Kowalsky_etal_WRR_2001

Forward modeling of ground-penetrating radar datausing digitized outcrop images and multiplescenarios of water saturation

M. B. Kowalsky1

Department of Civil and Environmental Engineering, University of California, Berkeley, California

P. Dietrich and G. TeutschInstitute of Applied Geology, University of Tubingen, Tubingen, Germany

Y. RubinDepartment of Civil and Environmental Engineering, University of California, Berkeley, California

Abstract. Simple petrophysical models and a sedimentologically interpreted outcropphotograph corresponding to the plane of a ground-penetrating radar (GPR) survey arecombined to create models for the simulation of GPR. This makes possible thecomparison of GPR field data, synthetic GPR sections, and a lithology image. On thebasis of this comparison the usefulness of the method for identifying hydrologicallysignificant lithofacies and the sensitivity of the results to different subsurface conditionsmay be investigated. In particular, GPR simulations are performed for an outcrop modelat three states of water saturation: uniformly drained (uniform residual saturation),nonuniformly saturated, and fully saturated. As predicted by reflection coefficientcalculations, comparison among the synthetic simulations highlights the importance of theexisting pore water distribution in determining the “visibility” of lithologic elements inGPR sections. Comparisons of the synthetic GPR sections with the field data show overallagreement, though the occurrence of various observed reflections depends on the presenceand distribution of pore water. Conclusions are also drawn about extending outcropanalog-derived results to investigations of real (fully saturated) aquifers.

1. Introduction

Ground-penetrating radar (GPR) surveys are increasinglyused to assist in subsurface characterization. The potential ofthe method for gaining information about subsurface structurearises from the apparent correlation between material type andelectrical properties, in which contrasts cause reflections ofelectromagnetic waves. Successful applications of GPR are asfar ranging as agriculture [Freeland et al., 1998], archeology[Tohge et al., 1998], and hydrological analyses [Greaves et al.,1996; Rubin et al., 1998; Chen et al., 2001]. While many GPRinvestigations have been carried out above the groundwatertable, the sensitivity of GPR to the presence of pore water inthe unsaturated zone is well known [Asprion, 1998]. In somecases, partial saturation is advantageous because enhancedcontrasts in electromagnetic parameters result and can evenallow for the estimation of water content and permeability[Hubbard et al., 1997]. However, the presence of water can alsorender poor GPR data quality [Asprion, 1998; Vandenbergheand van Overmeeren, 1999]. Whether for applications aiming todelineate subsurface structures or aiming to estimate hydro-

logic parameters, a methodical approach is desirable to assistin the analysis of GPR data and to evaluate the influence ofsoil conditions on such data.

One tool that can help in this goal is provided by the outcropanalog concept. The introduction of outcrop analogs in thegeosciences has offered a glimpse at real subsurface heteroge-neity and corresponding physical parameters [e.g., Davis et al.,1997] and has allowed for overall conceptual advancements insuch applications as predicting contaminant transport and theeffect of absorption kinetics on flow modeling [Klingbeil, 1998]and using geostatistical methods to build flow models fromborehole data [Whittaker and Teutsch, 1999].

Outcrop information has been used to validate geophysicalmethods as well. For example, Dietrich et al. [1998] evaluatedtomographic methods using an outcrop model. Rea and Knight[1998] compared GPR data with a nearby outcrop and went sofar as to evaluate the agreement between the geostatisticalparameters seen in the outcrop and those seen in the GPRdata. Reflections were assumed to occur with changes in ma-terial type, and since the outcrop was bimodal (it consistedmainly of two materials), reflections were assumed to corre-spond to boundaries between the materials. With images ofmaterial boundaries as detected by GPR and as seen in adigitized photo of the outcrop, variogram analyses were per-formed, and the variograms between the respective cases werecompared. The effect that entrapped water could have on theresults was not addressed.

Another application of GPR is radar stratigraphy, i.e., the

1Also at Earth Sciences Division, Lawrence Berkeley National Lab-oratory, Berkeley, California.

Copyright 2001 by the American Geophysical Union.

