Article ebong

Estimation of geohydraulic parameters from fractured shales
and sandstone aquifers of Abi (Nigeria) using electrical resistivity
and hydrogeologic measurements
Ebong D. Ebong a,⇑
, Anthony E. Akpan a
, Anthony A. Onwuegbuche b
a
Applied Geophysics Programme, University of Calabar, PMB 1115, Calabar, Cross River State, Nigeria
b
Department of Physics, Abia State University, Uturu, Abia State, Nigeria
a r t i c l e i n f o
Article history:
Received 25 October 2013
Received in revised form 18 February 2014
Accepted 25 March 2014
Available online 3 April 2014
Keywords:
Electrical resistivity
Geohydraulic parameters
Groundwater
Hydraulic conductivity
Ikom-Mamfe Embayment
Abi-Nigeria
a b s t r a c t
Geohydraulic parameters are essential elements in groundwater resource management and conservation.
Most of these parameters especially the hydraulic conductivity and transmissivity are usually estimated
from pumping test carried out on drilled boreholes. This paper presents a study conducted in Abi area of
the Ikom-Mamfe Embayment with the objective of estimating aquifer parameters from 30 evenly
distributed vertical electrical soundings using the Schlumberger configuration and hydrogeologic
measurements from 28 boreholes within the area as an alternative way of generating an initial data
for groundwater characterisation and quality assessment in the area. The results showed low resistivity
645 Xm, hydraulic conductivity 62.0 Â 10À5
m/s (61.7 m/day) and transmissivity 65.2 Â 10À4
m2
/s
(645 m2
/day) for the water-bearing aquifer horizons in the northeastern and northwestern parts of
the study area due to the nature of the aquifer system that were predominantly fractured shale. The sand
based aquifers had higher values in the neighbourhood of $100–800 Xm, $4.0 Â 10À5
–1.0 Â 10À4
m/s
($3.46–9.04 m/day) and $6.94 Â 10À4
–3.81 Â 10À3
m2
/s ($60–330 m2
/day) for the respective parameters
mentioned above. The potability of the groundwater system as observed from hydrogeologic measure-
ments of water samples from most boreholes were relatively poor, having electrical conductivity
and total dissolved solids values of $250–931.0 lS/cm and $500–623.77 mg/l respectively due to the
influence of clay minerals within the aquifer horizon. Some of the vertical electrical sounding points were
taken in the vicinity were pumping tests and lithologic data were available for adequate comparison of
the results.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Abi is within the Ikom-Mamfe Embayment (IME) known to have
water shortage challenges especially in the dry season when the
available surface and groundwater resources dry up in some local-
ities. This problem has led to the prevalence of water borne diseases
such as guinea worm, cholera, dysentery and others, since the rural
dwellers will have to resort to ponds and a few available streams
for their domestic water needs (Akpan et al., 2013). Successive
governments and other donor agencies such as the United Nations
Children Emergency Fund (UNICEF), European Union (EU), Micro
Project Programme in the nine Niger Delta States (MPP9), Niger
Delta Development Commission (NDDC) amongst others have been
tackling these problems by funding boreholes to be drilled in the
area and other social amenities to alleviate the suffering of the
people. Many of such boreholes have not been successful due to
generalised regional subsurface geologic description and poor
understanding of the hydrostratigraphy, inadequate knowledge of
the aquifer geometry and characteristics, location of water recharge
and discharge areas and their dynamic fluctuations with time
(Akpan et al., 2013). Recently, there has been growing interest in
understanding, characterising and mapping the spatial distribution
of aquifers in the area.
Hydro-research institutions and other water related agencies
are currently embarking on intensive site specific investigations
that will generate localised information needed by the various
donor agencies in siting sustained water yielding boreholes in
the area. Besides, this information is also necessary in assessing
groundwater quality and aquifer protective capacity since the
shallower aquifers are likely susceptible to contamination from
http://dx.doi.org/10.1016/j.jafrearsci.2014.03.026
1464-343X/Ó 2014 Elsevier Ltd. All rights reserved.
⇑ Corresponding author. Tel.: +234 803 270 6889.
E-mail addresses: dickebong@yahoo.co.uk, ebongdickson@unical.edu.ng
(E.D. Ebong).
