1. Forward modeling of ground-penetrating radar data
using digitized outcrop images and multiple
scenarios of water saturation
M. B. Kowalsky1
Department of Civil and Environmental Engineering, University of California, Berkeley, California
P. Dietrich and G. Teutsch
Institute of Applied Geology, University of Tu¨bingen, Tu¨bingen, Germany
Y. Rubin
Department of Civil and Environmental Engineering, University of California, Berkeley, California
Abstract. Simple petrophysical models and a sedimentologically interpreted outcrop
photograph corresponding to the plane of a ground-penetrating radar (GPR) survey are
combined to create models for the simulation of GPR. This makes possible the
comparison of GPR field data, synthetic GPR sections, and a lithology image. On the
basis of this comparison the usefulness of the method for identifying hydrologically
significant lithofacies and the sensitivity of the results to different subsurface conditions
may be investigated. In particular, GPR simulations are performed for an outcrop model
at three states of water saturation: uniformly drained (uniform residual saturation),
nonuniformly saturated, and fully saturated. As predicted by reflection coefficient
calculations, comparison among the synthetic simulations highlights the importance of the
existing pore water distribution in determining the “visibility” of lithologic elements in
GPR sections. Comparisons of the synthetic GPR sections with the field data show overall
agreement, though the occurrence of various observed reflections depends on the presence
and distribution of pore water. Conclusions are also drawn about extending outcrop
analog-derived results to investigations of real (fully saturated) aquifers.
1. Introduction
Ground-penetrating radar (GPR) surveys are increasingly
used to assist in subsurface characterization. The potential of
the method for gaining information about subsurface structure
arises from the apparent correlation between material type and
electrical properties, in which contrasts cause reflections of
electromagnetic waves. Successful applications of GPR are as
far 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 GPR
investigations have been carried out above the groundwater
table, the sensitivity of GPR to the presence of pore water in
the unsaturated zone is well known [Asprion, 1998]. In some
cases, partial saturation is advantageous because enhanced
contrasts in electromagnetic parameters result and can even
allow for the estimation of water content and permeability
[Hubbard et al., 1997]. However, the presence of water can also
render poor GPR data quality [Asprion, 1998; Vandenberghe
and van Overmeeren, 1999]. Whether for applications aiming to
delineate subsurface structures or aiming to estimate hydro-
logic parameters, a methodical approach is desirable to assist
in the analysis of GPR data and to evaluate the influence of
soil conditions on such data.
One tool that can help in this goal is provided by the outcrop
analog concept. The introduction of outcrop analogs in the
geosciences 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 in
such applications as predicting contaminant transport and the
effect of absorption kinetics on flow modeling [Klingbeil, 1998]
and using geostatistical methods to build flow models from
borehole data [Whittaker and Teutsch, 1999].
Outcrop information has been used to validate geophysical
methods as well. For example, Dietrich et al. [1998] evaluated
tomographic methods using an outcrop model. Rea and Knight
[1998] compared GPR data with a nearby outcrop and went so
far as to evaluate the agreement between the geostatistical
parameters seen in the outcrop and those seen in the GPR
data. Reflections were assumed to occur with changes in ma-
terial type, and since the outcrop was bimodal (it consisted
mainly of two materials), reflections were assumed to corre-
spond to boundaries between the materials. With images of
material boundaries as detected by GPR and as seen in a
digitized photo of the outcrop, variogram analyses were per-
formed, and the variograms between the respective cases were
compared. The effect that entrapped water could have on the
results was not addressed.
Another application of GPR is radar stratigraphy, i.e., the
1
Also 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
1615

2. use of GPR to recognize characteristic radar facies and to
correlate them with specific depositional environments [Van-
denberghe and van Overmeeren, 1999]. Vandenberghe and van
Overmeeren [1999] systematically investigated the use of GPR
for the identification of various types of sedimentary struc-
tures. GPR surveys performed near, and in some cases only a
few meters away from, cliff faces (outcrops) allowed for a
comparison of cliff face photographs and GPR sections. Ad-
ditionally, some forward simulations were performed using
relative estimates of the reflectivity between modeled struc-
tures to help interpret the data; some large-scale features in
the GPR sections were identified in this manner as diffractions
from structural discontinuities such as intersecting channels
and interfaces at the bottoms of channels. In this study the
effects of pore water were considered at another site as well,
where sandy channels in a braided river deposit were probed
with GPR. In interpreting the data a disturbance in continuity
of the water table reflection was attributed to a region of
fine-grained particles in a channel fill situated above the water
table. Though not arrived at through a systematic modeling
approach, it was speculated that particles in this region have
higher moisture content and lower velocity than those in the
region lying directly below.
