water content and porosity estimated from ground-penetrating radar and resistivity
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DESCRIPTIONWater content and porosity estimated from ground-penetratingradar and resistivity
Journal of Applied Geophy
Water content and porosity estimated from ground-penetrating
radar and resistivity
Department of Geology, Earth Sciences Centre, Goteborg University, Box 460, SE-405 30 Goteborg, Sweden
Received 1 September 2004; accepted 29 April 2005
Both ground-penetrating radar and the resistivity method have proven to be useful tools for exploring water content
variations, since related parameters such as dielectric constant and the resistivity of rocks and sediments are highly dependent
on moisture content. These methods were used independently to estimate volumetric water content in the unsaturated zone and
porosity in the saturated zone in a 100-m sandy section. Two sample sites along the profile were also chosen for a shallow
geophysical investigation and soil sampling, to enable the calibration and verification of the indirect geophysical methods. The
grain distribution at these sites is dominated by medium-sized sand (0.25–0.5 mm). The water content was 6.9 vol.% and
calculated porosities are 37% and 40% respectively. At each of these sites the mean water content values calculated from
resistivity are within one percentage unit of measured water content while those calculated from ground-penetrating radar give
higher values by as much as 2.9 percentage units. The water contents in the unsaturated zone in the section, estimated from
resistivity and ground-penetrating radar, show very similar trends, although that deduced from ground-penetrating radar is
generally somewhat larger, consistent with the results from the sample sites. The mean porosity values obtained from the two
methods in the saturated zone are in good agreement.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Ground-penetrating radar; Resistivity; Volumetric water content; Porosity
Soil water content and porosity are important
variables in hydrological processes and are of pri-
mary interest in hydrogeological investigations.
Ground-penetrating radar (GPR) has proven to be a
0926-9851/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
E-mail address: [email protected].
promising technique for estimating water content in
soil (Greaves et al., 1996; Van Overmeeren et al.,
1997; Huisman et al., 2001). Using GPR in combi-
nation with mixing formulae, the water content can
be estimated from dielectric constants, which are
calculated from interval velocities of radar waves.
The GPR method has successfully been applied to
shallow (less than 50 m) geological surveys (Davis
and Annan, 1989). The advantage of the method is
sics 58 (2006) 99–111
Fig. 1. Map of southwestern Sweden showing the location of the
site discussed in the text.
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111100
its vertical and lateral resolution in high resistivity
environments. The main restriction of the method is
the limited penetration in conductive materials, such
as clays or soils with saline or contaminated pore
water. Empirical relationships relating electrical re-
sistivity to porosity have long been known (Archie,
1942). The water content in a clean sand formation
can be estimated with Archie’s saturation equation.
The applicability of geoelectric methods is not re-
stricted to certain sedimentary sequences. However,
the principle of equivalence, i.e. the thickness and
resistivity of a unit can vary within certain limits and
still give equivalent models (Parasnis, 1997), makes
it difficult to estimate true subsurface resistivities.
GPR and geoelectric methods have been used in
combination to estimate water content and porosity
in different ways. Dannowski and Yaramanci (1999)
used GPR to constrain the geometry used in geo-
electric inversion and compared the results from the
two methods. Garambois et al. (2002) combined
GPR and geoelectrics to estimate water content and
water conductivity variations in the unsaturated
In contrast to previous investigations, this study
aims to independently evaluate two methods, GPR
and resistivity, used to assess water content (porosity
in the saturated zone) according to the relationship of
Topp et al. (1980) and Archie’s saturation equation
(Ward, 1990) respectively. The Topp et al. (1980)
equation, relating the dielectric constant to water
content, was chosen among other mixing formulae
(Mavko et al., 1999) because of its simplicity and
good results (Greaves et al., 1996). Using standard
techniques, in combination with well known empiri-
cal relationships, additional parameters can easily be
obtained. This study uses geophysical data collected
in a 100 m profile during two consecutive days in
stable weather conditions. Two spots along the pro-
file were chosen for small-scale shallow investiga-
tions to allow calibration and verification of the
indirect geophysical methods. These investigations
included GPR measurements, vertical electrical
soundings, and soil sampling at a depth of 1 m.
