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Published online 25 February 2008
Published in Vadose Zone J 7:184-193 (2008)
DOI: 10.2136/vzj2006.0160
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SPECIAL SECTION: GROUND PENETRATING RADAR IN HYDROGEOPHYSICS

Measuring Water Content Heterogeneity Using Multifold GPR with Reflection Tomography

John H. Bradford*

Center for Geophysical Investigation of the Shallow Subsurface, Boise State Univ., 1910 University Dr., Boise, ID 83725. Presented at the 75th International meeting of the Society of Exploration Geophysicists, 2004, Houston, TX
* Corresponding author (johnb{at}cgiss.boisestate.edu).

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.


Received 1 November 2006.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Materials and Methods
 Field Examples
 Conclusions
 REFERENCES
 
Continuous multioffset acquisition of ground penetrating radar (GPR) data provides the capability to measure the lateral and vertical distribution of soil moisture. Multioffset data enable measurement of radar velocity, which in turn allows the estimation of soil moisture through an appropriate petrophysical relationship. Although rarely used in GPR investigations, reflection tomography coupled with prestack depth migration has the ability to measure lateral velocity variations with much greater resolution and accuracy than conventional methods of velocity analysis. I used reflection tomography in the post-migration domain to estimate radar velocity and the Topp equation to estimate subsurface moisture distribution in two and three dimensions. At a contaminated site near a former refinery I identified a near-vertical boundary separating coarse-grained sands and gravels from a unit containing a high fraction of silts and clays. At a chlorinated solvent waste site, I found significant heterogeneity in the moisture content distribution despite apparent homogeneity indicated by direct push methods.

Abbreviations: CMP, common midpoint • CPT, cone penetrometer • EM, electromagnetic • GPR, ground penetrating radar • LNAPL, light nonaqueous-phase liquid • NMO, normal moveout • PSDM, prestack depth migration • RMO, residual moveout


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Materials and Methods
 Field Examples
 Conclusions
 REFERENCES
 
I n the ground penetrating radar (GPR) frequency range (10 MHz–1 GHz), dielectric permittivities of earth materials are highly sensitive to bulk water content. Remarkably, this relationship is so strong that for materials ranging from sand to silt at soil moisture contents greater than about 5%, bulk dielectric permittivity is nearly independent of porosity and depends primarily on the volume of water (Topp et al., 1980).

Electromagnetic (EM) wave velocity is related to dielectric permittivity by the equation

Formula
where c is the speed of light in a vacuum, {varepsilon}0 is the permittivity of free space, and {varepsilon} is the dielectric permittivity of the material. This relationship assumes the magnetic permeability is equal to that of free space and the electric conductivity is low. The dominant role of water in the EM velocity of the three-phase system (soil matrix, air, and water) is due to the large dielectric permittivity contrast between water ({varepsilon}/{varepsilon}0 = 81) and the typical sand to silt soil matrix ({varepsilon}/{varepsilon}0 = 3.5–6) or air ({varepsilon}/{varepsilon}0 = 1).

Measurements of EM velocity using GPR, then, have the potential to provide accurate estimates of soil moisture content provided the data are acquired and processed appropriately (Greaves et al., 1996; Huisman et al., 2003; van Overmeeren et al., 1997). Here, I restrict the discussion to radar deployed at the surface with the primary objective of accurate velocity estimation. I compute the transform from velocity to moisture content using the Topp equation (Topp et al., 1980). Greaves et al. (1996) and Huisman et al. (2003) have given more thorough reviews of relevant mixing equations. Typically, investigators conduct GPR surveys in constant-offset mode where, at each sampling location, a single trace is collected at a set source–receiver offset (Fig. 1 ). This approach alone is not adequate to measure the GPR propagation velocity; however, velocity may be estimated by calibrating the travel time of a radar reflection to a horizon identified in a well. If point-like scatterers are present in a common-offset profile and produce diffraction hyperbolas, travel-time moveout analysis of the diffraction provides an estimate of the velocity above the scatterer (e.g., Bradford and Harper, 2005); however, this method is limited by the distribution of scatterers. A controlled method of measuring the GPR velocity requires multioffset measurements where multiple traces are acquired while expanding the source and receiver about a common midpoint (CMP). It is typical to acquire one or several sparsely located CMP gathers within a larger common-offset survey to measure a local one-dimensional velocity structure (e.g., Bradford et al., 1996; Young and Sun, 1996). Normal moveout (NMO) analysis provides an estimate of the vertical root mean square velocity distribution. Normal moveout analysis is often followed by Dix inversion (Dix, 1955) to estimate the interval velocity structure.