In fact, water has been observed to enhance the detectability
of some materials. For example, Beres et al. [1999, p. 15] rea-
soned that large changes in “porosity and water content at
erosional surfaces and boundaries of the open-framework
gravel produce the most-continuous reflections and correlate
best with outcrop data.” They explained the hydrogeologic
relevance of these elements by noting that their hydraulic con-
ductivities are 3 or 4 orders of magnitude higher than the
neighboring units and concluded that these elements can be
mapped with 3-dimensional (3-D) GPR analyses. This conclu-
sion highlights the need for a systematic, physically based
method 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 with
planes of GPR surveys [Beres et al., 1999; Bayer, 2000]. Sedi-
mentological interpretation of the photographs in this case
allows for a direct comparison of GPR data with lithology. If
electrical 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 field
data, forward modeling can allow for a controlled investigation
of electromagnetic wave sensitivity to different soil types and
conditions.
In the present study, a methodology is proposed in which a
carefully 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 saturation
are adopted in order to estimate electrical properties for each
lithological element in the outcrop. Then, the sensitivity of
GPR surveys to pore water is investigated through forward
simulations with models representing three cases of water sat-
uration: uniformly drained (uniform residual saturation), non-
uniformly saturated, and fully saturated. After comparing the
synthetic 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 structures
given various soil conditions.
2. Petrophysical Models
The 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 (␮0) for
most shallow subsurface materials (i.e., those containing no
metals). The electrical permittivity and conductivity for such
materials are, however, functions of, for example, porosity,
water content, and mineral composition [Scho¨n, 1996]. A com-
monly used form of the electric permittivity is the dielectric
constant k (or relative permittivity), defined as the dielectric
permittivity ␧ of the medium normalized by that of free space
␧0:
k ϭ ␧/␧0. (1)
For estimating the dielectric constant in the present work a
mixture model [Wharton et al., 1980] will be used. The use of
this model is desirable since it is physically rather than empir-
ically based and since it allows for the permittivity to be easily
calculated 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 ϭ ͓͑1 Ϫ ␸͒Vcl ͱkcl ϩ ͑1 Ϫ ␸͒͑1 Ϫ Vcl͒ͱks ϩ Sw␸ͱkw
ϩ ͑1 Ϫ Sw͒␸ͱka͔2
, (2)
where Vcl is the clay content in the mixture, ␸ is the porosity,
Sw is the water saturation (the fraction of the pore space filled
with water), and kcl, ks, kw, and ka are the dielectric constants
of the clay, sand grains, water, and air, respectively. The di-
electric constant may then be converted through (1) into the
electrical permittivity, which is needed for forward modeling.
Additionally, in low loss media the corresponding velocity may
be estimated by the following relationship:
v ϭ 1/ ͱ␮0␧. (3)
For estimation of the electrical conductivity the empirically
based model
␴eff
␴w
ϭ ͫ 1
Sw
n
a
␸mͬ
Ϫ1
(4)
is chosen, where ␴w is the electrical conductivity of the pore
fluid and a, m, and n are empirically determined [Archie, 1942;
Scho¨n, 1996]. Typical values for various subsurface materials
are given by Scho¨n [1996].
Attenuation is governed by the electromagnetic parameters
and is especially sensitive to water saturation and clay content,
an increase of either causing a decrease in penetration depth
for a GPR wave [Saarenketo, 1998]. Illustrating this point,
Vandenberghe and van Overmeeren [1999] described a field
survey and attributed limited radar penetration depth to the
presence of electrically conductive clayey material and a near-
surface water table. For a discussion on the estimation of
actual GPR penetration depth, given material properties, and
actual GPR system performance, the reader is directed to
works 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

3. a detailed photograph of the resulting outcrop was taken after
excavation. With representative hydrological parameters for
each lithologic element (measured in the laboratory) the dig-
itized outcrop image and the aforementioned petrophysical
models are used to construct models for GPR simulation; this
is 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). The
sedimentary deposits in this region were formed in a braided
river environment and consist mainly of layers of poorly to
well-sorted sand and gravel with no silt or clay.