The measurements and sampling were made during
two consecutive days at each site within a month of
the profile survey. The data from each site were
compared separately. The soil samples were analyzed
to determine grain size distribution and gravimetric
water content, which was converted to volumetric
water content. In addition, the P-wave seismic refrac-
tion was used to discriminate between the unsaturat-
ed and saturated zone, to support the results obtained
from the GPR and resistivity.
The objective of this paper is to compare and
evaluate the variations in water content (porosity in
the saturated zone) in sand estimated independently
by two standard geophysical techniques, ground-pen-
etrating radar and resistivity, in combination with the
relationship of Topp et al. (1980) and Archie’s satu-
ration equation (Ward, 1990).
2. Geological setting
The test site is located at Veddige 70 km south of
Goteborg on the Swedish west coast at an elevation
of 15 m (Fig. 1). The post-glacial marine limit in the
region is 65 m above sea level (Passe, 1986). During
the overall post-glacial regression a small transgres-
sion (the Tapes transgression) occurred in certain
parts of southwestern Sweden, reaching 17 m
above sea level in the area (Passe, 1986). Large
quantities of mostly glaciofluvial sediments, originat-
ing from a terminal moraine in the vicinity, were
redeposited in an old channel. The area is underlain
by wave-sorted sand and gravel which overlies the
Grain size distributions presented as the mean of two samples at
Measured h Calculated
30 m Gravel (N2) 16 6.9% 39.9%
Sand (0.071–2) 80
Silt (b0.071) 4
60 m Gravel (N2) 21 6.9% 37.3%
Sand (0.071–2) 75
Silt (b0.071) 4
Measured volumetric water content (h) is the mean of three sam-
ples. A grain density of 2.65 g/cm3 was used in the porosity
calculation. The samples were taken at about 1 m depth. See
Figs. 3 and 7 for locations of sample sites.
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111 101
glacial marine clay that in turn overlies sand and
gravel (Passe, 1986). The surveyed profile is located
on the redeposited sand with a maximum depth of
Soil samples were taken at a depth of 1 m at 30
and 60 m along the profile. These soil samples
were analyzed for gravimetric water content and
converted to volumetric water content using soil
and pore water density estimates between 1.58–
1.68 and 1.00 g/cm3 respectively. The two sample
sites gave the same result of 6.9 vol.%. The calcu-
lated porosities, using a grain density of 2.65 g/
cm3, are 37% and 40%. The pits revealed a sharp
boundary between soil and sand at 0.33 m. The
sand was analyzed to determine particle size distri-
bution and is mostly of medium size (0.25–0.5
mm), 58% at sample site 30 m and 42% at 60
Fig. 2. The seismic refraction model showing the interface between unsatur
in the outlined area which coincides with the GPR profile.
m. The information from these sample pits is sum-
marized in Table 1.
3. Seismic refraction
To determine the depth to the water table by a third
independent method, we made a P-wave refraction
survey using an ABEM Terraloc Mark 6 seismograph.
The data were collected using 36 geophones (10 Hz)
with 2-m spacing. Two spreads were measured, mak-
ing a total length of 142 m. The energy source was a
sledgehammer hitting a steel plate and three blows
with the hammer were stacked in each record. The
data were processed using the delay-time method
(Pakiser and Black, 1957) followed by ray-tracing
(Yacoub et al., 1970).
The seismic model shows the interface between
unsaturated and saturated zones declining from 8.1
to 10.1 m in the investigated area (outlined in Fig. 2).
The first layer with 375 m/s velocity is dry sand. The
second layer with 1465 m/s velocity is interpreted as
wet sand. The P-wave velocity increases greatly when
water saturation reaches 100% (Bachrach and Nur,
1998), the refraction method is therefore suitable to
determine the water table depth in coarser material
such as sand. The water table deduced from seismic
ated and saturated zones. The water table declines from 8.1 to 10.1 m
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111102
refraction is plotted in all further models calculated
from GPR and CVES.
