modeling of lithology and hydraulic conductivity of shallow sediments from resistivity measurements,...

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Modelling of Lithology andHydraulic Conductivity ofShallow Sediments fromResistivity Measurements UsingSchlumberger Vertical ElectricSoundingsHilmi S. Salem

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To cite this article: Hilmi S. Salem (2001): Modelling of Lithology and HydraulicConductivity of Shallow Sediments from Resistivity Measurements Using SchlumbergerVertical Electric Soundings, Energy Sources, 23:7, 599-618

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Modelling of Lithology and Hydraulic Conductivity ofShallow Sediments from Resistivity MeasurementsUsing Schlumberger Vertical Electric Soundings

HILMI S. SALEM

Atlantic Geo-Technology

Halifax, Nova Scotia, Canada

The vertical electric soundings (VES) technique has been eVectively used for severalpurposes related to investigations of surface soils and shallow sediments. Theseinclude detection of subsurface lithology, structures, stratiWcation, and dippinglayers; evaluation of physical properties that govern Xuid Xow and electric-currentconduction; delineation of aquifers; assessment of engineering-site properties (suchas pore-water saturation and clay content); and mapping various environmentalproblems (such as saline-water intrusion, groundwater contamination, and leachatetransport through porous media). In this study, Schlumberger VES-measurements,along with borehole and experimental data, were employed to image laminations,layering, and lithology of surface soils and subsurface aeration and saturated zonesof glacial sediments; and to model the electric resistivity and hydraulic conductivityvariations with depth and lithology. It is shown that the VES-technique can provide asubstantial improvement in the resolution of thin laminations within thick layers andcan also provide a good assessment of the hydraulic conductivity, water Xux, andwater movement. Numerous references, dealing with a wide range of VES-applica-tions for several purposes, were reviewed and cited in this study.

Keywords VES, applications, surface soils, aeration zone, aquifer, lithology,electric resistivity, hydraulic conductivity, water ¯ ux and movement, layering,laminations

Introduction

Applications of Vertical Electric Soundings ( VES) Technique

For several decades, the vertical electric soundings (VES) technique has been eŒec-

tively used in surveying several targets related to surface soils and subsurface shallow

sediments. These include mapping lithology, clay content, and structures; delineating

aquifers; assessing seepage; monitoring underground for engineering purposes;

understanding mechanisms and interactions of electric-current conduction and

hydraulic ¯ ow; detecting anisotropy; monitoring high potential zones; mapping

low/high salinity zones for agricultural development; and evaluating environmental

problems. Following is a brief review of several studies carried out to investigate

diŒerent targets related to surface soils and shallow sediments, for which VES (with

or without other geophysical and hydrogeological techniques) was applied.

599

Energy Sources, 23:599 ± 618, 2001

Copyright # 2001 Taylor & Francis

0090-8312 /01 $12.00 ‡ .00

Received 30 May 2000; accepted 17 July 2000.Address correspondence to Hilmi S. Salem, Atlantic Geo-Technology, Suite 307, 26

Alton Drive, Halifax, Nova Scotia, Canada, B3N 1L9. E-mail: [email protected]

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Lithology, Clay Content, and Clay Deposits

Barker and Worthington (1973a), Frohlich (1973), Worthington (1976a, 1977a),Urish (1983), and Mazac et al. (1985) mapped variations in grain size, porosity,

and clay content. Biella and Tabbacco (1981) and Biella et al. (1983) investigated

variations in grain shape and degree of cementation. Meheni et al. (1996) and

Nowroozi et al. (1997) investigated subsurface layering and lithology. Hosain et al.

(1999) mapped thick layers of clay deposits.

Groundwater Exploration and Aquifer Delineation

Kui and Huisheng (1990) conducted tens of thousands of VES-pro® les to

delineate wide extended fresh- and saline-water aquifers in China. Frohlich

(1974), Worthington (1977b) , Kauahikaua (1986), Dodds and Ivic (1990),

Sandberg and Hall (1990), Schwarz (1990), Schneider et al. (1993), and Yadavet al. (1997) investigated aquifers and their characteristics and mapped depth of

bedrock.