During August and September 1999, a series of GPR surveys
accompanied excavation of the gravel quarry at Herten. The
excavation was performed to a depth of ϳ9 m (never reaching
the groundwater table) in such a way that the exposed face of
the previously GPR-surveyed region could be photographed;
high-resolution photographs were taken every 1–2 m, yielding
six parallel images in a span of 10 m, the dimensions of each
image being 16 m in length by ϳ7 m in depth. Inspection of the
parallel images indicates that the variation in the third dimen-
sion (perpendicular to the outcrop slices) is significant but
relatively gradual. It is also worth noting that the advancing
outcrop surface was somewhat uneven as a result of the un-
stable poorly consolidated sediments; ensuing distortion of the
image 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, the
outcrop photographs were then carefully interpreted to yield
maps of lithology [Bayer, 2000]. In the present study, one pro-
file from the work of Bayer [2000] is chosen, the photograph of
which 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, the
spatial distribution of the lithological elements was combined
with representative porosity values (that is, each lithologic unit
is assumed to have uniform properties throughout the entire
model and is assigned a single value) to yield the porosity
distribution shown in Figure 2b.
Though a more complete sedimentological description of
the outcrop image is available from Bayer [2000], the major
zones 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 sequentially
graded deposits occur with thin and discontinuous open frame-
work layers positioned horizontally in zone 1 and angled to
trough shaped in the right side of zone 2. (The higher porosity
wedge-shaped element in the left side of zone 2, which is
pinched 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, in
which the highly conductive open framework gravel units oc-
cur. These sequences are formed by the deposition of graded
material, alternating between sand-gravel mixtures with low
porosity and permeability and open framework gravel with
high porosity and permeability. The delineation of zones is
somewhat arbitrary. For example, the boundary between zones
2 and 3 on the right-hand side of the outcrop photo is not
clearly defined.
Ranging from 6.0 ϫ 10Ϫ7
to 1.0 m/s, the range in hydraulic
conductivity values represented by the various elements is
large; the largest hydraulic conductivities correspond to the
open framework gravel. However, it is important to note that
the relevance of various hydrological elements depends on the
goals of a hydrogeological investigation. The connectivity of
units with high hydraulic conductivity could be important in
the scenario in which the first arrival of contaminants is im-
portant. However, for planning the site remediation strategy of
a reactive contaminant, for example, it is conceivable that in
addition to or instead of the high-conductivity zones, the iden-
tification of materials with high adsorption capacity, such as
sand, is sought [Kleineidam et al., 1999]. Whether the use of
geophysical methods improves characterization in these cases
is 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 the
detectability of various hydrological elements for different sub-
surface conditions.
3.2. Water Distribution Scenarios
The effects of entrapped water on GPR are not always
considered in geophysical surveys conducted in the unsatur-
ated zone. Nevertheless, downward infiltration of surface wa-
ter and fluctuations in the groundwater table leave entrapped
pore water, the amount of which and the uniformity of which
is a function of time, mean grain diameter, and pore distribu-
tion [Bear, 1988].
In evaluating the aforementioned field data it is important to
consider that it rained some days before the GPR measure-
ments. Retained water was therefore suspected to be present
in the subsurface during the measurements and to have influ-
Figure 1. Location of the Herten gravel quarry field site.
1617KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES

4. Figure 2. Outcrop modeling procedure. (a) A sedimentologically interpreted [Bayer, 2000] and digitized
photograph from an outcrop at the Herten field site. (b) Representative porosity distribution. This image is
used 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 at
residual saturation (Sw ϭ 0.08) and that the remaining materials (shown in white) have additional retained
water (Sw ϭ 0.17). The units on the axes are meters.
KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES1618

5. 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 highly
heterogeneous. Since investigating the general response of
GPR to soil conditions is the goal of this study, rather than
trying to reproduce exactly and explain every feature of the
Herten GPR field data, a simple approach is used to put forth
some reasonable water distributions. The three scenarios of
water distribution chosen for forward modeling are as follows:
1. The first model contains so-called drained elements at a
uniform residual saturation (Sw ϭ 0.08) and will be referred
to as the drained model.
2. The second model is of nonuniform saturation with
open framework gravel modeled as drained and at residual
saturation (Sw ϭ 0.08) and with the remaining elements
modeled at higher water content (Sw ϭ 0.17); the motivation
for this is based on the relationship between mean grain di-
ameter and retained water [e.g., Bear, 1988]. The simplified
approach to assigning water distribution is intended to yield a
model with plausible contrasts in water saturation rather than
one with the most accurate water distribution possible (a more
accurate water distribution might be obtained through flow
simulations). The distribution of water saturation for this
model is shown in Figure 2c. The black regions are those
modeled as completely drained (at residual saturation), while
those with higher water content (less drained) are shown in
white. The first and second models are intended to represent
potential conditions in the unsaturated zone.