Figure 1
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  		FIG. 1. Illustration of conventional common-offset radar acquisition (top), where a single source receiver pair is recorded for each sampling location, and multioffset acquisition (bottom), where multiple-source receiver pairs, each with a different offset, are recorded at each sampling location.

 
In continuous, multioffset mode, the data are acquired in a geometry that results in multioffset measurements at every CMP position (Fig. 1). Such acquisition takes advantage of the well-established geometries of CMP acquisition developed in reflection seismology (Yilmaz, 2001). In this mode, it is possible to make laterally and vertically continuous GPR velocity measurements along a two-dimensional profile or throughout a three-dimensional volume (e.g., Bradford, 2006a,b; Greaves et al., 1996). Laterally continuous velocity measurements enable accurate time to depth image transforms and have the potential to identify lateral heterogeneity with precision. In addition to improved characterization through accurate depth imaging and material property characterization, CMP data have a number of advantages over conventional fixed-offset GPR data including improved suppression of coherent and random noise (Bradford and Clement, 2003; Bradford, 2004b; Liberty and Pelton, 1994; Pipan et al., 1999, 2003). Noise suppression is seen through the process of stacking, whereby the data acquired at different offsets are vertically summed. In addition, coherent noise may be attenuated by suppressing data with travel-time curves that differ from the target reflections using any one of a variety of dip filtering methods (Yilmaz, 2001).

One objective of any multioffset processing scheme is maximizing the accuracy of the measured velocity distribution and final GPR image. While the most common strategy follows an NMO-based processing scheme, this approach is subject to the fundamental assumptions of NMO velocity analysis, which include small offset/depth ratios, small vertical and horizontal velocity gradients, and planar flat lying reflections. These assumptions are often violated in the shallow subsurface. For example, EM velocity can decrease by a factor of two or more across the water table as the sediment grades from dry to full water saturation. This large velocity contrast can result in severe departure from NMO, leading to large overestimates of interval velocity (Al-Chalabi, 1973, 1974; Bradford, 2002). When NMO velocity analysis fails, more rigorous methods of velocity estimation are required.

Fortunately, an array of sophisticated velocity analysis tools are available that were originally developed for analysis of seismic reflection data. Because of the similarity in the kinematics of EM wave propagation and elastic wave propagation, these tools are often equally applicable to GPR velocity analysis. It is well established that prestack depth migration (PSDM) is currently the most accurate tool available for reflection imaging at depth. In addition to an accurate image of electric impedance contrasts, an integral component of PSDM processing is constructing an accurate estimate of the velocity distribution that is not subject to the assumption of NMO analysis. As a result of advances in computational hardware and software, PSDM has become a standard part of the processing flow in hydrocarbon exploration seismic data processing (see Leading Edge special issues on migration: June 2005, December 2002, May 2001). Perhaps the most important benefit of PSDM is the ability to correctly image data in the presence of large lateral velocity contrasts. Despite having seen little application in shallow geophysical applications, the same advantages as are found in deeper investigations may be found in both shallow seismic and GPR applications (e.g., Bradford, 2006b; Bradford et al., 2006; Leparoux et al., 2001; Morozov and Levander, 2002).

My objective is to first review the method of PSDM and reflection tomography in the post-migration domain. Then, through a set of case studies that includes one modeling and two field examples, I show that PSDM coupled with reflection tomography can image lateral variations in GPR velocity structure, leading to improved understanding of soil moisture heterogeneity within the vadose zone and at the interface with the saturated zone. The two field experiments have been taken from contaminated site investigations: a former refinery near Cincinnati, OH, that is heavily contaminated with light nonaqueous-phase liquids (LNAPLs), and the Department of Energy's Hanford Site, in the state of Washington, at a disposal pit that received a large volume of chlorinated solvent waste (dense nonaqueous-phase liquid).