Paper number 2001WR900015.0043-1397/01/2001WR900015$09.00

WATER RESOURCES RESEARCH, VOL. 37, NO. 6, PAGES 1615–1625, JUNE 2001

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use of GPR to recognize characteristic radar facies and tocorrelate them with specific depositional environments [Van-denberghe and van Overmeeren, 1999]. Vandenberghe and vanOvermeeren [1999] systematically investigated the use of GPRfor the identification of various types of sedimentary struc-tures. GPR surveys performed near, and in some cases only afew meters away from, cliff faces (outcrops) allowed for acomparison of cliff face photographs and GPR sections. Ad-ditionally, some forward simulations were performed usingrelative estimates of the reflectivity between modeled struc-tures to help interpret the data; some large-scale features inthe GPR sections were identified in this manner as diffractionsfrom structural discontinuities such as intersecting channelsand interfaces at the bottoms of channels. In this study theeffects of pore water were considered at another site as well,where sandy channels in a braided river deposit were probedwith GPR. In interpreting the data a disturbance in continuityof the water table reflection was attributed to a region offine-grained particles in a channel fill situated above the watertable. Though not arrived at through a systematic modelingapproach, it was speculated that particles in this region havehigher moisture content and lower velocity than those in theregion lying directly below.

In fact, water has been observed to enhance the detectabilityof some materials. For example, Beres et al. [1999, p. 15] rea-soned that large changes in “porosity and water content aterosional surfaces and boundaries of the open-frameworkgravel produce the most-continuous reflections and correlatebest with outcrop data.” They explained the hydrogeologicrelevance of these elements by noting that their hydraulic con-ductivities are 3 or 4 orders of magnitude higher than theneighboring units and concluded that these elements can bemapped with 3-dimensional (3-D) GPR analyses. This conclu-sion highlights the need for a systematic, physically basedmethod to determine which lithologic elements can be delin-eated with GPR and under what conditions.

Recently, subsurface excavations accompanied GPR sur-veys, yielding outcrop photographs collocated exactly withplanes of GPR surveys [Beres et al., 1999; Bayer, 2000]. Sedi-mentological interpretation of the photographs in this caseallows for a direct comparison of GPR data with lithology. Ifelectrical properties can be adequately estimated, the oppor-tunity exists as well for forward modeling based on the out-crop-derived models. Aside from the validation of GPR fielddata, forward modeling can allow for a controlled investigationof electromagnetic wave sensitivity to different soil types andconditions.

In the present study, a methodology is proposed in which acarefully interpreted and digitized outcrop image allows real-istic models to be created for the simulation of GPR. First,petrophysical models based on porosity and water saturationare adopted in order to estimate electrical properties for eachlithological element in the outcrop. Then, the sensitivity ofGPR surveys to pore water is investigated through forwardsimulations with models representing three cases of water sat-uration: uniformly drained (uniform residual saturation), non-uniformly saturated, and fully saturated. After comparing thesynthetic simulations, the field data, and the outcrop image,some conclusions are drawn about the usefulness of the mod-eling approach and of GPR in identifying subsurface structuresgiven various soil conditions.

2. Petrophysical ModelsThe material properties, which govern electromagnetic wave

propagation, are magnetic permeability and electrical permit-tivity and conductivity. The magnetic permeability is approxi-mately constant and equal to that of the free space (m0) formost shallow subsurface materials (i.e., those containing nometals). The electrical permittivity and conductivity for suchmaterials are, however, functions of, for example, porosity,water content, and mineral composition [Schon, 1996]. A com-monly used form of the electric permittivity is the dielectricconstant k (or relative permittivity), defined as the dielectricpermittivity « of the medium normalized by that of free space«0:

k 5 «/«0. (1)

For estimating the dielectric constant in the present work amixture model [Wharton et al., 1980] will be used. The use ofthis model is desirable since it is physically rather than empir-ically based and since it allows for the permittivity to be easilycalculated while varying parameters such as the water satura-tion and porosity. The petrophysical model may be formulated(as by Hubbard et al. [1997]) as

k 5 @~1 2 w!Vcl Îkcl 1 ~1 2 w!~1 2 Vcl!Îks 1 SwwÎkw

1 ~1 2 Sw!wÎka#2, (2)

where Vcl is the clay content in the mixture, w is the porosity,Sw is the water saturation (the fraction of the pore space filledwith water), and kcl, ks, kw, and ka are the dielectric constantsof the clay, sand grains, water, and air, respectively. The di-electric constant may then be converted through (1) into theelectrical permittivity, which is needed for forward modeling.Additionally, in low loss media the corresponding velocity maybe estimated by the following relationship:

v 5 1/ Îm0« . (3)

For estimation of the electrical conductivity the empiricallybased model

seff

sw5 F 1

Swn

awmG 21

(4)

is chosen, where sw is the electrical conductivity of the porefluid and a , m , and n are empirically determined [Archie, 1942;Schon, 1996]. Typical values for various subsurface materialsare given by Schon [1996].