3. The third model contains all fully saturated elements
(Sw ϭ 1) and represents an aquifer below the groundwater
table. 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 extended
to 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 electromagnetic
parameters on the basis of the porosity values shown in Figure
2b and the Sw distributions (as described in section 3.2) can be
achieved through the use of the petrophysical models shown in
(1)–(4). Sieve analyses of soil samples from sites geologically
analogous to the site which is modeled in the present study
showed negligible amounts of clay. Therefore, in estimating
the electrical permittivity and conductivity the volume of clay
Vcl 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 Knoll
and Knight [1994]) and to 80 and 1 for water and air, respec-
tively.
To illustrate the influence of soil porosity and saturation on
the electromagnetic parameters, the dielectric constant and
velocity are calculated as a function of porosity for various
water saturation values using (1)–(3) and are shown in Figures
3a and 3b. On the basis of the representative porosity mea-
surements and chosen Sw values the distributions of values
used for the outcrop elements in the three synthetic models are
shown as well.
Electrical conductivity is calculated with (4) and plotted as a
function of porosity for varying values of Sw, as shown in
Figure 3c. The parameters a and m are assigned values of 0.88
and 1.37, respectively (average values for unconsolidated
sand), and n is set equal to 2 [Scho¨n, 1996]. Site-specific mea-
surements could improve the accuracy of these values and
insure that these models best represent the materials at the
Herten 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 be
0.4 mS/cm, a typical value for the investigated site.
The relative change in electrical conductivity with increasing
water saturation is seen to be much larger than that in velocity.
The nonlinear response of ␴ to Sw is evident in (4), in which Sw
is raised to the power of n. The values for the elements in each
of the three synthetic models are shown as well in Figures 3a
and 3b.
In considering the plots shown in Figure 3, one expects only
small reflections to occur in the drained model, with no units in
particular causing dominant reflections. Since the dielectric
constant and electrical conductivity values slightly increase
with porosity, one also expects the order of elements to help
determine the relative reflectivity of the elements (that is,
interfaces between elements with a larger porosity contrast will
have larger differences in electromagnetic parameters than
those with a smaller contrast in porosity). In the nonuniformly
Figure 3. Variation of (a) dielectric constant, (b) velocity, and (c) electric conductivity with porosity for
various values of water saturation Sw (in increments of 0.1) as calculated with petrophysical models. Note that
in Figure 3c the lowest curve corresponds to Sw ϭ 0.01 ( 0); the remaining curves in Figure 3c proceed with
Sw ϭ 0.1, 0.2, ⅐ ⅐ ⅐ , 1.0. On the basis of the porosity estimates for each lithologic element the values for the
elements 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

6. saturated model the largest contrast should exist between the
drained open framework gravel layers and the undrained ele-
ments. Among the undrained elements the contrasts in elec-
tromagnetic parameters are comparatively small. For the fully
saturated 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 reflections
might 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 between
lithofacies with significant velocity contrasts that are antici-
pated to cause GPR reflections. However, the magnitudes of
reflections are functions of additional factors and are better
quantified through the calculation of the reflection coefficients.
3.4. Reflection Coefficients
To help determine which material interfaces correspond to
contrasts in electrical properties high enough to create signif-
icant GPR reflections, the reflection coefficients are calculated
for each synthetic model. As an approximation, normal inci-
dence of the vertically traveling wave front is assumed in the
calculations, 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 materials
is calculated by
Rn ϭ
K2 Ϫ K1
K2 ϩ 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 saturated
models. Because of the large decrease in velocity for fully saturated materials, the gray scale for Figure 4c is
different than the scale for Figures 4a and 4b.
KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES1620

7. where K is the complex propagation constant for each material
and is a function of ␴, ␧, ␮, and radar wave frequency [e.g.,
Turner and Siggins, 1994]. To account for resolution in a GPR
survey being typically around a quarter wavelength, the reflec-
tion coefficients were calculated sequentially from the top of
the 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 reflections
would be generated which are distinct from the reflection gen-
erated by the overlying reflector. The average wavelengths are
112, 107, and 73 cm for the uniformly drained, nonuniformly
saturated, and fully saturated models, respectively.