   Materials and Methods
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Field Examples
 Conclusions
 REFERENCES
 
The wave field that GPR records at the surface is the result of EM wave scattering from discontinuities in subsurface electrical properties. This scattered wave field is a distorted map of electric impedance contrasts—small-scale discontinuities produce diffraction hyperbolas, and dipping horizons appear to have smaller dip angles and greater length than their true geometry. The objective of wave-field migration is to collapse scattered energy back to its point of origin, thereby producing an accurate subsurface image. As long as precise amplitude reconstruction is not a primary interest (e.g., we are only measuring wave-field kinematics), and with the basic assumption that the subsurface electrical properties are independent of frequency, many of the migration algorithms developed for seismic data analysis can be applied directly to GPR data without modification (Bradford et al., 1996; Bradford, 2006a; Bradford and Harper, 2005; Bradford and Loughridge, 2003; Fisher et al., 1992a,b; Pipan et al., 2003). Post-stack migration methods, where the data are processed to simulate zero-offset data acquisition, are subject to the assumptions and inaccuracies of the premigration velocity estimation method, which typically includes NMO analysis.

Prestack depth migration operates on the data before stacking and is not subject to the assumptions of NMO analysis. The output of PSDM is a set of common image point (CIP) gathers in depth, which is a set of traces, each acquired at a different offset, with coherent events indicating energy reflected from a common point in the subsurface. Traces in the CIP gathers are stacked to suppress noise and produce a final subsurface image. A few researchers have explored the potential of this approach in the analysis of GPR data (Deeds and Bradford, 2002; Leparoux et al., 2001; Pipan et al., 2003). Bradford (2006a) reviewed PSDM velocity analysis methods as applied to GPR data.

Prestack depth migration depends strongly on the depth velocity model so that accurate velocity estimation is critical. Because of this strong dependence, the migration process itself is used to improve the accuracy of the velocity estimates. When the data are migrated with the correct velocity model, a reflection in the CIP gather is imaged at a depth that is independent of offset (Fig. 2 ). If the velocity model is wrong, reflectors are not flat lying, and this apparent offset-dependent depth is defined as residual moveout (RMO). Residual moveout shows increasing depth with offset if the velocity above the reflector is too high or decreasing depth with offset if the velocity is too low (Fig. 2).


Figure 2
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  		FIG. 2. Prestack depth migration common image point gathers showing residual moveout (RMO) sensitivity to small velocity (Vel.) errors, for a simple one-dimensional model simulating the water table reflection with a 0.12 m/ns vadose zone and 0.07 m/ns water-saturated zone. The RMO is negative when the velocity is too low, and positive when the velocity is too high.

 
Stork (1992) presented a method of reflection tomography that seeks to minimize RMO in CIP gathers in the post-migration domain. This method of tomography takes advantage of reflector coherence and continuity in the post-migrated domain, thereby improving the processor's ability to evaluate specific reflecting horizons, particularly in a complex subsurface setting. In a PSDM processing flow that utilizes Stork's method, the preprocessing steps include a typical NMO processing sequence with a prime objective of producing a starting velocity model. Prestack depth migration is then applied with the starting velocity model and RMO of the output is measured along horizons that are picked by the processor. Tomography updates the velocity model and PSDM is applied with the new velocity model. The process may be continued iteratively until the RMO is reduced to an acceptable level. For all data presented here, I have used Stork's (1992) method of reflection tomography that is implemented in the ProMAX data processing package.

One important advantage of reflection tomography over NMO velocity analysis is that the velocity model minimizes the observed RMO in all the CIP gathers in a global sense. Because of this, tomography is capable of measuring lateral changes in velocity with much better resolution than NMO analysis, which assumes that the velocity does not vary within the acquisition offset range. Reflection tomography has become the preferred method of velocity model building in seismic exploration (Guo and Fagin, 2002). Despite the advantages of this approach, the use of PSDM, and particularly reflection tomography, remains limited in shallow geophysical investigations. I have found Stork's method robust for processing both shallow seismic (Bradford et al., 2006) and GPR (Bradford, 2006a) data.

