fig. 4. Low electrically resistive anomalies extending horizontally across the entire measurement volume will be underpredicted using the adopted ERT inversion routine. As a result, too-high electrical conductivity and tracer concentration estimates were produced locally.
Although the pore water velocity was also slightly overpredicted for the majority of the simulated days (Fig. 13e), the estimated values are nonetheless quite close to the true value (diff erence ≤10%). Th e determination of the pore water velocity is therefore considered quite robust. On the other hand, the longitudinal dispersivity appears to be diffi cult to determine correctly (Fig. 13f ) due to smoothing of the model parameters and the chosen vertical discretization. Initially the tracer plume was narrow and the vertical discretization too coarse to capture the plume properly. As the plume penetrated deeper into the profi le and became more dispersed, however, the method did a better job in capturing the shape of the plume and the dispersivity was estimated more accurately. On the other hand, when the plume was located deeper in the subsurface and came close to the bottom of the measurement volume, where the resolution of the ERT method is low, the error increased again.
Th e correct estimation of the transport parameters is seen to depend highly on how well the vertical changes in electrical resistivity are captured by the ERT method. Th e survey design, FIG. 13. Results of the one-dimensional moment analysis: (a-c) results computed using fi eld data; (d-f) results computed using synthetic data. i.e., electrode spacing, borehole separation, and measurement confi guration, should therefore be optimized toward the vertical resolution to produce reliable results.

Conclusions
Cross-borehole ERT and GPR provide a promising alternative to existing methodologies designed to monitor tracer infi ltration. We have demonstrated that when both cross-borehole methods are combined, tracer mass profi les and images can be obtained. Th e one-dimensional profi les enable a determination of important transport parameters through moment analysis, while the two-dimensional images provide a means to better understand and visualize transport dynamics. Th e moment analysis also helped understand the observed water loss and clearly illustrated how even small structural changes in layered sediments can result in capillary barriers and associated lateral fl ow, thus aff ecting the downward migration dramatically. Lateral fl ow was not expected to be such a dominant fl ow mechanism at the selected fi eld site and the infi ltration design, aimed at analyzing one-dimensional properties, was therefore not ideal.
Th e fi ndings in this work stress the importance of investigating the limitations of the geophysical methods. We illustrated this by examining how the chosen ERT inversion method inherently changes the shape and magnitude of the tracer plume. Th is is one of many factors that could have an impact on the results. Future work should therefore concentrate on fi nding ways to deal with these shortcomings. Th is could be attempted by further developing the work concerning transfer functions, and thereby accounting for the spatial variability of the resolution of the geophysical methods, or by adopting completely new approaches, such as integrated data fusion (described in Moysey et al. [2006] and explored in, e.g., Binley and Beven [2003]). In this methodology, the collected geophysical data is used to evaluate the likelihood of a series of plausible geophysical models by computing forward data for these models and comparing the misfi t of the collected and modeled data. By using the data directly, without fi rst producing tomographic images through inversion, uncertainties introduced by the inversion procedure are avoided.