The distributions of Rn values for each model are shown in
Figure 5. From these images it is apparent that regions of high
reflectivity vary between the models. Four numbered regions
are indicated with ovals to help anticipate and explain poten-
tial differences in the forward simulations. Region 1 indicates
an 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 elements
that should cause relatively large reflections only in the second
model. Thus strong reflections within the zones containing
open framework gravel are not expected without a contrast in
water saturation (as in the second model) between the open
framework gravel and the surrounding materials within the
zones. Additionally, region 4 shows the bottom border of the
sand-gravel wedge formation and is seen to be reflective in the
uniformly drained and fully saturated models but not in the
nonuniformly saturated model.
These examples already show the importance of water sat-
uration in terms of the reflectivity of the different lithologic
units. In addition, they demonstrate that the visibility of a
reflector depends on (1) its reflectivity relative to that of
nearby interfaces or nearby regions with contrasting water con-
tent (i.e., a “weak” reflector might be “masked” by a nearby
stronger reflector) and (2) the resolution of a survey; increas-
Figure 5. Reflection coefficient distributions calculated assuming normal incidence for each model and a
frequency of 100 MHz for the (a) uniformly drained, (b) nonuniformly saturated, and (c) fully saturated
models. Four regions are indicated with ovals to highlight similarities and differences.
1621KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES

8. ing the frequency of a survey increases resolution, but the
benefit 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 at
additional frequencies is left for future work.
Some of the issues raised might be resolved by refining the
method for calculating reflection coefficient distribution within
highly heterogeneous environments. However, not all wave
phenomena, such as 2-D effects and complex wave interfer-
ence patterns, are easily predicted from reflection coefficient
images alone. Effects such as these may be further explored
through 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 difference
time domain solution (second order in time and fourth order in
space) 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). To
simulate the GPR reflection survey performed at the Herten
site, the source/receiver configuration corresponding to that of
the field measurements is used, the source and receiver points
being located ϳ1 m apart. The air-ground interface is not
modeled to simplify analysis; instead, a Ricker wavelet source
with a center frequency of 100 MHz (chosen to approximately
match the frequency seen in the field data) is placed in the
upper layer of the model. Approximately four traces per wave-
length are simulated along the survey line since finer resolution
is typically not expected with closer spacing. Since the code is
2-D, 3-D effects (reflections arriving from reflectors not situ-
ated in the modeled 2-D slice) are not modeled and are not
anticipated to be significant since, as noted in section 3.1, the
variation in the direction parallel to the modeled profile is
gradual.
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 potential
bound-water relaxation mechanism occurring in materials at
low saturation. They present a relatively straightforward nu-
merical procedure to implement such processes. In the present
study, determination of frequency dependence for the electri-
cal properties of the lithological units in their varying degrees
of water saturation is not attempted. Instead, the values for the
electrical permittivity and conductivity are assumed constant
with frequency and are calculated for simplicity from the
petrophysical 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 magnetic
permeability, which is assumed constant and equal to that of
free space (␮0), are used as input for the finite difference
procedure. The effect of frequency-dependent wave phenom-
ena on such GPR modeling of an outcrop image is left for
future investigation.
To minimize wave reflection by the boundaries back into the
model space, adsorbing boundaries are implemented [e.g.,
Casper and Kung, 1996]. Although slight reflections from the
boundaries to the left and right of the source remain, they are
subtracted from the simulated waveforms (after being calcu-
lated through an additional simulation). See Figure 6 for a
depiction of the model geometry; a simulated wave field is
superposed over the model space as a visual aid.
4. Results
The GPR field data [from Bayer, 2000] corresponding to the
outcrop plane modeled along with the simulated GPR sections
are shown in Plates 1a–1d. The average velocities of the
drained, the nonuniformly saturated, and the fully saturated
models were used to convert the synthetic traces, recorded as
functions of time, into functions of depth assuming vertical
travel paths. To accomplish the same for the field data, the
average 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 staggered
grid finite difference code (fourth order in space, second order in time) was developed which requires as input
the electromagnetic wave propagation parameters. A Ricker wavelet source with a center frequency of 100
MHz is used to simulate a surface survey with source and receiver points located ϳ1 m apart and with traces
collected 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 over
the model space for illustrative purposes.
KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES1622

9. Plate 1. Comparison of (a) field data and (b) uniformly drained, (c) nonuniformly saturated, and (d) fully
saturated simulations. The average velocities of the models were used to convert reflection times to depth for the
simulations, 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 due
to the drained open framework gravel dominant in the field data and the nonuniformly saturated model but not
in the others. Region 4 corresponds to a dominant reflection seen in the uniformly drained and fully saturated
simulation (but not in the nonuniformly saturated simulation); a dominant reflection in the field data in this region
is not clearly seen.
1623KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES

10. sumed. In addition, an energy decay function was used to
correct for overall attenuation in both the field data and the
simulated 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 reflections
arriving from 2-D paths (paths other than directly down from
the source to a reflector and directly back up to the receiver),
the overall image of the reflections corresponds very well to the
lithologic units from the outcrop image (compare Plate 1 with
Figure 2b).
The simulated images also show strong agreement with the
reflection coefficient images (Figure 5), the differences be-
tween simulations arising where predicted. In some cases, re-
flections from lithologic units are seen regardless of water
saturation, whereas in other cases the visibility of reflections
depends on water saturation. Specific examples from the sim-
ulation results will next be described. A dominant reflection is
seen in region 1 for all simulations (i.e., regardless of satura-
tion). This results from the contrast in porosity and therefore
in electromagnetic parameters (regardless of saturation) be-
tween one of the open framework gravel units (with ␸ ϭ 0.23)
and a matrix-supported unit (with ␸ ϭ 0.13). However, the
open framework units on the right side of zone 2 (with ␸ ϭ
0.23 or 0.26), for example, are surrounded by a component-
supported gravel with similar bulk porosity (␸ ϭ 0.22); as
explained 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 the
drained open framework gravel, regions 2 and 3 show (1)
strong reflections in the nonuniformly saturated model (where
the surrounding units are at a higher water content) and (2)
weak reflections in the remaining simulations, where there is
no contrast in water saturation. Region 4, in contrast, corre-
sponds to a dominant reflection seen in the uniformly drained
simulation and seen, though less easily, in the fully saturated
simulation, though not clearly seen in the nonuniformly satu-
rated simulation.
The synthetic GPR sections show overall agreement with the
field data (Plate 1a) but show, individually, distinct differences.
When compared to the uniformly drained simulation, improve-
ment is seen in the nonuniformly saturated simulation, in
which the reflection in region 2 is emphasized as it is in the
field data. In the uniformly drained simulation the reflection in
region 4 is instead emphasized. Seen in region 3, reflections off
of the internal features (open framework gravel units) within
zone 5 are also emphasized in the nonuniformly saturated
simulation and the field data. However, in the region beneath
oval 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 the
simulations; the lithological element in this location is nowhere
else present in the outcrop profile and contains a high propor-
tion of fines which are conducive to large amounts of retained
water. Therefore this reflection could be due to a saturation
contrast that was present in the field but not modeled with the
simple assumptions of water saturation used for the present
work.
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 included
in the forward simulations, and (3) the synthetic GPR section
shown for the fully saturated (real aquifer analog) model dif-
fers substantially from the GPR sections of the unsaturated
simulation models.
5. Summary and Conclusions
An approach has been described which allows for a better
understanding of what can be seen with GPR. Using simple
petrophysical relationships, porosity estimates, and some water
distribution scenarios, the calculation of reflection coefficients
for and the GPR modeling of an outcrop analog yield images
that predict main reflections seen in field data. Simulation
through a drained model represents what should be seen if the
assumption of a “dry” analog were correct. Simulation through
a partially drained model represents what might more realis-
tically be seen in the unsaturated zone, where pore water
remains entrapped in a heterogeneous distribution. In reality,
the extent of entrapped water and the degree of its spatial
heterogeneity are determined by many factors, including the
permeability distribution, which is related to the pore size
distribution and, ultimately, to the sedimentary environment
responsible for sediment deposition. The simulated GPR sec-
tion for the fully saturated model is that which is expected in a
real aquifer (below the groundwater table). On the basis of the
comparison of the simulations it is possible to see if structures
identified in the unsaturated zone should be similarly identifi-
able in the saturated zone. In fact, the simulated GPR sections
obtained for the unsaturated zone (the nonuniformly saturated
model in particular) and for the fully saturated zone show
substantial differences. This suggests that further consider-
ation is required in order to extend conclusions drawn about
which lithologic units are visible at a relatively shallow outcrop
analog site to those which should be visible much deeper, in a
region within the saturated zone, for which no outcrop analog
is available for study.