To illustrate the capability of reflection tomography to resolve small-scale lateral and vertical heterogeneity, I constructed an aquifer model with the EM velocity structure shown in Fig. 3A . The background velocity model is laterally invariant with a negative velocity gradient from the surface to the water table at a depth of 8 m, a sharp decrease in velocity representing the transition to water-saturated sediments, and a low-velocity clay aquitard at a depth of 16 m. Within the background medium, I embedded two 3- by 3-m, high-velocity blocks in the background model, one in the vadose zone and one in the saturated zone. I used a finite difference solution to the scalar wave equation to simulate EM wave propagation through the model. The model parameters include a 50-MHz source pulse, 50 receiver positions, 0.3-m receiver spacing, 0.6-m source spacing, and 2-m minimum offset. This geometry is similar to that used in the field examples given below. The model produced a total of 70 common source gathers distributed symmetrically about the high-velocity anomalies. At the dominant source frequency, the velocity anomalies are on the order of one wavelength in the vadose zone and two wavelengths in the saturated zone.


Figure 3
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  		FIG. 3. A synthetic example of imaging lateral aquifer heterogeneity: (A) radar velocity model, where the velocity decreases gradually from the surface to the water table, then drops sharply, simulating full water saturation (a clay layer is present at 16 m; 3- by 3-m-high velocity anomalies are placed in the vadose and saturated zones); (B) simulated common midpoint normal moveout (NMO) stack comparable to a conventional fixed offset ground-penetrating radar survey; (C) unconstrained reflection tomogram and (D) results of prestack depth migration (PSDM) using (C); (E) tomogram with linear gradient and boundary discontinuity constraints and (F) results of PSDM using (E). Unconstrained inversion has good lateral resolution but poor vertical resolution of the anomalies. Allowing velocity discontinuities across horizons and applying a linear gradient constraint produces excellent resolution of the anomalies.

 
I first produced an NMO stack of the data, which is similar to a conventional common-offset GPR survey (Fig. 3B) and is an image of the scattered wave field. I then estimated the velocity model with an unconstrained inversion, although smoothing was applied to the tomographic model (2-m lateral and 0.5-m vertical smoothing). In this inversion, the lateral position of the velocity anomalies are well resolved, but the velocity anomalies are spread out vertically (Fig. 3C). Prestack depth migration with this model produces a good image of the model boundaries with some distortion beneath the saturated-zone anomaly due to underestimating the velocity perturbation (Fig. 3D). I then imposed two additional constraints. First, recognizing that there are no sharp velocity changes within the layers, I imposed the constraint that only linear vertical velocity gradients are allowed between reflecting horizons. Additionally, I allowed the model to have discontinuities across reflecting horizons, recognizing that reflections are only generated at sharp material transitions. The smoothing parameters were the same as in the unconstrained example. With this set of constraints, reflection tomography accurately reconstructs the shape and size of the velocity anomalies (Fig. 3E). The velocity of the vadose zone anomaly is underestimated by 4.3% and the saturated zone anomaly is underestimated by 6.3%. Prestack depth migration with the constrained inversion model is similar to that for the unconstrained model (Fig. 3F). From this analysis, I concluded that reflection tomography is capable of resolving wavelength-scale velocity anomalies, both laterally and vertically, from continuous multioffset GPR data.

In field data, of course, it is rare to know a priori the form of the velocity distribution within any given layer (e.g., the linear gradient assumption above). We may get some indication of the distribution through constructing the starting velocity model. For example, it is not unusual to find high direct wave (surface) velocities and a lower velocity at the water table reflection, indicating a negative gradient from the surface to depth, and in that case we might include a vertical gradient constraint as in the synthetic example above. In the absence of a priori information, the objective of imposing a constraint is to minimize tomography artifacts and stabilize the solution. With this understanding then, it is important to recognize that the measured distribution between any two horizons used in the analysis is an accurate estimate of the average velocity, but that the error is scale dependent. In a recently completed controlled field study, Bradford and Clement (2006) found that the error in the velocity result from reflection tomography was on the order of 1% or less when averaged across a few wavelengths.


   Field Examples
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Field Examples
Conclusions
 REFERENCES
 
Former Refinery Site
Background
At this site, just outside Cincinnati, OH, an estimated minimum of 4,000,000 gallons of leaded gasoline and diesel fuel were released to the environment from the early 1930s to the early 1980s. This contaminant now forms a thick zone of hydrocarbon that interacts dynamically with the fluctuating water table. Approximately 2,500,000 gallons of contaminant have been removed through extraction wells during the last 10 to 15 yr, but a significant volume of hydrocarbon remains. The water table fluctuates 3 to 5 m annually. Under low water table conditions, the hydrocarbon accumulates in the pore space at the top of the water-saturated zone. When water levels rise, the LNAPL is spread vertically so that, under high water table conditions, the contaminant remains in the pore space below the water table, forming a thick smear zone. The sediment column is variable, ranging from coarse sands and gravels to silty and clayey sands. At a depth of 24 to 30 m, a clay aquitard is present. The water table is roughly 9 to 18 m below the ground surface, depending on topographic relief and temporal groundwater variations. The Great Miami River bounds the contaminant plume to the south (Fig. 4 ). The plume has an irregular lobate shape to the north and west. The transport gradient is toward the west, although the level of the river changes substantially seasonally and these changes intermittently drive a north/south component of the head gradient.