Attenuation is governed by the electromagnetic parametersand is especially sensitive to water saturation and clay content,an increase of either causing a decrease in penetration depthfor a GPR wave [Saarenketo, 1998]. Illustrating this point,Vandenberghe and van Overmeeren [1999] described a fieldsurvey and attributed limited radar penetration depth to thepresence of electrically conductive clayey material and a near-surface water table. For a discussion on the estimation ofactual GPR penetration depth, given material properties, andactual GPR system performance, the reader is directed toworks such as that by Noon et al. [1998].

3. Case Study (Herten Gravel Quarry)In the present study, an outcrop site was chosen where

geophysical measurements were taken before excavation, and

KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES1616

a detailed photograph of the resulting outcrop was taken afterexcavation. With representative hydrological parameters foreach lithologic element (measured in the laboratory) the dig-itized outcrop image and the aforementioned petrophysicalmodels are used to construct models for GPR simulation; thisis performed for three different cases of water saturation.

3.1. Description of Field Site and Measurements

The field site is at a gravel quarry in the city of Herten,situated at the southwest border of Germany (Figure 1). Thesedimentary deposits in this region were formed in a braidedriver environment and consist mainly of layers of poorly towell-sorted sand and gravel with no silt or clay.

During August and September 1999, a series of GPR surveysaccompanied excavation of the gravel quarry at Herten. Theexcavation was performed to a depth of ;9 m (never reachingthe groundwater table) in such a way that the exposed face ofthe previously GPR-surveyed region could be photographed;high-resolution photographs were taken every 1–2 m, yieldingsix parallel images in a span of 10 m, the dimensions of eachimage being 16 m in length by ;7 m in depth. Inspection of theparallel images indicates that the variation in the third dimen-sion (perpendicular to the outcrop slices) is significant butrelatively gradual. It is also worth noting that the advancingoutcrop surface was somewhat uneven as a result of the un-stable poorly consolidated sediments; ensuing distortion of theimage may have caused some inaccuracy in the sedimentologi-cal mapping of the outcrop.

Using sediment size and texture information along with con-sideration of the sedimentological processes as constraints, theoutcrop photographs were then carefully interpreted to yieldmaps of lithology [Bayer, 2000]. In the present study, one pro-file from the work of Bayer [2000] is chosen, the photograph ofwhich is shown in Figure 2a. For each representative lithologi-cal unit, measurements were performed in the laboratory [e.g.,

Klingbeil, 1998; Klingbeil et al., 1999] giving, for example, po-rosity and hydraulic conductivity values and geochemical pa-rameters. Using the sedimentologically interpreted image, thespatial distribution of the lithological elements was combinedwith representative porosity values (that is, each lithologic unitis assumed to have uniform properties throughout the entiremodel and is assigned a single value) to yield the porositydistribution shown in Figure 2b.

Though a more complete sedimentological description ofthe outcrop image is available from Bayer [2000], the majorzones representing separate sedimentary processes are delin-eated and labeled from 1 to 6 and described briefly. Zones 1,4, and 6 are mostly composed of sand- and stone-rich compo-nent-supported gravel. In zones 1 and 2 some thin sequentiallygraded deposits occur with thin and discontinuous open frame-work layers positioned horizontally in zone 1 and angled totrough shaped in the right side of zone 2. (The higher porositywedge-shaped element in the left side of zone 2, which ispinched out in the middle of the cross section, is a well-sorted,well-rounded sand-gravel formation.) On average, the hydrau-lic conductivity in zone 2 is lower than in the other zones.Whereas zones 1, 4, and 6 represent typical accretionary ele-ments, zones 3 and 5 contain mostly cut-and-fill sequences, inwhich the highly conductive open framework gravel units oc-cur. These sequences are formed by the deposition of gradedmaterial, alternating between sand-gravel mixtures with lowporosity and permeability and open framework gravel withhigh porosity and permeability. The delineation of zones issomewhat arbitrary. For example, the boundary between zones2 and 3 on the right-hand side of the outcrop photo is notclearly defined.