Journal of African Earth Sciences 96 (2014) 99–109
Contents lists available at ScienceDirect
Journal of African Earth Sciences
journal homepage: www.elsevier.com/locate/jafrearsci

anthropogenic activities. Geohydraulic parameters are key param-
eters usually employed in investigating wide range of hydrologic
and hydrogeologic problems such as groundwater flow modeling,
prediction, aquifer characterisation, protection, management and
remediation (Okiongbo and Akpofure, 2012; Mastrocicco et al.,
2010). The hydraulic parameters of interest in aquifer investigation
and characterisation include the hydraulic conductivity (Gemail
et al., 2011), porosity (Aristodemou and Thomas-Betts, 2000),
transmissivity and diffusivity (Kirsch and Yaramanci, 2009;
Niwas and Singhal, 1985), longitudinal conductance and transverse
resistance technically referred to as the Dar-Zarrouk Parameters
(DZP) (Egbai, 2011; Ekwe et al., 2006) and storage coefficient.
These parameters are useful in estimating the flow of water
through a porous medium as well as assessing its response to
pumping (Chang et al., 2011). Pumping tests, permeameter exper-
iments (Butler and Dietrich, 2004), slug tests (McCall et al., 2002)
and grain size analyses (Alyamani and Sen, 1993) are the standard
techniques for determining these parameters. These approaches
are invasive, relatively expensive and can generate information
to a lesser degree in the adjoining areas. In locations where the
boreholes are widely spaced, interpolation of aquifer properties
between boreholes will be difficult and often times erroneous,
since geologic formations do vary over relatively small distances
(Muldoon and Bradbury, 2005; Bogoslovsky and Ogilvy, 1977).
Geophysical techniques such as electrical resistivity method
offer a more economical and non-invasive alternative for estimat-
ing these parameters and extrapolating their spatial spread in loca-
tions where little or no information about them exist (Dhakate and
Singh, 2005; Christensen and Sorensen, 1998). The spatial distribu-
tion of geoelectric and geohydraulic parameters has been used to
characterise the heterogeneity of groundwater yielding aquifers
and their overlying vadose zones (Börner, 2009). Consequently,
results estimated exclusively from geophysical data are tradition-
ally prone to errors incurred in the process of transforming geo-
physical data into equivalent geological models. These errors are
basically due to the indirect mode of information extraction from
the data, inversion errors such as geologic constraints and param-
eters used to generate the starting model and the quality of the
data acquired. With recent advances in geophysical technology
such as the introduction of microprocessor controlled geophysical
data acquisition systems, inversion algorithms and direct informa-
tion extraction methodologies such as surface nuclear magnetic
resonance technique (Günther and Müller-Petke, 2012; Daigle
and Dugan, 2011), spectral induced polarization (Ikard et al.,
2012; Jouniaux and Ishido, 2012), electrical resistivity tomography
and the development of enhanced analytical and interpretational
tools for classical geophysical data (Kulessa et al., 2012; Jouniaux
et al., 2009), the prospects of solving these problems satisfactorily
has improved tremendously (Vereecken et al., 2004).
Presently, a hybrid alternative that involves a joint interpreta-
tion of hydrogeological and hydrogeophysical parameters gener-
ated from constrained modeling of geophysical data has been
found to be an alternative approach for characterising aquifers
(Aristodemou and Thomas-Betts, 2000; Khalil and Abd-Alla,
2005). Interest in this option has grown significantly and many
practitioners have continued to adopt this approach in estimating
aquifer properties (Sultan, 2013; Chandra et al., 2008). Although
several geophysical techniques for hydrogeological investigations
exist, instrument availability, portability and economic consider-
ations have continued to favour the application of direct current
(dc) electrical resistivity method (Okiongbo and Akpofure, 2012;
Batte et al., 2010). Also, the existence of a close relationship
between aquifer properties and bulk resistivity is another factor
that has made the dc resistivity to be preferred over other
techniques. The dc electrical resistivity method is also useful in
investigating other forms of hydrogeophysical problems including
assessment of aquifer vulnerability and depth to water table
(Gemail et al., 2011; Yadav et al., 2010), mapping of aquifer
salinity and its distribution (Jørgensen et al., 2012; Kirkegaard
et al., 2011), determination of aquifer characteristics and distribu-
tion (Mele et al., 2010), monitoring of flow and groundwater flow
dynamics (Adhikari et al., 2011), monitoring of water quality and
contaminant transport (Zarroca et al., 2011; Gemail et al., 2011),
groundwater potential studies (Poulsen et al., 2010) and aquifer
protective capacity (Okiongbo and Akpofure, 2012; Braga et al.,
2006). The spatial distribution of geoelectric and geohydraulic
parameters has also been used in mapping aquifer heterogeneities,
prediction of contaminants transport, computing their vulnerability
index and resource management (Akpan et al., 2013; Börner,
2009).