4. Ground-penetrating radar
Two different GPR techniques were used in this
study, the common-offset and the common midpoint
(CMP) methods. The former was used to get an
overview of the subsurface and to reveal any steeply
declining surface, while the latter was used to get
velocities with depths at regular intervals along the
profile. Additional CMP soundings were measured at
the two sample sites at 30 and 60 m to enable com-
parisons between water contents deduced from GPR
and known water contents.
GPR data is usually collected with the common-
offset method, in which the transmitting and receiving
antennae are a fixed distance apart (Davis and Annan,
1989). The 100 m common-offset profile was mea-
sured using a Ramac GPR system from Mala Geosci-
ence. Antennae were 2 m apart with a centre-
frequency of 50 MHz. The antennae were orientated
parallel to each other and perpendicular to the profile.
The data were collected every 0.2 m at a sample
frequency of 500 MHz. To improve the signal-to-
noise ratio, every trace was vertically stacked using
the auto-stack option, which means that every trace
was stacked between 32 and 64 times. A bhip chainQ,calibrated to actual length, was used to measure dis-
tance. This is a simple way to control the distance
between each trace measured. A cotton-thread runs
out as the operator slowly walks the profile. Every 0.2
m (in this case) the radar is triggered and a radar pulse
is transmitted and subsequently received by the an-
tenna. A more labour-intensive way to obtain data is
to make an entire GPR survey using the multi-offset
CMP technique (Fisher et al., 1992). In this case the
radar data can be used for traditional seismic proces-
sing and are sorted in CMP-gathers, which are used in
velocity analyses. The one-dimensional velocity mod-
els analyzed from CMP-gathers are then interpolated
for the construction of a two-dimensional velocity
profile. However, a less laborious way, used in this
survey, to obtain such a 2-D velocity profile is to
conduct individual multi-offset CMP soundings at
appropriate intervals along the profile. These mea-
surements can easily be collected in the field using
the hip chain measuring device.
In a multi-offset CMP sounding the separation
between transmitting and receiving antenna is contin-
ually increased from a fixed central location while the
two-way travel time to reflectors are measured. Any
subsurface contrast in electromagnetic properties
results in energy being reflected back to the surface.
Each reflection measured in this manner is used to
derive the RMS (root mean square) velocity down to
it. The CMP soundings were conducted using 50 MHz
antennae with a sampling frequency of 500 MHz. At
each CMP location the antenna separation was in-
creased from 0 to 20 m, with increments of 0.2 m.
The measuring device was placed at the midpoint. The
true distance walked was corrected in the processing
of data. To ensure that the antennae were moved
equally from the midpoint, the measurements were
performed stepwise using a measuring tape to control
distances. Two persons are needed for this procedure.
The spacing of individual CMP soundings, which
should be measured in a profile, is a compromise
between lateral and vertical variations of radar wave
velocity and the time and effort to make the measure-
ments. In this case we chose to conduct a spacing of 5
m and a total number of 21 CMP’s, which took about
2 h to collect. At the sample sites, CMP soundings
were conducted in two directions to reveal possible
three-dimensional geometry. The antennae centre fre-
quency used was 200 MHz with a sampling frequency
of 2000 MHz. The trace increment was 0.1 m. The
vertical auto-stack function was used in all CMP
The processing of GPR data (50 MHz) included
time-zero adjustments and low-cut filtering (dewow),
which removes low-frequency induction effects on the
radar equipment. The data were also compensated for
geometrical spreading and attenuation. The linear part
of the gain was set to 0.02 (1/pulse width) and the
exponential part was set to 0.03 dB/m (Davies and
Annan, 1989). AGC scaling was used for display. The
semblance approach (Yilmas, 1987) was used to pick
preliminary RMS (or normal move-out) velocities. If
the CMP data contains many and closely-spaced (in
time) reflections it could be difficult to distinguish
between real reflections arising from the interface
between two electrically different media, and just a
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111 103
complicated reflected wavelet. The compensation for
geometrical spreading and attenuation helped to pick
strong reflections in true amplitude display. To refine
the velocity picks, hyperbolae were superimposed on
the actual CMP gather to attain optimal fit.
