water content and porosity estimated from ground-penetrating radar and resistivity

www.elsevier.com/locate/jappgeo

Journal of Applied Geophy

Water content and porosity estimated from ground-penetrating

radar and resistivity

Anita Turesson

Department of Geology, Earth Sciences Centre, Goteborg University, Box 460, SE-405 30 Goteborg, Sweden

Received 1 September 2004; accepted 29 April 2005

Abstract

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

1. Introduction

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.

doi:10.1016/j.jappgeo.2005.04.004

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

zone.

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

Table 1

Grain size distributions presented as the mean of two samples at

each site

Sample

site

Grain size

distribution (mm)

Weight-

percent

Measured h Calculated

porosity

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

14 m.

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

3.1. Method

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).

3.2. Result

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


refraction is plotted in all further models calculated

from GPR and CVES.

4. Ground-penetrating radar

4.1. Method

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

measurements.

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


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:

Vi ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2RMS;ntn � v2RMS;n�1tn�1

tn � tn�1

sð1Þ

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

respectively.

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):

VccffiffiffiffiffiKV

p ð3Þ

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

a ð4Þ

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

constant.

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

4.3. Results

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.


Fig. 4 (continued).


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.


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%

(mean 28%).

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).

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.

5. Resistivity

5.1. Method

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


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

indicated.

pore fluid, / is the porosity, and a and m are

constants.

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

(Ward, 1990).

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

the section.

file and is used in the water content calculation. Sample locations are


5.3. Results

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

seismic refraction.

Fig. 9. This section shows the difference between volumetric water contents deduced from GPR and resistivity.


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

10-m depth.

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

content.

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


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

terminal moraine.

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.

Acknowledgement

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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