Geotechnology , Subsurface Structures, ArtiWcial InWltration, and Archaeology

Ogilvy et al. (1969), Llopis et al. (1988), and Butler and Llopis (1990) assessedgeotechnical sites of anomalous seepage by detecting and mapping seepage paths

and monitoring changes in conditions as a function of time. Bristow (1966), Dey and

Morrison (1979), Barker (1981), Moore and Stewart (1983) , Butler (1984), Acworth

and Gri� ths (1985), Raiche et al. (1985), Barker (1988), Taylor and Fleming (1988),

Stewart and Wood (1990), and Pous et al. (1996) mapped subsurface structures (suchas fracture zones, joints, and cavities) in sandstones and carbonates. Subsurface

structures usually generate low resistivity anomalies because they serve as active

¯ ow conduits or because they are ® lled in some cases with clays and other conducting

materials. The VES-technique has also proved to be eŒective in monitoring arti® cial

in® ltration through porous media (Cahyna, 1990) and in investigating archaeologicalsites (Panissod et al., 1997).

Electric Current and Hydraulic Flow Interactions

Researchers have investigated mechanisms of electric-current conduction and

hydraulic ¯ ow by determining petrophysical and hydrophysical properties ofporous media. They obtained, for example, increasing and decreasing relationships

between electric resistivity and hydraulic conductivity. This paradox is due to vari-

ations in lithology; mineralogy, size, and shape of grains; pore-water salinity; clay

content; and porosity (Buhle and Brueckman, 1964; Zohdy, 1969; Barker and

Worthington, 1973a; Bose et al., 1973; Worthington, 1975, 1976b; Kelly, 1977;Heigold et al., 1979; Mazac and Landa, 1979; Kosinski and Kelly, 1981; Urish,

1981; Leonard-Mayer, 1984; Kelly, 1985; Mazac et al., 1985; Niwas and Singhal,

1985; Huntley, 1986; Worthington, 1986; Mazac et al., 1988, 1990a; Yaramanci and

Flach, 1992; Yadav, 1995; Lile et al., 1997).

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Anisotropy

Nobes et al. (1990) correlated the formation resistivity factor to anisotropy of layersand cementation of grains in order to evaluate the seismic risk of unconsolidated

sediments. Other researchers investigated the anisotropy in¯ uence on transmission of

electric current and hydraulic ¯ ow through porous media, as a result of variations of

physical and lithological properties in the horizontal and vertical directions of

layered media or due to dipping of layers and presence of fractures (Zohdy, 1965;Singh and Singh, 1970; Habberjam, 1972; Barker and Worthington, 1973b; Hab-

berjam, 1975; Worthington, 1976b; Campbell, 1977; Schimschal, 1981; Urish, 1981;

Nunn et al., 1983; Kelly and Reiter, 1984; Matias and Habberjam, 1984; Ritzi and

Andolsek, 1992; Sauck and Zabik, 1992; Bolshakov et al., 1995; Loke and Barker,

1995; Li and Uren, 1997; Salem 1999; Watson and Barker, 1999).

High Potential Zones

The VES-technique has also been successfully used to evaluate the hydraulic trans-

missivity in relation to the electric transverse resistance in order to map high poten-tial zones within porous media (Duprat et al., 1970; Scaracia, 1976; Mazac and

Landa, 1979; Niwas and Singhal, 1981; Singhal and Niwas, 1983; Ponzini et al.

1984; Frohlich and Kelly, 1985; Niwas and Singhal, 1985; Yadav and Abolfazli,

1998; Salem, 1999).

Agriculture and Pedology

Researchers have also used the VES-technique to investigate high salinity zones of

surface soils and shallow sediments in order to provide solutions for salinization

problems that seriously aŒect farmlands, especially in arid and semi-arid regions.

Salinization problems resulting from high evaporation rates that lead to enrichment

of salt minerals have caused a great loss of huge agricultural areas. If the salinizationprocesses are understood, the problems of salinization can be relatively contained by

using appropriate land-management practices. Several VES-surveys were conducted

to assess soil systems and high salinity of farmlands and to implement hydrological

and engineering solutions for land reclamation (Roy and Elliot, 1980; Street andEngel, 1988; West and Linford, 1988; Humphreys et al., 1990; Street and Engel,

1990; Robian et al., 1996).