Ranging from 6.0 3 1027 to 1.0 m/s, the range in hydraulicconductivity values represented by the various elements islarge; the largest hydraulic conductivities correspond to theopen framework gravel. However, it is important to note thatthe relevance of various hydrological elements depends on thegoals of a hydrogeological investigation. The connectivity ofunits with high hydraulic conductivity could be important inthe scenario in which the first arrival of contaminants is im-portant. However, for planning the site remediation strategy ofa reactive contaminant, for example, it is conceivable that inaddition to or instead of the high-conductivity zones, the iden-tification of materials with high adsorption capacity, such assand, is sought [Kleineidam et al., 1999]. Whether the use ofgeophysical methods improves characterization in these casesis an issue which may be considered through outcrop modeling.However, before such issues can be addressed for GPR meth-ods, it is necessary to first gain an understanding about thedetectability of various hydrological elements for different sub-surface conditions.

3.2. Water Distribution Scenarios

The effects of entrapped water on GPR are not alwaysconsidered in geophysical surveys conducted in the unsatur-ated zone. Nevertheless, downward infiltration of surface wa-ter and fluctuations in the groundwater table leave entrappedpore water, the amount of which and the uniformity of whichis a function of time, mean grain diameter, and pore distribu-tion [Bear, 1988].

In evaluating the aforementioned field data it is important toconsider that it rained some days before the GPR measure-ments. Retained water was therefore suspected to be presentin the subsurface during the measurements and to have influ-

Figure 1. Location of the Herten gravel quarry field site.

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Figure 2. Outcrop modeling procedure. (a) A sedimentologically interpreted [Bayer, 2000] and digitizedphotograph from an outcrop at the Herten field site. (b) Representative porosity distribution. This image isused to construct models with various water saturation distributions (Sw) for GPR forward modeling. (c)Nonuniformly saturated model, obtained by assuming that the open framework gravel (shown in black) is atresidual saturation (Sw 5 0.08) and that the remaining materials (shown in white) have additional retainedwater (Sw 5 0.17). The units on the axes are meters.

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enced the GPR data [Bayer, 2000]. Given the complex se-quence of lithologic units with highly contrasting permeabili-ties, the distribution of water was thought to be highlyheterogeneous. Since investigating the general response ofGPR to soil conditions is the goal of this study, rather thantrying to reproduce exactly and explain every feature of theHerten GPR field data, a simple approach is used to put forthsome reasonable water distributions. The three scenarios ofwater distribution chosen for forward modeling are as follows:

1. The first model contains so-called drained elements at auniform residual saturation (Sw 5 0.08) and will be referredto as the drained model.

2. The second model is of nonuniform saturation withopen framework gravel modeled as drained and at residualsaturation (Sw 5 0.08) and with the remaining elementsmodeled at higher water content (Sw 5 0.17); the motivationfor this is based on the relationship between mean grain di-ameter and retained water [e.g., Bear, 1988]. The simplifiedapproach to assigning water distribution is intended to yield amodel with plausible contrasts in water saturation rather thanone with the most accurate water distribution possible (a moreaccurate water distribution might be obtained through flowsimulations). The distribution of water saturation for thismodel is shown in Figure 2c. The black regions are thosemodeled as completely drained (at residual saturation), whilethose with higher water content (less drained) are shown inwhite. The first and second models are intended to representpotential conditions in the unsaturated zone.

3. The third model contains all fully saturated elements(Sw 5 1) and represents an aquifer below the groundwatertable. This case is included to help determine whether conclu-sions regarding the detectability of hydrologically relevant tar-gets with GPR at an unsaturated outcrop site can be extendedto GPR surveys in the saturated zone (i.e., in a real aquifer).

3.3. Calculation of the Electromagnetic Parameters

A systematic approach for estimating the electromagneticparameters on the basis of the porosity values shown in Figure2b and the Sw distributions (as described in section 3.2) can beachieved through the use of the petrophysical models shown in(1)–(4). Sieve analyses of soil samples from sites geologicallyanalogous to the site which is modeled in the present study

showed negligible amounts of clay. Therefore, in estimatingthe electrical permittivity and conductivity the volume of clayVcl is set to zero. The individual k values are set to 6.9 for sand(the value for quartz as measured in the laboratory by Knolland Knight [1994]) and to 80 and 1 for water and air, respec-tively.

To illustrate the influence of soil porosity and saturation onthe electromagnetic parameters, the dielectric constant andvelocity are calculated as a function of porosity for variouswater saturation values using (1)–(3) and are shown in Figures3a and 3b. On the basis of the representative porosity mea-surements and chosen Sw values the distributions of valuesused for the outcrop elements in the three synthetic models areshown as well.