Figure 4
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  		FIG. 4. Map showing the position of Lines 1 and 2 relative to the approximate free light nonaqueous-phase liquid plume extent (shown in gold) based on monitoring well data. The monitoring well locations are indicated by black dots. The yellow contour indicates the distribution of the maximum plume thickness under low water table conditions and shows heterogeneity in contaminant transport. A "no data" zone was present near the center of Line 1, preventing continuous imaging from the on-plume to off-plume area. The western section of Line 1 discussed in the text is highlighted in red.

 
Data Acquisition and Processing
In January 2002, a three-person crew acquired approximately 500 linear m of two-dimensional multifold GPR data along two transects (Fig. 4). Line 1 was placed to span the western leading edge of the plume, while Line 2 was entirely over the contaminated area although the north end of Line 2 near the northern extent of the plume. Collecting data farther to the north was not possible due to property restrictions. A set of cuttings logs acquired during installation of the numerous monitoring wells are available to constrain the interpretation. These logs also indicate the depth and thickness of contaminated zones, where the logging geologist either detected hydrocarbon odor or visually detected hydrocarbon. Data were acquired under high-water-table conditions, with the contaminant forming a 3- to 5-m-thick smear zone and essentially no floating product. Plans were made to revisit the site during low-water-table conditions, but had to be canceled due to ongoing site development activities.

The field crew acquired data using 50-MHz antennas in 25-fold common-source point gathers with 0.6-m source and receiver intervals, 1.8-m near offset, and maximum offset of 16.5 m. Additional acquisition details are given in Table 1 . Data quality varied from excellent to poor with maximum reflection depth ranging from 12 to 25 m. Processing consisted of a time-zero correction, band-pass filtering (12–25–100–200 MHz), automatic gain control (30-ns time gate), and two-dimensional PSDM reflection tomography (unconstrained with a 24-m horizontal and 2-m vertical smoother) along both profiles. All prestack migrations were done in the common-offset domain using a Kirchhoff algorithm with topographic corrections included in the migration algorithm.


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  		TABLE 1. Parameters for the refinery site two-dimensional survey.

 
Results
Line 1 showed good data quality to the east and west. Unfortunately a "no data" zone in the center of the profile prevented continuous imaging from the on-plume to off-plume areas. The western end of this profile is the only location where data was acquired in the uncontaminated area, thereby providing a background response (Fig. 4). There are three significant reflections in the PSDM image (Fig. 5 )—the top of the saturated zone at a depth of 14.5 m and two reflections within the saturated zone at depths of 16 and 18 m. I used these roughly horizontal horizons to measure the moveout for tomographic inversion. The starting velocity model for reflection tomography was a simple two-layer model constructed by laterally averaging the NMO velocities in the vadose and saturated zones, then applying Dix inversion to estimate the saturated-zone interval velocity. The reflection tomogram reveals a small but measurable amount of lateral variability in radar velocity. Conversion to moisture content indicates lateral water content variation of 1 to 2% in both the vadose and saturated zones (Fig. 5).


Figure 5
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  		FIG. 5. (A) Prestack depth migration (PSDM) image of the western end of Line 1 (Fig. 4). The vertical scale is relative to the Line 2 datum for comparison. (B) Results of velocity tomography. Some minor lateral heterogeneity is evident. The largest vertical contrast occurs at the water table at a depth of about 15 m. (C) Moisture content estimate using the Topp equation. The minimum water content below the water table is about 29% (v/v). Note that the depth scale is from the common site datum to facilitate direct comparison with Line 2.