Environment

Nowadays, the environmental problems aŒecting, in particular, aquifers and their

water storage, as a result of high salinization and contamination and lowering of

water level, are very serious ones. For example, in their hydrogeological study on the

very high rate of groundwater salinization in the Gaza Strip, Yakirevich et al. (1998)

indicated that the Gaza Strip aquifer system is greatly salinized and the salinizationproblem has increased. The over-exploitation of groundwater from this coastal

aquifer and the very low rate of annual recharge have forced the Mediterranean

Sea water to intrude, easily and rapidly, into the aquifer system. Analysis based on

numerical simulation and sample tests showed that the rate of salt water intrusion

Modelling of Lithology and Hydraulic Conductivity Using VES 601

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into the Gaza Strip aquifer is expected, during the next few years (until 2006), to be

20± 45 m/yr (Yakirevich et al., 1998).For such severe salinization problems and others of less impact, the VES-tech-

nique has shown to be very eŒective. The VES-technique is of direct advantage in

aquifers’ protection because it provides a substantial evaluation of hydrological and

petrophysical properties. The VES-technique has been widely used in mapping fresh

water± salt water interface and salt water intrusion and in monitoring bodies of saline

groundwater (Swartz, 1937; Flathe, 1955, 1967; Van Dam and Meulenkamp, 1967;Zohdy, 1969; Monkhouse and Fleet, 1975; Bugg and Lloyd, 1976; Gorhan, 1976;

Henriet, 1976; Bisdorf and Zohdy, 1979; Barker, 1981; Fretwell and Stewart, 1981;

Gri� ths et al., 1981; Barker, 1982; Tellam et al., 1985; Kauahikaua, 1986; Mazac

et al., 1987; Seara and Granda, 1987; Barker, 1990a; Hagemeyer and Stewart, 1990;

Salem, 1995).On the other hand, the VES-technique has been successfully used to locate

subsurface contaminated zones. Stollar and Roux (1975) and Barker (1990b) delin-

eated locations of contaminant plume around land® lls and spoil tips. Skuthan et al.

(1979) and Mazac et al. (1990b) used VES to select locations of dumps and to detect

perforations in the dumps’ sealing in order to avoid contamination problems thatmay aŒect the groundwater and its surrounding geological environment. Urish

(1984) mapped high levels of groundwater mineralization caused by nuclear-waste

deposits aŒecting glacial aquifers. Mazac et al. (1990c) and Benson et al. (1997)

mapped the extent of groundwater contamination caused by oil migration.

Cahyna et al. (1990) mapped the extent of land® ll slag-type materials containing

cyanide complexes that migrate and contaminate groundwater. Ross et al. (1990)investigated underlying clay layers of a large number of old land® lls and chemical-

and industrial-waste disposal sites and detected vertical and lateral migration of

waste ¯ uids. LaBrecque et al. (1984), Davis et al. (1988), Buselli et al. (1988,

1990), Hagrey (1992), Daily et al. (1995), De Lima et al. (1995), Osiensky and

Donaldson (1995), Cardarelli and Bernabini (1997), Liu and Cheng (1997), Osiensky(1997), and Daily et al. (1998) mapped subsurface and groundwater contamination

caused by transport of industrial contaminants and land® ll-waste leachates. Slater

et al. (1997) conducted cross-borehole electric imaging during migration processes

of saline-water tracer to investigate ® eld-scale transport in unsaturated zones.

Hagrey and Michaelsen (1999) mapped water and solute movement in the vadosezone of highly heterogeneous soils in order to detect transport and migration of

contaminants.

Further details on the theory and applications of the VES-technique, as well as

the electric properties and their relations to the hydraulic ¯ ow through porous

media, are given in Maillet (1947), Keller and Frischknecht (1966), Kunetz (1966),

Keller (1967), Battacharya and Patra (1968), Astier (1971), Plotnikov (1972), Zohdyet al. (1974), Telford et al. (1976), Koefoed (1980), McNeill (1980), Keller (1982), De

Marsily (1986), Ward (1990a,b,c), Burger et al. (1992), Kelly and Mares (1993),

Zhdanov and Keller (1994), Reynolds (1997), Fang (1998), Hallenburg (1998a,b),

SchoÈ n (1998), and Sharma (1998).