Electrical conductivity is calculated with (4) and plotted as afunction of porosity for varying values of Sw, as shown inFigure 3c. The parameters a and m are assigned values of 0.88and 1.37, respectively (average values for unconsolidatedsand), and n is set equal to 2 [Schon, 1996]. Site-specific mea-surements could improve the accuracy of these values andinsure that these models best represent the materials at theHerten site. However, for the basic understanding of the in-fluence of water saturation on the visibility of different litho-logical units such high accuracy of the parameters is unneces-sary. The electrical conductivity of the pore fluid is taken to be0.4 mS/cm, a typical value for the investigated site.

The relative change in electrical conductivity with increasingwater saturation is seen to be much larger than that in velocity.The nonlinear response of s to Sw is evident in (4), in which Sw

is raised to the power of n . The values for the elements in eachof the three synthetic models are shown as well in Figures 3aand 3b.

In considering the plots shown in Figure 3, one expects onlysmall reflections to occur in the drained model, with no units inparticular causing dominant reflections. Since the dielectricconstant and electrical conductivity values slightly increasewith porosity, one also expects the order of elements to helpdetermine the relative reflectivity of the elements (that is,interfaces between elements with a larger porosity contrast willhave larger differences in electromagnetic parameters thanthose with a smaller contrast in porosity). In the nonuniformly

Figure 3. Variation of (a) dielectric constant, (b) velocity, and (c) electric conductivity with porosity forvarious values of water saturation Sw (in increments of 0.1) as calculated with petrophysical models. Note thatin Figure 3c the lowest curve corresponds to Sw 5 0.01 (Þ0); the remaining curves in Figure 3c proceed withSw 5 0.1, 0.2, z z z , 1.0. On the basis of the porosity estimates for each lithologic element the values for theelements used in the models for forward simulation are also plotted (crosses, uniformly drained; circles,nonuniformly saturated; triangles, fully saturated).

1619KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES

saturated model the largest contrast should exist between thedrained open framework gravel layers and the undrained ele-ments. Among the undrained elements the contrasts in elec-tromagnetic parameters are comparatively small. For the fullysaturated model, there should be an overall increase in reflec-tivity between all units as compared to the drained model.Depending on the spatial order of occurrence, some reflectionsmight dominate in this case as well.

The velocity distributions resulting from the above petro-physical considerations are shown for each model in Figure 4.Inspection of these distributions shows interfaces betweenlithofacies with significant velocity contrasts that are antici-pated to cause GPR reflections. However, the magnitudes ofreflections are functions of additional factors and are betterquantified through the calculation of the reflection coefficients.

3.4. Reflection Coefficients

To help determine which material interfaces correspond tocontrasts in electrical properties high enough to create signif-icant GPR reflections, the reflection coefficients are calculatedfor each synthetic model. As an approximation, normal inci-dence of the vertically traveling wave front is assumed in thecalculations, although the wave fronts clearly intersect litho-logic elements at oblique angles. A general indication of high-reflectivity regions is nonetheless expected.

The normal reflection coefficient Rn between two materialsis calculated by

Rn 5K2 2 K1

K2 1 K1, (5)

Figure 4. Velocity distributions calculated using the introduced petrophysical models and porosity mea-surements for the (a) uniformly drained, (b) nonuniformly saturated (partially drained), and (c) fully saturatedmodels. Because of the large decrease in velocity for fully saturated materials, the gray scale for Figure 4c isdifferent than the scale for Figures 4a and 4b.

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where K is the complex propagation constant for each materialand is a function of s, «, m, and radar wave frequency [e.g.,Turner and Siggins, 1994]. To account for resolution in a GPRsurvey being typically around a quarter wavelength, the reflec-tion coefficients were calculated sequentially from the top ofthe model downward, and regions positioned less than a quar-ter wavelength below a reflector were assigned reflection co-efficient values of zero; that is, it is assumed that no reflectionswould be generated which are distinct from the reflection gen-erated by the overlying reflector. The average wavelengths are112, 107, and 73 cm for the uniformly drained, nonuniformlysaturated, and fully saturated models, respectively.

The distributions of Rn values for each model are shown inFigure 5. From these images it is apparent that regions of highreflectivity vary between the models. Four numbered regionsare indicated with ovals to help anticipate and explain poten-tial differences in the forward simulations. Region 1 indicatesan interface between zones that is expected to contain a high

reflection coefficient (as shown by shades of gray) for all mod-els. Regions 2 and 3 contain open framework gravel elementsthat should cause relatively large reflections only in the secondmodel. Thus strong reflections within the zones containingopen framework gravel are not expected without a contrast inwater saturation (as in the second model) between the openframework gravel and the surrounding materials within thezones. Additionally, region 4 shows the bottom border of thesand-gravel wedge formation and is seen to be reflective in theuniformly drained and fully saturated models but not in thenonuniformly saturated model.