As shown with the synthetic examples in this study, the
detection of subsurface structures depends on the degree and
distribution of subsurface water saturation as well as on the
physical properties of the materials present (including porosity
and clay content). In reality, additional factors influence data
quality 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 drained
model, the modeling of retained water improved the agree-
ment between the synthetic waveforms and the GPR field data
in some regions. This suggests that water was indeed present in
a heterogeneous distribution and influenced the GPR field
measurements, confirming a hypothesis of Bayer [2000]. It
might be further derived from these results that a suitable
improvement for shallow subsurface characterization lies in
the collection of multiple GPR surveys at the same site under
different soil moisture conditions (e.g., during different sea-
sons or before and after rain storms).
Concerning the preparation of a field survey, the prescribed
approach could be very useful if outcrop analogs are available;
analog images might be used together with forward modeling
or 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

11. adequately delineate hydrologically relevant targets. The scope
of the outcrop analog concept should be further extended with
the intent being (1) to determine the hydrologically relevant
features for different sedimentary environments, (2) to deter-
mine which of these features may be identified using GPR
methods (and how best to use the data to do so), and (3) to
examine 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. Going
one step beyond, the methodology could be applied to assist in
the estimation of water saturation. For example, in addition to
using 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 lithological
elements is not always possible. In this case, a more practical
use of GPR data might be, first, for the identification of the
sedimentary 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 of
some GPR information (that with higher confidence) and
borehole information, for example, along with information
known 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 their
insightful comments. This research is part of the special research
program (SFB) 275, TP C3, and was supported by NSF grant EAR
9628306. The first author would also like to acknowledge the support
by the DAAD (German Academic Exchange Program).
References
Archie, G. E., The electrical resistivity log as an aid in determining
some reservoir characteristics, Trans. Am. Inst. Min. Metall. Pet.
Eng., 146, 54–62, 1942.
Asprion, U., Ground-penetrating radar (GPR) analysis in aquifer-
sedimentology: Case studies, with an emphasis on glacial systems of
SW Germany, Tuebinger Geowiss. Arb., A43, Univ. Tuebingen, Tu-
ebingen, Germany, 1998.
Bayer, P., Aquifer-Anolog-Studie in grobklastischen “braided river”
Ablagerungen: Sedimentaere/hydrogeologische Wandkartierung
und Kalibrierung von Georadarmessungen, Diplomkartierung,
Univ. Tuebingen, Tuebingen, Germany, 2000.
Bear, J., Dynamics of Fluids in Porous Media, pp. 485–486, Dover,
Mineola, New York, 1988.
Beres, M., P. Huggenberger, A. Green, and H. Horstmeyer, Using two-
and three-dimensional georadar methods to characterize glacioflu-
vial architecture, Sediment. Geol., 129, 1–24, 1999.
Bergmann, T., J. O. A. Robertsson, and K. Holliger, Finite-difference
modeling of electromagnetic wave propagation in dispersive and
attenuating media, Geophysics, 63, 856–867, 1998.
Casper, D. A., and K.-J. S. Kung, Simulation of ground-penetrating
radar waves in a 2-D soil model, Geophysics, 61, 1034–1049, 1996.
Chen, J., S. Hubbard, and Y. Rubin, Estimating the hydraulic conduc-
tivity at the south oyster site from geophysical tomographic data
using Bayesian techniques based on the normal linear regression
model, Water Resour. Res., in press, 2001.
Davis, J. M., J. L. Wilson, F. M. Phillips, and M. B. Gotkowitz, Rela-
tionship between fluvial bounding surfaces and the permeability
correlation structure, Water Resour. Res., 33(8), 1843–1854, 1997.
Dietrich, P., T. Fechner, J. Whittaker, and G. Teutsch, An integrated
hydrogeophysical approach to subsurface characterization, in
Groundwater Quality: Remediation and Protection, edited by M. Her-
bert and K. Kovar, IAHS Publ., 250, 513–520, 1998.
Ezzedine, S., Y. Rubin, and J. Chen, Bayesian method for hydrological
site characterization using borehole and geophysical survey data:
Theory and application to the Lawrence Livermore National Labo-
ratory Superfund site, Water Resour. Res., 35(9), 2671–2683, 1999.
Freeland, R. S., R. E. Yoder, and J. T. Ammons, Mapping shallow
underground features that influence site-specific agricultural pro-
duction, J. Appl. Geophys., 40, 19–27, 1998.