4.2. Water content deduced from GPR
From CMP-gathers the RMS velocity to reflectors
is determined. The interval velocity, between reflec-
tors, is calculated using the Dix (1955) equation:
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2RMS;ntn � v2RMS;n�1tn�1
tn � tn�1
Where Vi is the interval velocity, vRMS are the
RMS velocity and tn and tn� 1 is the reflected ray
two-way travel times to the nth and (n�1)th reflectors
The GPR produces high frequency electromagnetic
energy in the 10 to 1000 MHz range. The term used to
describe the high frequency electromagnetic proper-
ties of materials is called the dielectric constant or the
relative permittivity. The complex dielectric constant
is given by:
KT ¼ KVþ j KWþ rdc=xe0ð Þf g ð2Þ
Where KV is the real part of the dielectric constant,and KW is the imaginary part of the dielectric constant
or the electric loss, rdc is the zero-frequency conduc-
tivity, x is the angular frequency, e0 is the free-space
permittivity (8.854�10�12 F/m), and j is (�1)1 / 2.
In soils where the electric loss is small, that is with
a lower conductivity than 10 mS/m, the following
Fig. 3. The GPR common-offset profile with depth represented by time. Th
and the lowest picked reflector used in velocity analyses between 215 and
relationship can be used to calculate the real part of
the dielectric constant (KV; Davis and Annan, 1989):
Where V is the propagation velocity of an electro-
magnetic wave in a medium with a real dielectric
constant of KV, c is the velocity of an electromagnetic
wave in free space (3�108 m/s).
Topp et al. (1980) found that the real part of the
dielectric constant (KV) seems to be highly sensitive to
volumetric water content, but only weakly sensitive to
soil type and density. They used a wide range of soil
samples, sandy loam to clay, to derive an empirical
relationship between the apparent (measured) dielec-
tric constant and volumetric water content:
hv ¼ � 5:3� 10�2 þ 2:92� 10�2Ka � 5:5
� 10�4K2a þ 4:3� 10�6K3
Where hv is the volumetric water content (the ratio
of water volume to total sample volume). For low-loss
materials KacKV where Ka is the apparent dielectric
The water content (h) equals the product of porosity(/) and water saturation (Sw). In water saturated soils
the water content (h) is a measure of porosity (/).
h ¼ /dSw ð5Þ
The 100 m long, GPR common-offset profile is
presented in a time–depth section in Fig. 3. The
e arrows show the water table between 20 and 100 m at about 150 ns
260 ns. Sample locations are indicated.
Fig. 4. Examples of CMP measurements used in the velocity analyses with a one-dimensional velocity model (continuous line: interval velocity,
dotted line: RMS velocity), hyperbolic adaptions and semblance images at a) 30 m, b) 60 m and c) 90 m along the profile.
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111104
Fig. 4 (continued).
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111 105
distinct reflector between 20–100 m at about 150 ns is
interpreted as the water table in sand, which also is
supported by the seismic refraction model (Fig. 2).
The slightly declining reflector below that, from 215
to 260 ns, marks the lowest reflector picked in veloc-
ity analyses. Note the diffractions from cables (known
Fig. 5. The GPR two-dimensional interval-velocity profile constructed from
water table deduced from seismic refraction.
locations) in the upper part at about 72 and 85 m.
Examples of CMP gathers with semblance and calcu-
lated interval velocities are shown in Fig. 4. The 21
CMP gathers were used to construct the two-dimen-
sional velocity section converted to depths (Fig. 5).
This section shows interval velocities between 72 and
21 one-dimensional velocity models. The continuous line shows the
Fig. 6. Volumetric water content section calculated from GPR interval velocities using the relationship of Topp et al. (1980). The continuous line
shows the water level deduced from seismic refraction.
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111106
149 m/As. The line marks the water table deduced
from the seismic method. The mean interval velocity
in the saturated zone is 76 m/As. The dielectric con-
stants were calculated using Eq. (3) and the Topp et al.
(1980) relationship (Eq. (4)) was used to convert the
dielectric constants to volumetric water content (Fig.