These examples already show the importance of water sat-uration in terms of the reflectivity of the different lithologicunits. In addition, they demonstrate that the visibility of areflector depends on (1) its reflectivity relative to that ofnearby interfaces or nearby regions with contrasting water con-tent (i.e., a “weak” reflector might be “masked” by a nearbystronger reflector) and (2) the resolution of a survey; increas-

Figure 5. Reflection coefficient distributions calculated assuming normal incidence for each model and afrequency of 100 MHz for the (a) uniformly drained, (b) nonuniformly saturated, and (c) fully saturatedmodels. Four regions are indicated with ovals to highlight similarities and differences.

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ing the frequency of a survey increases resolution, but thebenefit of increased frequency can be offset by the correspond-ing increase in attenuation and therefore decreased penetra-tion depth [e.g., Noon et al., 1998]. The simulation of surveys atadditional frequencies is left for future work.

Some of the issues raised might be resolved by refining themethod for calculating reflection coefficient distribution withinhighly heterogeneous environments. However, not all wavephenomena, such as 2-D effects and complex wave interfer-ence patterns, are easily predicted from reflection coefficientimages alone. Effects such as these may be further exploredthrough the simulation of GPR, which is applied in section 3.5.

3.5. Simulation of GPR

In the present study, a 2-D staggered grid finite differencetime domain solution (second order in time and fourth order inspace) of the electromagnetic wave equation is used to com-pute synthetic waveforms (see Levander [1988] for a descrip-tion of how to implement such finite difference schemes). Tosimulate the GPR reflection survey performed at the Hertensite, the source/receiver configuration corresponding to that ofthe field measurements is used, the source and receiver pointsbeing located ;1 m apart. The air-ground interface is notmodeled to simplify analysis; instead, a Ricker wavelet sourcewith a center frequency of 100 MHz (chosen to approximatelymatch the frequency seen in the field data) is placed in theupper layer of the model. Approximately four traces per wave-length are simulated along the survey line since finer resolutionis typically not expected with closer spacing. Since the code is2-D, 3-D effects (reflections arriving from reflectors not situ-ated in the modeled 2-D slice) are not modeled and are notanticipated to be significant since, as noted in section 3.1, thevariation in the direction parallel to the modeled profile isgradual.

Many subsurface materials have been shown to have fre-quency-dependent electrical properties [Turner and Siggins,1994]. Furthermore, Bergmann et al. [1998] demonstrate the

potential importance of including frequency-dependent behav-ior in the simulation of GPR, such as that of the potentialbound-water relaxation mechanism occurring in materials atlow saturation. They present a relatively straightforward nu-merical procedure to implement such processes. In the presentstudy, determination of frequency dependence for the electri-cal properties of the lithological units in their varying degreesof water saturation is not attempted. Instead, the values for theelectrical permittivity and conductivity are assumed constantwith frequency and are calculated for simplicity from thepetrophysical models shown in (1), (2), and (4) with the mea-sured porosity values and chosen Sw distributions. These cal-culated parameter fields, along with the value of the magneticpermeability, which is assumed constant and equal to that offree space (m0), are used as input for the finite differenceprocedure. The effect of frequency-dependent wave phenom-ena on such GPR modeling of an outcrop image is left forfuture investigation.

To minimize wave reflection by the boundaries back into themodel space, adsorbing boundaries are implemented [e.g.,Casper and Kung, 1996]. Although slight reflections from theboundaries to the left and right of the source remain, they aresubtracted from the simulated waveforms (after being calcu-lated through an additional simulation). See Figure 6 for adepiction of the model geometry; a simulated wave field issuperposed over the model space as a visual aid.

4. ResultsThe GPR field data [from Bayer, 2000] corresponding to the

outcrop plane modeled along with the simulated GPR sectionsare shown in Plates 1a–1d. The average velocities of thedrained, the nonuniformly saturated, and the fully saturatedmodels were used to convert the synthetic traces, recorded asfunctions of time, into functions of depth assuming verticaltravel paths. To accomplish the same for the field data, theaverage velocity of the nonuniformly saturated model was as-

Figure 6. GPR simulation geometry. To simulate the GPR survey done at the Herten Site, a 2-D staggeredgrid finite difference code (fourth order in space, second order in time) was developed which requires as inputthe electromagnetic wave propagation parameters. A Ricker wavelet source with a center frequency of 100MHz is used to simulate a surface survey with source and receiver points located ;1 m apart and with tracescollected about every quarter-wavelength. The discretization in space and time is set to 5.7 cm and 0.2 ns,respectively, and the air-ground interface is not modeled. The snapshot of a radiating wave is superposed overthe model space for illustrative purposes.