Greaves, R. J., D. P. Lesmes, J. M. Lee, and M. N. Toksoz, Velocity
variations and water content estimated from multi-offset, ground-
penetrating radar, Geophysics, 61, 683–695, 1996.
Hubbard, S. S., Y. Rubin, and E. Major, Ground-penetrating-radar-
assisted saturation and permeability estimation in bimodal systems,
Water Resour. Res., 33(5), 971–990, 1997.
Kleineidam, S., H. Ruegner, B. Ligouis, and P. Grathwohl, Organic
matter facies and equilibrium sorption of phenanthrene, Environ.
Sci. Technol., 33, 1637–1644, 1999.
Klingbeil, R., Outcrop analog studies: Implications for groundwater
flow and contaminant transport in heterogeneous glaciofluvial qua-
ternary deposits, dissertation, pp. 36–43, 47–52, Geowiss. Fak.,
Univ. Tuebingen, Tuebingen, Germany, 1998.
Klingbeil, R., S. Kleineidam, U. Asprion, T. Aigner, and G. Teutsch,
Relating lithofacies to hydrofacies: Outcrop-based hydrogeological
characterisation of Quarternary gravel deposits, Sediment. Geol.,
129, 299–310, 1999.
Knoll, M., and R. Knight, Relationships between dielectric and hydro-
logic properties of sand-clay mixtures, paper presented at Fifth In-
ternational Conference on Ground Penetrating Radar, Environ. and
Eng. Geophys. Soc., Kitchener, Ont., Canada, 1994.
Levander, A. R., Fourth-order finite-difference P-SV seismograms,
Geophysics, 53, 1425–1436, 1988.
Noon, D. A., G. F. Stickley, and D. Longstaff, A frequency-
independent characterisation of GPR penetration and resolution
performance, J. Appl. Geophys., 40, 127–137, 1998.
Rea, J., and R. Knight, Geostatistical analysis of ground-penetrating
radar data: A means of describing spatial variation in the subsurface,
Water Resour. Res., 34(3), 329–339, 1998.
Rubin, Y., S. S. Hubbard, A. Wilson, and M. Cushey, Aquifer charac-
terization, in The Handbook of Groundwater Engineering, edited by
J. W. Delleur, pp. 10.1–10.68, CRC Press, Boca Raton, Fla., 1998.
Saarenketo, T., Electrical properties of water in clay and silty soils,
J. Appl. Geophys., 40, 73–88, 1998.
Scho¨n, J. H., Physical Properties of Rocks: Fundamentals and Principles
of Petrophysics, pp. 379–478, Pergamon, New York, 1996.
Tohge, M., F. Karube, M. Kobayashi, A. Tanaka, and K. Ishii, The use
of ground-penetrating radar to map an ancient village buried by
volcanic eruptions, J. Appl. Geophys., 40, 49–58, 1998.
Turner, G., and A. F. Siggins, Constant Q attenuation of subsurface
radar pulses, Geophysics, 59, 1192–1200, 1994.
Vandenberghe, J., and R. A. van Overmeeren, Ground-penetrating
radar images of selected fluvial deposits in the Netherlands, Sedi-
ment. Geol., 128, 245–270, 1999.
Wharton, R. P., G. A. Hazen, R. N. Rau, and D. L. Best, Electromag-
netic propagation logging: Advances in technique and interpreta-
tion, SPE, 9267, Am. Inst. of Min. Metall. and Pet. Eng., New York,
1980.
Whittaker, J., and G. Teutsch, Numerical simulation of subsurface
characterization methods: Application to a natural aquifer ana-
logue, Adv. Water Resour., 22(8), 819–829, 1999.
P. Dietrich and G. Teutsch, Institute of Applied Geology, University
of Tuebingen, Sigwartstrausse 10, 72076 Tubingen, Germany.
(peter.dietrich@uni-tuebingen.de; georg.teutsch@uni-tuebingen.de)
M. B. Kowalsky and Y. Rubin, Department of Civil and Environ-
mental Engineering, University of California, 435 Davis Hall, Berke-
ley, CA 94720. (MBKowalsky@lbl.gov; rubin@ce.berkeley.edu)
(Received August 28, 2000; revised January 10, 2001;
accepted January 11, 2001.)
1625KOWALSKY ET AL.: MODELING OF GPR DATA USING OUTCROP IMAGES

12. 1626