Study Area

The study area, in the Segeberger forest (northern Germany), shows less than 1 m

diŒerence in topography. The altitude of the forest ranges, in general, from 25 to

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65 m above sea level. The area receives annual precipitation of 800 mm/yr, distrib-

uted as 500 mm evaporation, 60 mm runoŒ, and 240 mm in® ltration, recharging theaquifer system (Einsele & Schultz, 1973). The sediments of the area are characterized

by a high degree of heterogeneity, both laterally and vertically. These Pleistocene-

glacially originated sediments are composed of gravels, sands, and silts, with a small

fraction of clays. They have wide ranges of grain sizes and shapes and a variety of

mineralogical compositions.

In this study, VES-measurements were conducted to assess the electric resistivityvariations with lithology and depth; delineate the aquifer’s thickness and depth;

monitor the layering and laminations; evaluate the hydraulic conductivity of the

surface soils, the aeration zone, and the body of the aquifer; and evaluate the

aquifer’s potential and the water movement through the subsurface.

Methodology

Field Measurements

The apparent resistivity (Ra, in «.m) was measured using a GGA-30 equipment. This

equipment consists of a power unit (GGA-30L), measuring the low frequency direct

current `̀ DC’ ’ (I, in ampere), and a potentiometer unit (GGA-30M), measuring thepotential diŒerence (V, in volt). Both units were assembled in two separate hard

plastic cases to eliminate the humidity eŒect. Nonpolarizable electrodes were used to

minimize the polarization eŒect caused by the movement of charged particles (ions)

through the pore spaces towards the current electrodes. These ions usually tend to

inhibit the electric-current conduction and thus aŒect the measurements.


Figure 1. Schlumberger con® guration of VES.

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The Schlumberger con® guration (array) was used for four electrodes (AMNB)

were located along a straight line (L; pro® le length) (Figure 1). The current (I) wasdriven through one pair of the electrodes (A and B), and the potential diŒerence (V)

was measured with the other pair of the electrodes (M and N). The apparent resis-

tivity (Ra) was obtained as the ratio of V to I, using a proportionality factor (known

as the geometrical coe� cient µ) which depends on the array’s geometrical arrange-

ment. Mathematically, the Schlumberger arrangement (Figure 1) can be expressed as

follows:

V ˆ µ…IR†=2º …1†

which leads to

V ˆ …IR=2º†‰f…1=AM† ¡ …1=BN†g ¡ f…1=AN† ¡ …1=BN†gŠ …2†

which leads to

R ˆ º…V=I†‰f…AB=2†2 ¡ …MN=2†2g=MNŠ …3†

The measured electric resistivity (R) (Equations 1± 3) is apparent resistivity sinceit re¯ ects the average resistivity confronting the current conducted through a hetero-

geneous medium that consists of several layers. If the medium is homogeneous,

isotropic, and semi-in® nite, then the measured resistivity is the true one.

The electric pro® les conducted for the area ranged in length (L) from 120 to 200

m, crossing each other. Several trials (diŒerent individual measurements) were car-ried out for each pro® le in order to choose the best reading of the apparent resistivity

(Ra), which lies between the maximum and minimum values of each reading. This

procedure (choosing the best reading) helped to eliminate the errors which might be

produced during the survey due to geological, physical, and/or technical in¯ uences.

These in¯ uences can generally be caused by any dipping of the subsurface layers,alteration of thick and thin layers (macro- and micro-anisotropy) , intercalation of

diŒerent grain sizes and shapes, presence of water pipes and electric cables, electro-

lytic (ionic) eŒects, and/or shifts in the array from the ideal position. If any of these

in¯ uences exists, the value of the geometrical factor, µ, will be aŒected and thus the

measured resistivity will also be aŒected.