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Plate 1. Comparison of (a) field data and (b) uniformly drained, (c) nonuniformly saturated, and (d) fullysaturated simulations. The average velocities of the models were used to convert reflection times to depth for thesimulations, and the average velocity for the partially drained model was used to do the same for the field data.Region 1 highlights a reflection seen in all models, regardless of saturation. Regions 2 and 3 show reflections dueto the drained open framework gravel dominant in the field data and the nonuniformly saturated model but notin the others. Region 4 corresponds to a dominant reflection seen in the uniformly drained and fully saturatedsimulation (but not in the nonuniformly saturated simulation); a dominant reflection in the field data in this regionis not clearly seen.

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sumed. In addition, an energy decay function was used tocorrect for overall attenuation in both the field data and thesimulated waveforms, and for the simulated waveforms a cor-rection for cylindrical divergence was additionally performed.Since loss of angled features (which corresponded to real struc-ture) in the GPR images was observed with migration, migra-tion was not performed on the field or simulated data. Al-though the resulting reflector images can include reflectionsarriving from 2-D paths (paths other than directly down fromthe source to a reflector and directly back up to the receiver),the overall image of the reflections corresponds very well to thelithologic units from the outcrop image (compare Plate 1 withFigure 2b).

The simulated images also show strong agreement with thereflection coefficient images (Figure 5), the differences be-tween simulations arising where predicted. In some cases, re-flections from lithologic units are seen regardless of watersaturation, whereas in other cases the visibility of reflectionsdepends on water saturation. Specific examples from the sim-ulation results will next be described. A dominant reflection isseen in region 1 for all simulations (i.e., regardless of satura-tion). This results from the contrast in porosity and thereforein electromagnetic parameters (regardless of saturation) be-tween one of the open framework gravel units (with w 5 0.23)and a matrix-supported unit (with w 5 0.13). However, theopen framework units on the right side of zone 2 (with w 50.23 or 0.26), for example, are surrounded by a component-supported gravel with similar bulk porosity (w 5 0.22); asexplained in the reflection coefficients discussion (see above),an increased reflection might be expected to occur in this case,with increasing water saturation contrast between the ele-ments. This is observed in the simulations; because of thedrained open framework gravel, regions 2 and 3 show (1)strong reflections in the nonuniformly saturated model (wherethe surrounding units are at a higher water content) and (2)weak reflections in the remaining simulations, where there isno contrast in water saturation. Region 4, in contrast, corre-sponds to a dominant reflection seen in the uniformly drainedsimulation and seen, though less easily, in the fully saturatedsimulation, though not clearly seen in the nonuniformly satu-rated simulation.

The synthetic GPR sections show overall agreement with thefield data (Plate 1a) but show, individually, distinct differences.When compared to the uniformly drained simulation, improve-ment is seen in the nonuniformly saturated simulation, inwhich the reflection in region 2 is emphasized as it is in thefield data. In the uniformly drained simulation the reflection inregion 4 is instead emphasized. Seen in region 3, reflections offof the internal features (open framework gravel units) withinzone 5 are also emphasized in the nonuniformly saturatedsimulation and the field data. However, in the region beneathoval 3 in the field data (the right side of zone 3 in Figure 2b),a strong reflection is seen which is not seen in any of thesimulations; the lithological element in this location is nowhereelse present in the outcrop profile and contains a high propor-tion of fines which are conducive to large amounts of retainedwater. Therefore this reflection could be due to a saturationcontrast that was present in the field but not modeled with thesimple assumptions of water saturation used for the presentwork.

Overall consideration of Plate 1 suggests that (1) water sat-uration and distribution affect the visibility of individual lith-ologic units, (2) modeling of some regions of the GPR field

data is improved when the presence of pore water is includedin the forward simulations, and (3) the synthetic GPR sectionshown for the fully saturated (real aquifer analog) model dif-fers substantially from the GPR sections of the unsaturatedsimulation models.