6). The main part of the unsaturated zone shows water
content between 10% and 12% but there are areas
with lower water content (7–10%). The western part
deviates with higher water content. In the saturated
zone the water content varies between 22% and 31%
The CMP soundings at the sample sites revealed
no three-dimensional heterogeneity. The interval ve-
locities 127 m/As (at 30 m) and 125 m/As (at 60 m)
yielded water contents of 9.4 and 9.8 vol.% respec-
tively. These water contents differ by up to 2.9 per-
centage units from measured water content at these
sites (Table 2).
GPR wave velocity and vertical electrical soundings (VES) measured nor
Sample site GPR velocity m/As Calculated h (%) VE
30 m (N–S) 127 9.4 11,
30 m (E–W) 127 9.4 7
60 m (N–S) 125 9.8 6
60 m (E–W) 125 9.8 5
Equivalent VES models resistivities (q) up to 1.2% fit, and the RMS (root
calculate the volumetric water content (h) from Archie’s formula (Eq. (7))
Figs. 3 and 7 for locations of sample sites.
The resistivity method is based on measuring the
electrical potential which results from an applied direct
electrical current flowing in the ground. The distribu-
tion of the electrical potential field depends in turn on
the resistivity of the ground. In a multi-electrode array
the measured result is displayed as a two-dimensional
variation of apparent resistivity. Software applications
for inversion of two-dimensional apparent resistivity
to solve for true resistivity can be classified as either
smooth inversion (DeGroot-Hedlin and Constable,
1990) or block inversion (Inman, 1975) methods,
each of which has some disadvantages. Smooth inver-
sion has a tendency to smear both resistivity and depth
to interfaces even in the case of well-defined structures
with sharp resistivity contrasts. On the other hand
th–south (N–S) and east–west (E–W) directions
S q (Vm) RMS error (%) Calculated h (%)
300–11,500 –11,700 0.9 5.3–5.3–5.2
500–7600–7800 1.3 6.8–6.7–6.6
500–6600–6800 1.6 7.4–7.3–7.2
600–5800–6100 3.2 8.1–7.9–7.7
mean square) errors for the best model (middle value) are given. To
, pore water conductivity of 13 mS/m and m =n =1.7 was used. See
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111 107
block inversion requires a starting model close to the
truth, which is rarely known precisely and is difficult
to construct especially in complex cases. We decided
to use the smooth inversion routine.
The continuous vertical electrical soundings
(CVES) were conducted with an ABEM Lund imaging
system, using Wenner measurement geometry. The
electrode spacing varied from 3 to 72 m in the 240 m
profile. The CVES profile was centred on the GPR
profile. A software package based on the smoothness-
constrained least-square method (DeGroot-Hedlin and
Constable, 1990) was used to invert apparent resistivity
to true resistivity. At the sample sites, 30 and 60 m,
vertical electrical soundings (Schlumberger geometry)
were measured in two directions, using the ABEM
equipment. A total of 13 measurements were done
moving the current electrodes equally and stepwise
from the midpoint, with distances increasing from 0.5
to 8 m between the midpoint and current electrodes.
5.2. Water content deduced from resistivity
Electrical conduction in soil is largely electrolytic,
taking place in connected pore spaces and along grain
boundaries. The relationship between resistivity (the
inverse of conductivity) and porosity in sedimentary
clay-free rocks is expressed by the formation factor,
which is the ratio of the resistivity of the porous media
to that of the pore fluid (Archie, 1942; Ward, 1990).
F ¼ qqw
¼ ad/�m ð6Þ
Where F is the formation factor, q is the bulk
resistivity of the rock, qw is the resistivity of the
Fig. 7. The resistivity model. The outlined area coincides with the GPR pro
pore fluid, / is the porosity, and a and m are
A general form of Archie’s saturation equation is:
q ¼ qw/�mS�nw ð7Þ
Where q and qw is the bulk resistivity of the rock
and the resistivity of the water respectively, / is the
porosity, Sw is the fractional water saturation, and n is
the saturation exponent, which normally is equal to 2
For a water-saturated rock Eq. (7) is reduced to:
q ¼ qw/�m ð8Þ
Jackson et al. (1978) found that the exponent m
was dependent on the shape of the particles, increas-
ing as they became less spherical, while variation in
size appeared to have little effect. Samples of natural
sand have values of m in the range 1.4 to 1.6.