Analysis

The two components of the VES-measurements (apparent resistivity (Ra) and half

electrode spacing (AB/2)) were analyzed using three iterative computer programs

based on calculating the total kernel function (Zohdy, 1973, 1974; Last, 1980). TheZohdy (1973) program and the Last (1980) program have the ability to invert Ra and

AB/2 into true resistivities (Rt) and corresponding thicknesses (h) of the subsurface

layers (i± n). The Zohdy (1974) program was used as a reversal technique to trans-

form Rt and h into Ra and AB/2 in order to adjust the VES-data and to cancel any

disturbing readings.The advantage of the Zohdy (1973) program lies in the fact that it yields

an approximately true resistivity, thickness, and depth of each layer monitored

by the array. The program originally gives a detailed model (DM) consisting of

several thin laminations (as many as the soundings points). Then the DM is trans-

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formed into a reduced (equivalent) model (RM). According to the principle of

equivalence, a reduced model composed, for example, of three layers is equivalent

to a detailed model composed of a greater number of layers, especially when the

error value is 2% or less (Zohdy, 1989). The error value represents the diŒerence

between the observed (measured) resistivity (Ra) and the modelled (calculated) resis-

tivity (Rm) for each sounding point. The Last (1980) program needs an initial model

that consists of resistivity and thickness of each layer. The Last program then

extrapolates the initial model by iterating the observed resistivities. The iteration

process continues until a small, or no, discrepancy between the observed and calcu-

lated resistivities is reached and until a smoothed, best-® tting curve (calculated

curve) is obtained.

The Zohdy (1973) program diŒers from the Last (1980) program in that its

iterative procedure is fully automatic, i.e., without any control from the interpreter.

In addition, unlike the Last program, the Zohdy program does not require an initial

model. It also gives detailed and reduced models of the resistivities, thicknesses, and

depths of the layers. On the other hand, unlike the Las program, the Zohdy program

does not provide a curve of the resistivity versus the half electrode spacing. In view of

these diŒerences between both programs, the Zohdy (1973) program was originally

used to obtain a reduced model that was introduced into the Last (1980) program.

This procedure was done in order to obtain the best solution of the resistivities,

thicknesses, and depths of the monitored layers and to obtain the ® nal smoothed

and best ® tting curves. A range of error values of 0.2± 1.5% , which is less than the

allowed value (2% ), was obtained. An example of the observed resistivity (Ra),

obtained from four trials, and the modelled resistivity (Rm), along with the error


Table 1

An example of the results obtained from four trials of the VES-measurements for

one of the pro® les, showing the half electrode spacing (AB/2), in m, and the

corresponding apparent (observed) resistivity (Ra), in «.m, along with the modelled

(calculated) resistivity (Rm), in «.m, and the error values, in % , between Ra of the

fourth trial and Rm (given in bold and plotted in Figure 2).

Ra…«:m† Ra…«:m† Ra…«:m† Ra…«:m† Rm…«:m†AB/2 (m) [1st trial] [2nd trial] [3rd trial] [4th trial] [modelled] Error (% )

1.468 511 515 511 522 522 0.2

2.155 665 652 641 661 661 0.1

3.163 823 805 788 813 813 0.1

4.642 940 922 905 929 929 0.16.814 942 932 926 936 936 0.1

10.001 781 786 796 786 787 0.2

14.680 524 534 549 534 535 0.3

21.547 321 324 329 324 325 0.4

31.627 254 253 249 252 252 0.146.422 296 295 293 294 293 0.1

68.139 389 389 393 388 386 0.3

100.014 506 506 512 503 503 0.1

146.800 640 640 647 639 637 0.1

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values and the half electrode spacing (AB/2), are given in Table 1 and plotted in

Figure 2.

Results and Discussion

Electric Resistivity

The obtained sounding curves are characterized (as shown in Figure 2) by a ® nal

segment of approximately 45o, which indicates the presence of a signi® cant basallayer with a relatively medium to high resistivity and in® nite thickness. The resis-

tivity-thickness reduced model is composed of seven layers, including the basal layer

(Table 2; Figure 3). For practical purposes of interpretation, the seven-layer model is

summarized in four distinguished units, including the basal unit (Table 3). The wide

range of resistivity (Table 3) is attributed to the high degree of heterogeneity, both

laterally and vertically, as a result of variations of the grain and pore characteristicsand the pore-water salinity, as well as the presence of some clays. The resistivity

variations with depth and lithology are interpreted below with respect to the reduced

model (Table 2; Figure 3), which is summarized in four units (Table 3), and the data

obtained from boreholes drilled in the study area.