 
Significantly greater heterogeneity is present along Line 2. Common-source gathers along the line indicate substantial stratigraphic complexity (Fig. 6 ). Backdipping events and departure from NMO in the common-source gathers indicate steeply dipping horizons. Moreover, a steepening of the direct arrival toward the south end of the profile indicates a significant lateral decrease in vadose zone velocity near the surface. This velocity decrease, coupled with a substantial increase in signal attenuation, suggests a significant lateral change in lithology. The conventional NMO stack along this profile (Fig. 6) reveals a package of horizons dipping steeply toward the north from 0 to 145 m along the profile. I refer to this section of the profile as Zone 1. The character of the data changes abruptly beyond 145 m, with the data being strongly attenuated and no evidence of the steeply dipping reflections, although the vadose zone thins substantially to the south due to topographic variation. I refer to the southern section of data as Zone 2.


Figure 6
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  		FIG. 6. (A) Common-source gathers along Line 2 (Fig. 4). Steeply dipping reflections are evident from backdipping moveout (e.g., transmitter [TX] = 45 m). A significant decrease in surface velocity past 145 m is evident where the dips of the direct ground arrival steepen, as indicated by the dashed lines (e.g., TX = 198 m). (B) The normal moveout common midpoint (CMP) stack reveals dipping strata in the near surface and a clear reflection from the water table. At distances >145 m, the signal is severely degraded due to increased attenuation. Note the approximately 40-ns push down of the water table reflection at distances >145 m. (C) Prestack depth migration (PSDM) with the laterally variable velocity model places the water table at the correct position in depth across the entire profile.

 
Cuttings logs show that Zone 1 sediment consists primarily of coarse-grained sand and gravel. Historical overhead photos suggest that all natural sediment in Zone 1 was excavated and replaced with artificial fill. Zone 2 well logs indicate a higher percentage of fine-grained material, which is consistent with observations in other wells known to penetrate the undisturbed sediments and explains the observation of increased attenuation in this area.

The water table reflection is evident in the reflection section across the entire profile, although it arrives later in time within Zone 2. In Zone 1, a second prominent horizontal reflection is present below the water table. In the PSDM section (Fig. 6), this horizon appears to be continuous across Zone 1, although the reflection is weaker at the north end. This second reflection occurs at a depth of ~18 m and is consistent with the base of the contaminated interval measured during construction of nearby (<50 m) monitoring wells. The deeper reflection is not imaged in Zone 2, probably because its amplitude is below the noise level due to high signal attenuation.

Reflection tomography reveals a heterogeneous velocity structure in the vadose zone with a large lateral gradient where the fill transitions from gravel (Zone 1) to silty sand and clayey sand (Zone 2). Across the Zone 1–Zone 2 boundary, the velocity decreases sharply by approximately 30% (Fig. 7 ). The decrease in velocity corresponds to a roughly 60% increase in water content across the lateral boundary. Uncertainty in the moisture content estimate in Zone 2 is high, as the increased fine-grained materials in Zone 2 may lead to departure from the Topp equation and overestimation of water content. The increase in fine-grained materials in Zone 2 probably correlates with decreased permeability. This decreased permeability is manifest in the contaminant distribution, where decreased transport within Zone 2 has resulted in an irregular, lobate distribution of LNAPL within the plume (Fig. 4).


Figure 7
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  		FIG. 7. (A) Reflection tomogram from Line 2 (Fig. 4). Note the abrupt lateral decrease in vadose zone velocity at 145 m, and the anomalously high saturated-zone velocities on the left side of the profile. Horizons used for residual moveout analysis are shown in black. (B) Moisture content estimated from the velocity model in (A). Moisture content increases laterally from 10% (v/v) in Zone 1 to nearly 20% in Zone 2. (C) The moisture content anomaly is computed by subtracting the moisture estimate in (B) from the starting model. The moisture content anomaly just below the water table is consistent with estimated water displacement due to measured amounts of free light nonaqueous-phase liquid.