In solving Archie’s formula (Eq. (7)) for volumet-
ric water content, which is the product of porosity
and water saturation, parameters such as the electri-
cal conductivity of pore water, m and n had to be
estimated. To do this, volumetric water content was
calculated using a range of conductivities (2–40 mS/
m) and m =n(1.3–2). After comparison between cal-
culated and measured water content from the two
sample sites conductivity was estimated at 13 mS/m
and m =n =1.7. This conductivity for pore water is
supported by measurement in a nearby well which
was also 13 mS/m. In this investigation it was
assumed that these parameters would not change in
file and is used in the water content calculation. Sample locations are
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111108
The 240 m long resistivity profile is presented in
Fig. 7. The area investigated and compared to GPR
measurements is outlined. Two anomalies with lower
resistivities are seen at about 72 and 85 m. These are
probably due to artefacts from cables, also seen in the
GPR section (Fig. 3). Although the cables are less
than 1 m below surface, the effects of resistivity
distortion are seen to considerably greater depths.
The water content was calculated using Archie’s equa-
tion (Eq. (7)), with water resistivity set to 77 Vm (the
inverse of 13 mS/m) and m =n =1.7. The resistivity-
based water content section (hresistivity; Fig. 8) is more
varied than the corresponding GPR section (hGPR;
Fig. 6), containing both lower and higher values,
although the general trend is the same with the ex-
ception of the two artefacts mentioned above. The
water content in the unsaturated zone is between 5%
and 14% with the lowest value about 2 percentage
units lower than in corresponding hGPR profile. The
increasing water content in the western part can also
be seen in the hGPR profile. In the saturated zone the
water content varies between 16% and 40% (neglect-
ing the anomalies).
The electrical soundings at the sample sites show
some anisotropy, especially at 30 m. At each site mean
water content values calculated from resistivity, 6.0%
(30 m) and 7.6% (60 m), are within 1 percentage unit
of the measured water content, 6.9% (Table 2).
Fig. 8. The volumetric water content section calculated from resistivity us
and m =n =1.7. The continuous line shows the water table deduced from
6. Discussion and conclusion
Referring to data from the sample pits (Tables 1
and 2) the volumetric water content calculated from
the Topp et al. (1980) equation is higher than both
the measured value and that calculated from the
Archie equation. Considering the corresponding pro-
files, hGPR and hresistivity (Figs. 6 and 8), the same
trend is true for the larger part of the section, which
can be seen in Fig. 9 showing the difference between
these two results. However, except for the two
anomalies the hresistivity shows higher water content
near to the surface. This could be due to the fact that
the smallest electrode spacing is 3 m which enables a
shallower measurement of water content than for
hGPR where the first picked reflector in the velocity
analysis is at a depth of about 4 m. The hresistivityprofile seems to be more detailed due to a denser
sample grid with depth, but also probably due to the
smooth inversion routine, which renders a gradual
change of resistivities even if sharp boundaries exist
in the subsurface (Olayinka and Yaramanci, 2000,
2002). On the other hand the less detailed hGPR is
restricted by the number of reflections present in the
subsurface and by the distance between the CMP’s.
So in general, the difference in data density accounts
for some of the differences between the two methods
seen in Fig. 9.
In the saturated zone the water content, which is
the porosity when the pores are saturated, varies
ing Archie’s (1942) equation. Water conductivity is set to 13 mS/m
Fig. 9. This section shows the difference between volumetric water contents deduced from GPR and resistivity.
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111 109
between 22% and 31% in hGPR (Fig. 6) with a mean
of 28%. The corresponding range for hresistivity (Fig.