The ® rst unit, representing the surface soils, exhibits a resistivity (Rt) range of345± 1110 «.m, corresponding to a range of thickness (h) of 0.8± 1.1 m (Tables 2 and

3; Figure 3). The variations of the surface-soil resistivity are attributed to local

conditions prevailing at the measuring stations. The relatively higher values of Rt

indicate hard and dry soils and the presence of gravels and coarse sands, and the

606 H. S. Salem

Figure 2. An example of the obtained electric sounding curves, showing the apparent

(observed) electric resistivity (Ra) and the modelled (calculated) electric resistivity (Rm),

both in «.m, in relation to the half electrode spacing (AB/2), in m.

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Table

2

Are

du

ced

(eq

uiv

ale

nt)

mo

del

sho

win

gd

epth

(Z)

an

dth

ick

nes

s(h

),b

oth

inm

,tr

ue

elec

tric

resi

stiv

ity

(Rt)

,in

«.m

,and

hyd

rau

lic

con

duct

ivit

y(K

),in

m/s

,o

fse

ven

layer

sm

on

ito

red

fro

mth

ree

VE

S-p

ro®

les.

Red

uce

d(e

qu

ivale

nt)

mo

del

Pro

®le

no

.1

Pro

®le

no

.2

Pro

®le

no

.3

Z(m

)h

(m)

Rt… «

:m†

K(m

/s)

Z(m

)h

(m)

Rt… «

:m†

K(m

/s)

Z(m

)h

(m)

Rt… «

:m†

K(m

/s)

70.8

0.8

820±1000

9:2

8£

10

¡4

70.9

0.9

345±386

1:2

5£

10

¡4

71.1

1.1

1092±1110

1:1

3£

10

¡3

72.1

1.3

3080±3520

2:2

4£

10

¡3

73.3

2.4

2000±2200

1:2

5£

10

¡3

74.7

3.6

1463±1529

8:1

4£

10

¡4

73.7

1.6

1000±1308

5:4

9£

10

¡4

76.8

3.5

246±320

5:1

9£

10

¡4

77.2

2.5

475±650

1:7

7£

10

¡3

75.4

1.7

120±400

4:3

6£

10

¡4

712.3

5.5

120±140

8:4

7£

10

¡5

712.0

4.8

353±429

7:6

0£

10

¡4

79.7

4.3

65±115

7:1

3£

10

¡5

718.9

6.6

70±86

6:7

7£

10

¡5

722.8

10.8

107±122

1:5

2£

10

¡4

739.5

29.8

87±132

1:2

1£

10

¡4

772.5

53.6

1022±1200

2:8

7£

10

¡3

743.4

20.6

430±600

1:4

1£

10

¡3

39.5

±?

?700±887

?72.5

±?

?1300±1517

?43.4

±?

?740±1675

?

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relatively lower values indicate wet grains of ® ner sizes and diŒerent mineralogical

composition, such as ® ne sands, silts, and clays. The ® ner the size of the grains, the

greater the speci® c surface area per unit of bulk volume, grain volume, or pore

volume, which enables the grains to adsorb charged ions at their surfaces (double-

layer theory) and thus the conduction of electric current will be easier (Salem and

Chilingarian, 1999a,b).

The second unit, representing the aeration zone above the water table, exhibits

an Rt range of 1000± 3520 «.m, corresponding to an h range of 1.3± 3.6 m (Tables 2

and 3; Figure 3). This unit shows relatively higher resistivity values than the other

units because of the leaching of electrolytes during the in® ltration of water rechar-

ging the underlying aquifer and because of the presence of greater amounts of

gravels and coarse sands.