 
From 30 to 120 m, where the overburden is dominated by gravel, high velocities relative to background are present below the water table within the contaminated interval. A velocity increase is expected where low-permittivity hydrocarbon displaces high-permittivity water within the pore space. The velocity approaches the background velocity farther to the north, where borehole data indicate a significant decrease in LNAPL concentration. The change in velocity due to LNAPL is a close approximation to replacing water with air in the pore space. It follows that, in the absence of a lithologic change, subtracting the moisture distribution computed from the inverted velocity model from the background moisture distribution provides a rough estimate of contaminant concentration (Bradford, 2004a; Redman and DeRyck, 1994). This computation shows a 0.07 maximum decrease in water fraction within the contaminated interval (Fig. 7). Dividing the maximum measured thickness of free LNAPL (0.15 m) measured under low-water table conditions by the thickness of the contaminated interval (2.5 m) gives a total LNAPL fraction of 0.06. It is reasonable to attribute the departure from background velocity entirely to the presence of the LNAPL. Alternatively, lithologic changes coincident with the lateral increase in velocity below the water table may cause the velocity increase, which is within the range of saturated sediment velocities. The high concentration of LNAPL at this site, however, probably has as strong impact on the velocity distribution.

Hanford Site, 200 West Area
Background
At the USDOE's Hanford Site in southwest Washington, CCl4 was used extensively in the processing of plutonium. The Z-9 trench in the 200 West Area (Fig. 8 ) received the majority of CCl4, and is thought to be the primary source area for a large CCl4 plume that now exists at the Hanford Site (Rohay et al., 1994). In April 2002, the field crew acquired a three-dimensional survey adjacent to the Z-9 trench. The objective of the survey was to identify lateral variability in water content in the upper 10 to 15 m. Shallow sediments at the site consist of sandy artificial fill (0–4 m) overlying the sands and gravels of the Hanford formation, which extends to a depth of 30 m. The water table is present at a depth of 70 m and is well below the target zone for this survey. Of particular note at this site is the apparent lack of heterogeneity. There is little surface topography and cone penetrometer (CPT) logs located throughout the area indicate no substantial lateral changes in lithology.


Figure 8
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  		FIG. 8. Location of the survey within the 200 West Area at the Hanford Site and the survey geometry.

 
Data Acquisition and Processing
The active survey patch was 14 by 27 m (Fig. 8). The field crew acquired data with 100-MHz antennas in 25-fold common-source point gathers with a 0.6-m source interval, 0.3-m receiver interval, near offset of 0.9 m, and far offset of 8.2 m. Profiles were oriented at 0, 45, and 90° relative to the long direction of the three-dimensional patch. The data were sorted into 0.45-m CMP bins. Additional details are listed in Table 2 .


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  		TABLE 2. Acquisition parameters for the Hanford Site three-dimensional survey.

 
Data processing consisted of a time-zero correction, band-pass filtering (25–50–400–800 MHz), automatic gain control (20-ns time gate), eigenvector filtering to attenuate coherent noise from surface scatter (discussed in greater detail below), two-dimensional PSDM reflection tomography along all profiles in all azimuths followed by merging the two-dimensional velocity profiles, and three-dimensional smoothing of the resulting velocity volume. Finally, I applied three-dimensional Kirchhoff prestack time migration. Because of the shooting geometry, a number of 0-fold CMP bins were present. Kirchhoff migration handles nonuniform spatial sampling effectively and the migrated output is interpolated via the migration operator onto the regular grid.

The raw data contained coherent noise scattered from surface objects associated with the nearby soil vapor extraction plant (Fig. 8), including an overhead power line and several large metallic structures. Substantial sections of reflection events were completely obscured by the coherent noise in the CMP gathers (Fig. 9 ) and stacked profiles (Fig. 10 ). Successful imaging with PSDM depends in large part on the removal of such coherent noise. In multifold data, it is possible to use dip filtering to remove surface scattering events. Dip filtering exploits the large moveout velocity difference between surface events traveling at air velocity and reflection events traveling at much lower subsurface velocity. To attenuate the air velocity scatter, I applied an eigenvector filter in the prestack CMP domain (Fig. 9), retaining the 18 to 100% highest eigenimages. The stacked sections show substantial improvement after eigenvector filtering, with clear reflections present throughout the three-dimensional volume and little evidence of the surface scatter (Fig. 10).


Figure 9
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  		FIG. 9. Comparison of common midpoint (CMP) gathers from the three-dimensional Hanford Site survey (A) before and (B) after eigenvector filtering to suppress the air velocity scattering noise. The off-end events are horizontal in the CMP domain and are effectively separated from the subsurface reflections. Surface scatter events are indicated with arrows. CDP Y is the inline position as shown in Fig. 8.