5. Summary and ConclusionsAn approach has been described which allows for a better

understanding of what can be seen with GPR. Using simplepetrophysical relationships, porosity estimates, and some waterdistribution scenarios, the calculation of reflection coefficientsfor and the GPR modeling of an outcrop analog yield imagesthat predict main reflections seen in field data. Simulationthrough a drained model represents what should be seen if theassumption of a “dry” analog were correct. Simulation througha partially drained model represents what might more realis-tically be seen in the unsaturated zone, where pore waterremains entrapped in a heterogeneous distribution. In reality,the extent of entrapped water and the degree of its spatialheterogeneity are determined by many factors, including thepermeability distribution, which is related to the pore sizedistribution and, ultimately, to the sedimentary environmentresponsible for sediment deposition. The simulated GPR sec-tion for the fully saturated model is that which is expected in areal aquifer (below the groundwater table). On the basis of thecomparison of the simulations it is possible to see if structuresidentified in the unsaturated zone should be similarly identifi-able in the saturated zone. In fact, the simulated GPR sectionsobtained for the unsaturated zone (the nonuniformly saturatedmodel in particular) and for the fully saturated zone showsubstantial differences. This suggests that further consider-ation is required in order to extend conclusions drawn aboutwhich lithologic units are visible at a relatively shallow outcropanalog site to those which should be visible much deeper, in aregion within the saturated zone, for which no outcrop analogis available for study.

As shown with the synthetic examples in this study, thedetection of subsurface structures depends on the degree anddistribution of subsurface water saturation as well as on thephysical properties of the materials present (including porosityand clay content). In reality, additional factors influence dataquality such as 3-D effects and unidentifiable sources of noise;the presented modeling is likely a best-case scenario. However,it is shown that even with noise-free (simulated) GPR sections,successful detection of subsurface targets depends on the pres-ence and distribution of pore water.

As noted, compared to the simulated image for the drainedmodel, the modeling of retained water improved the agree-ment between the synthetic waveforms and the GPR field datain some regions. This suggests that water was indeed present ina heterogeneous distribution and influenced the GPR fieldmeasurements, confirming a hypothesis of Bayer [2000]. Itmight be further derived from these results that a suitableimprovement for shallow subsurface characterization lies inthe collection of multiple GPR surveys at the same site underdifferent soil moisture conditions (e.g., during different sea-sons or before and after rain storms).

Concerning the preparation of a field survey, the prescribedapproach could be very useful if outcrop analogs are available;analog images might be used together with forward modelingor reflection coefficient estimation to help predict what sub-surface conditions are required or if it is even possible to

KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES1624

adequately delineate hydrologically relevant targets. The scopeof the outcrop analog concept should be further extended withthe intent being (1) to determine the hydrologically relevantfeatures for different sedimentary environments, (2) to deter-mine which of these features may be identified using GPRmethods (and how best to use the data to do so), and (3) toexamine more thoroughly the possibility of extending the re-sults from an outcrop analog investigation done in the unsat-urated zone to the characterization of a real aquifer. Goingone step beyond, the methodology could be applied to assist inthe estimation of water saturation. For example, in addition tousing GPR for delineating the structure of subsurface lithol-ogy, the presented methodology allows for an integrated ap-plication of geophysical and flow modeling using models de-rived from field data and information from an outcrop.

In reality, perhaps the delineation of individual lithologicalelements is not always possible. In this case, a more practicaluse of GPR data might be, first, for the identification of thesedimentary environment and then in combination with mul-tiple types of data through geostatistics-based procedures [e.g.,Ezzedine et al., 1999; Chen et al., 2001]. The combination ofsome GPR information (that with higher confidence) andborehole information, for example, along with informationknown about the sedimentological environment (from an out-crop analog or otherwise), may be an optimal way to incorpo-rate as much good information as possible, including that be-low the resolution of GPR or borehole interpolation alone,into site characterization.

Acknowledgments. The authors thank Evert Slob and the anony-mous reviewers for their thorough reviews of the manuscript and theirinsightful comments. This research is part of the special researchprogram (SFB) 275, TP C3, and was supported by NSF grant EAR9628306. The first author would also like to acknowledge the supportby the DAAD (German Academic Exchange Program).

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P. Dietrich and G. Teutsch, Institute of Applied Geology, Universityof Tuebingen, Sigwartstrausse 10, 72076 Tubingen, Germany.([email protected]; [email protected])

M. B. Kowalsky and Y. Rubin, Department of Civil and Environ-mental Engineering, University of California, 435 Davis Hall, Berke-ley, CA 94720. ([email protected]; [email protected])

(Received August 28, 2000; revised January 10, 2001;accepted January 11, 2001.)

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