The third unit, representing the body of the aquifer, starts at a depth (Z) ranging

from º 5–7 m (water-table depth). The layers within this thick unit exhibit an Rt

range of 65± 1200 «.m, corresponding to an h range of º 2± 54 m (Tables 2 and 3;

Figure 3). The resistivity of this thick unit can be classi® ed into two main ranges: a

lower range (65± 650 «.m) and a higher range (1022± 1200 «.m). The lower range

corresponds to the layers within Z of º 40 and 43 m, as monitored from the ® rst and

third pro® les, respectively (Figure 3), and to the upper part of the aquifer within Z of

º 19 m, as monitored from the second pro® le (Figure 3). The higher range of resis-

tivity corresponds to the layer within Z of º 19± 73 m, as monitored from the second

pro® le (Figure 3). The resistivity variations within the aquifer’s body are attributed

to changes in the lithology, size, and shape of the grains, pore-water salinity, por-

osity; and clay content. As shown in Figure 3, the aquifer terminates at Z of º 40

and 43 m, as monitored from the ® rst and third pro® les, and at Z º 73 m, as

monitored from the second pro® le. The variations of depth and thickness of the

various layers within the saturated unit (Tables 2 and 3; Figure 3) are attributed to

the lens con® guration of the layers, characterizing the glacial deposits (Salem, 2000).

608 H. S. Salem

Figure 3. Variations of true electric resistivity (Rt), in «.m, with depth (Z), in m, and lithology

for the surface soils and subsurface layers, monitored from three VES-pro® les.

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The fourth unit, forming the basal layer, exhibits a range of resistivity of 700±

1675 «.m (Tables 2 and 3; Figure 3). For all practical purposes of interpretation, this

unit is considered to have an in® nite thickness. It is composed of till (boulder clay)

that consists of several minerals, such as clays, calcite, quartz and feldspars. Themultimineral composition and the lens con® guration of this unit contribute, respect-

ively, to its resistivity and depth variations (Figure 3).

Hydraulic Conductivity and Water Movement

The hydraulic conductivity (K, in m/s) was obtained for the ® rst 6 layers of thereduced model (Table 2) in accordance with Equation (4), which was empirically

derived with respect to the grain-size distribution and the formation resistivity factor

(F), dimensionless:

K ˆ 7:7 £ 10¡6…F2:09† …4†

The formation resistivity factor, F, was obtained using the equation of Archie

(1942):

F ˆ Rb=Rw …5†

where Rb ˆ bulk resistivity ˆ Rt (true resistivity of layer i), obtained from the sur-

face electric measurements; Rw ˆ pore-water resistivity, obtained from the pore-

water analysis.

The Rw varies widely for the surface soils (43± 250 «.m; average ˆ 131 «.m),

the aeration zone (30± 56 «.m; average ˆ 40 «.m), and the aquifer (13± 83 «.m;

average ˆ 38 «.m). It is evident that the pore water generally becomes less resistive(more conductive) with depth because of the in¯ uence of water circulation. It is

important to mention that Rw of the basal unit underlying the aquifer is not available

because the unit is not penetrated by the wells drilled in the study area.

The main three units (surface soils, aeration zone, and aquifer) monitored by the

VES-survey exhibit a general K range of between 6:77 £ 10¡5 and 2:87 £ 10¡3 m/s(Tables 2 and 3). From pump tests conducted for the same area, Schroeter (1983)

obtained a K range of between 1:0 £ 10¡5and 8:0 £ 10¡4 m/s. According to the

results obtained in this study, the saturated zone (aquifer) exhibits a K average

value of 7:5 £ 10¡4 m/s. Using Darcy’s law, the groundwater ¯ ux (q) equals


Table 3

A summary of the reduced model, showing ranges of depth (Z) and thickness (h),

both in m, true electric resistivity (Rt), in «.m, and hydraulic conductivity (K), in

m/s, of four major units, including the basal unit with in® nite thickness and

unknown hydraulic conductivity.

Z (m) h (m) Rt …«:m† K (m/s)

0.0± 1.1 0.8± 1.1 345± 1110 1:25 £ 10¡4 – 1:13 £ 10¡3

2.1± 4.7 1.3± 3.6 1000± 3520 5:49 £ 10¡4 – 1:25 £ 10¡3

5.4± 72.5 1.7± 53.6 65± 1200 6:77 £ 10¡5 – 2:87 £ 10¡3

72.5± ? In® nite 700± 1675 ?