 

Figure 10
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  		FIG. 10. (A) Common midpoint stack taken from the center of the three-dimensional volume. Surface scatter (indicated with arrows) obscures subsurface reflections on either end of the profile. (B) The same stack after eigenvector filtering to suppress air velocity noise. (C) Prestack depth migration (PSDM) image after noise suppression.

 
Results
Two subhorizontal reflections at ~4- and 6-m depth dominate radar stratigraphy at the site (Fig. 10). I computed the tomogram based on residual moveout along these two horizons and constrained the inversion to linear vertical gradients between the horizons (Fig. 11 ). Above 4 m, gently dipping horizons are present with some foreset beds. This shallow stratigraphy is related to backfill at the site. The 4- and 6-m reflections are nearly parallel and deepen slightly toward low in-line positions.


Figure 11
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  		FIG. 11. (A) In-line velocity tomogram from the center of the volume, and (B) moisture content estimate based on (A). There was significantly greater moisture variation than we expected. The velocity low on the left of the profile correlates with a shallow depression of the 4- and 6-m horizons.

 
While stratigraphy at the site is relatively simple, tomographic inversion indicates significant lateral and vertical heterogeneity in the near-surface water distribution. Velocity decreases toward low in-line positions, reaching a minimum of 0.095 m/ns, a decrease of 12% from the background velocity. This velocity decrease corresponds to an increase in moisture content to nearly 0.19, a 35% increase above the background value of 0.14. The largest increase in water content occurs between the 4- and 6-m reflections. The results suggest that water is preferentially accumulating within the stratigraphic low and that the 6-m horizon is the upper surface of a relatively low permeability unit, which causes water to accumulate in the overlying formation. Examining the stratigraphic velocity and water content geometry in three dimensions, I found that the moisture content increase is coincident with the stratigraphic depression throughout the volume (Fig. 12 ).


Figure 12
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  		FIG. 12. (A) Three-dimensional prestack time migrated image at the Hanford Site, showing a detailed stratigraphy of the upper 6 m. (B) Depth slices through the velocity model at 2 and 5.5 m show significant three-dimensional variability. (C) Water content increases toward low in-line positions and high cross-line positions of the volume. A water content high correlates with the stratigraphic low between 4- and 6-m depth.

 

   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Field Examples
 Conclusions
REFERENCES
 
Because it does not depend on the assumptions of NMO analysis and globally optimizes the velocity model to explain moveout in the recorded wave field, reflection tomography in the post-migration domain has the ability to resolve lateral velocity variations with finer resolution and greater accuracy than conventional velocity analysis methods. While rarely applied in GPR investigations, this processing strategy can significantly improve our ability to understand the distribution of water in the near surface. At two contaminated waste sites, I measured substantial variation in the lateral and vertical distribution of moisture in the subsurface.

At the former refinery site, large contrasts in radar velocity and estimated moisture content are associated with the lithologic transition from coarse-grained sand and gravel to a formation containing a significant component of silt and clay. This distribution of lithologies probably has a significant impact on contaminant transport at the site. Of course, the presence of a lithologic transition is evident from borehole observations alone, but the lateral sampling of the borehole measurements is too coarse to determine the geometry of the transition. Continuous multioffset GPR measurements and analysis enable identification of the coarse–fine-grained transition with relatively high precision.

At the Hanford site, the interpretation of a relatively homogenous moisture distribution based on inference from available CPT and borehole information is misleading. Three-dimensional multioffset GPR analysis revealed substantial lateral variability in the moisture distribution. This variability is probably due to subtle lithologic changes not easily recognized with conventional sampling techniques and probably has significant implications for contaminant transport in the vadose zone. The GPR analysis and geologic interpretation has the potential to improve subsurface flow models that are based on CPT or borehole measurements alone.


   ACKNOWLEDGMENTS
 
The U.S. Department of Energy funded this work under the Environmental Management Science Program, Grant no. DE-FG07-99ER15008. Boise State University acknowledges support of this research by Landmark Graphics Corporation via the Landmark University Grant Program. Allen Tanner and Jake Deeds at the University of Wyoming assisted in field data acquisition.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Field Examples
 Conclusions
 REFERENCES
 




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S. Lambot, A. Binley, E. Slob, and S. Hubbard
Ground Penetrating Radar in Hydrogeophysics
Vadose Zone J., February 25, 2008; 7(1): 137 - 139.
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