8) is wider, roughly between 16% and 40% but also
with a mean of 28%, calculated between depths of
10.80 and 12.89 m (excluding the anomaly between
82 and 90 m). In the sample pits the porosity was
measured at 37% and 40% respectively. This sug-
gests a decrease in porosity by approximately 10
percentage units at about 10 m depth. However,
the measured porosity from 1 m depth is the total
porosity which is the sum of effective, trapped and
isolated porosities whereas the porosity calculated at
10 m depth from the resistivity method is the effec-
tive porosity because the current is largely electro-
lytic. The GPR method is based on wave
propagation by analogy with seismic methods, so
in that sense the porosity calculated from GPR is
the total porosity. As the methods give very similar
results this would indicate that the effective porosity
equals the total porosity in this case and that no
trapped and isolated pores exist.
Porosity is governed by many factors such as the
uniformity of grain size, (sorting), grain shape, pack-
ing, and compaction during and after deposition.
Packing alone can contribute significantly to the
difference in porosity. The end members of packing
modes for spheres of uniform size, the cubic and
rhombohedral packing, have porosities of 48% and
26% respectively (Graton and Fraser, 1935). Sorting
also has a large influence on the porosity: up to 25%
difference between well-sorted and very poorly-
sorted sands of the same mean grain size were
reported by Beard and Weyl (1973). The dominant
factors in this study are not known but if the results
indicated by two methods are correct, it is likely that
more than one factor are responsible for the relatively
large decrease in porosity with depth. Unfortunately,
no direct control is available to verify the porosity at
A precondition for using the GPR in this type of
study is the presence of several electromagnetically
contrasting layers. This is not often a problem as
sandy material is commonly stratified. Another re-
quirement is that the layers are more or less horizontal
since the equation of Dix (1955) is valid only for
horizontal surfaces. The Topp et al. (1980) equation
requires values for dielectric constant for each layer,
derived from the interval velocity, as input for water
content calculation. Thus the RMS velocity has to be
carefully picked for each layer. In this study these
were determined using both the semblance approach
to select strong reflections and hyperbolae fitted to
CMP gathers to refine the two-way times and RMS
velocities. These velocities were thoroughly analysed
and the maximum estimated error could be F1 ns in
two-way-time and F0.003 m/ns in RMS velocity,
which would result in about 1.5% error in water
The smooth inversion method of DeGroot-Hedlin
and Constable (1990), used for the geoelectrical
data, has the advantage of being fully automatic
and not needing any prior information, however
the gradual change from high to low resistivities
which is inherent to this method makes it difficult
to determine an intrinsic value for porosity. A pre-
requisite for a reliable water-content model deduced
A. Turesson / Journal of Applied Geophysics 58 (2006) 99–111110
from resistivity is that true resistivities can be de-
rived. This could also be problematic due to the
equivalence principle relating depth and resistivity.
An alternative inversion routine, the block inversion
(Inman, 1975), has proven to be useful when the
subsurface layer geometry is simple (Dannowski and
Yaramanci, 1999). In more complex environments
the input model required for this inversion routine
may be too difficult to estimate to get a satisfying
result. In using the Archie equation several para-
meters, such as the constants m and n and some-
times also water conductivity, have to be estimated.
The small-scale investigation at the sample sites was
used to calibrate these parameters. Furthermore, it
was assumed that these parameters did not change in
the section. In this survey this assumption can be
justified by the facts that the constants m and n are
related to pore shape and pore fluid and that the
wave-sorted sandy material in the section has the
same origin and genesis as sand washed out from a
In summary, two methods, ground-penetrating
radar and resistivity, were independently evaluated
for their capability to assess water content and
porosity in a sandy section. The methods were
used in combination with empirical relationships.
Additional information from two sample sites was
used to relate the indirect methods to known water
content and porosity. This is of special importance
when using empirical relationship in different spe-
cific environments. The results obtained showed
very similar trends of water-content distribution,
although absolute values differ somewhat, and
there is a good agreement between the methods in
the saturated zone if the mean porosity is compared.
The use of two independent methods greatly
strengthens the results which can be obtained in
this type of study.
I would like to thank associate professor Gustaf
Lind, Earth Sciences Centre, Goteborg University, for
assistance during fieldwork and for constructive re-
view of the manuscript. I also thank professor David
Cornell, Earth Sciences Centre, Goteborg University,
for correction of the English language.
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