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6:7 £ 10¡2 m3 /s and the hydraulic ® lter velocity (or microscopic velocity; vf ) equals

7:5 £ 10¡7 m/s ( º 24 m/yr). If an average value of 0.3 is considered for the aquifer’sporosity (¿), as obtained from the VES-analysis, then the hydraulic distance velocity

(macroscopic velocity; vd) equals 2:5 £ 10¡6 m/s ( º 80 m/yr). By taking into

account the aquifer’ s average thickness (h º 44 m) and the distance velocity

(vd º 80 m/yr ˆ 0.22 m/d), then a drop of water needs º 200 days to cross the aquifer.

Schroeter (1983) experimentally obtained a range of distance velocity, vd, of between

2:32 £ 10¡6 and 5:56 £ 10¡6 m/s (ˆ 73–175 m/yr). Using the K and vd valuesobtained by Schroeter (1983), the travel time needed for a drop of water to cross

the aquifer’s average thickness ( º 44 m) will be between º 92 and 220 days, which

agrees well with the average travel time (200 days) obtained in this study from

surface electric measurements.

Conclusions

The VES technique has been widely and eŒectively used for various applications to

several purposes related to porous media. Over 160 references, including journal arti-

cles, books, reports, conference proceedings, and others, covering several applicationsof VES, as well as electric properties related to hydraulic properties, were reviewed and

cited in this study. Also, results of Schlumberger VES-measurements for surface soils

and shallow sediments were presented and discussed. It was shown that the VES-tech-

nique can provide good assessments of the lithology, physical properties, laminations,

and thicknesses and depths of the surface soils and the subsurface layers. A resistivity-

thickness model composed of seven layers was obtained. The investigated surface soilsand the underlying layers (composed of gravels; coarse, medium, and ® ne sands; silts;

and a small fraction of clays) exhibit a wide range of resistivity (65± 3520 «.m). The

resistivity variations are attributed to the in¯ uences of heterogeneity , both laterally and

vertically, and to the changes in the grain and pore texture and structure, mineralogy of

the grains, clay content, and salinity of the pore water.Using the results obtained from the VES-measurements, a range of the hydraulic

conductivity of between 6:77 £ 10¡5 and 2:87 £ 10¡3 m/s was obtained. This range

corresponds to the whole column of the surface soils, the aeration zone, and the

aquifer. The water ¯ ux and ® lter and distance velocities, as well as the time needed

for the in® ltrated water to cross the aquifer, were also obtained. An average periodof time of about 7 months, with an average microscopic (® lter) velocity of about

24 m/yr and an average macroscopic (distance) velocity of about 80 m/yr, is needed

for the water to cross the aquifer’s average thickness (º 44 m). The rate of water

movement depends on several in¯ uences, such as the aquifer’s thickness (which

varies from one location to another), variations of the lithology, hydraulic gradient,

hydraulic conductivity, and porosity due to variations in the grain and pore char-acteristics. These in¯ uences are particularly important when the sediments are

greatly heterogeneous and the layers are laminated and characterized by lens con-

® guration, as in the case of the present study. The results obtained in this study agree

well with experimental results and borehole measurements.

Nomenclature

F formation resistivity factor (dimensionless)

I electric current (ampere)

610 H. S. Salem

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K hydraulic conductivity (m/s)

L pro® le length (m)

R electric resistivity («.m)

Ra apparent (observed) resistivity («.m)

Rm modelled (calculated) resistivity («.m)

Rt Rb ˆ true (bulk) resistivity of layer i («.m)

Rw pore-water resistivity («.m)

V potential diŒerence (volt)

Z depth of layer i (m)

h thickness of layer i (m)

i–n number of monitored layers from i to n

µ geometrical coe� cient of Schlumberger con® guration (dimensionless)

q water ¯ ux (m3 /s)

vd distance (macroscopic) velocity of water movement (m/s)

vf ® lter (microscopic) velocity of water movement (m/s)

¿ porosity (fraction)

AB spacing of current electrodes (m)

AB/2 half spacing of current electrodes (m)

MN spacing of potential electrodes (m)

AMNB L ˆ line of measurement (m)

DC direct current

DM detailed (primary) model

RM reduced (equivalent) model

VES vertical electric soundings

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modeling of lithology and hydraulic conductivity of shallow sediments from resistivity measurements,...

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