This study is aimed at employing constrained subsurface
models generated from dc resistivity measurements, lithologic
and groundwater sample analysis data in estimating geohydraulic
parameters in Abi, Nigeria.
2. Site description and geology
Abi is located between Latitudes 5.76°N and 6.02°N of the
Equator and Longitudes 7.93°E and 8.17°E of the Greenwich
Meridian in Cross River State, Nigeria. It forms part of the Nigerian
segment of the Mamfe Embayment referred to as IME that covers
$2016 km2
extent in western Cameroon (Fig. 1) (Nguimbous-
Kouoh et al., 2012). The area has an average annual precipitation
of over 2200 mm, while the annual temperature range is between
23 and 27 °C in the rainy season and soars to $35 °C in the dry sea-
son. The average relative humidity for the area is about 88% (Akpan
et al., 2013). Towards the end of the dry season, the volume of
water in the rivers and streams usually decrease considerably
and water flow inside the Cross River is usually restricted to nar-
row channels within the river bed. At the peak of the rainy season,
the water levels in both the groundwater and the rivers usually
attain maximum heights while the major drain (Cross River) usu-
ally overflows its banks (Ebong, 2012). Seepages from the
Owutu-Afikpo-Adadama sandstone ridge system (OAASRS) flows
toward the surrounding low-lying areas, as a result the soil within
these regions are constantly wet and marshy in the rainy season
and dry having deep pressure cracks in the dry season (Egboka
and Uma, 1986).
Geologically, the IME that spans between Latitudes 5°150
N and
6°300
N of the Equator and Longitudes 7°450
E and 8°450
E of the
Greenwich Meridian, is the NW–SE splay segment of the NE–SW
trending Benue Trough and always referred to as a contiguous part
of the Lower Benue Trough. The IME is bounded to the west by the
Abakiliki Anticlinoriun, to the east and northeast by the Obudu
Plateau and the Cameroon Volcanic Line and in the southeastern part
by the Oban Massif of Cross River State, Nigeria (Fig. 1B). The IME is
characterised by low relief and gently undulating topography
(Eseme et al., 2002). It is tectonically believed to have its origin
traceable to the regional tectonic and magmatic events during
the Cretaceous times that was later affected by the regional
Santonian compressional episode (Odigi, 2011). Sedimentation in
the IME and its sub-basin such as the Afikpo Basin commenced
with the marine Albian Asu River Group (ARG) that was the first
lithostratigraphic unit resting unconformably on the Precambrian
Crystalline Basement (Fig. 1A and C) (Ekwueme, 2003; Ekwueme
et al., 1995). The ARG a non-marine to marginal marine character
sediment consists of impervious shale, limestone, sand lenses,
sandstone intercalations and ammonites (Odigi and Amajor,
2009; Petters et al., 1987). The Late Albian-Cenomanian thick flag-
gy impervious calcareous and non-calcareous black shale; siltstone
and sandstones of the Eze-Aku Group (EAG) rest on the ARG. The
100 E.D. Ebong et al. / Journal of African Earth Sciences 96 (2014) 99–109

thickness of this formation varies locally and may be as thick as
100 m in most areas (Ukaegbu and Akpabio, 2009). Murat (1972)
was of the view that the Eze-Aku shale shows deposits of marine
condition in a tectonically controlled basin. Dense, fine-grained
and sometimes dark coloured Tertiary volcanic rocks such as bas-
alts and dolerites intrude these Cretaceous sediments in some loca-
tions (Offodile, 1980). These Post-Cretaceous tectonic activities
that were believed to have originated from the adjoining Cameroon
Volcanic Province and other low grade metamorphism in the area
caused serious fracturing of the basement rocks and deformation
of the adjoining Cretaceous lithostratigraphic units (Akpan et al.,
2013; Nguimbous-Kouoh et al., 2012). Thus, the overlying
Cretaceous sequence is highly baked, domed and seriously
deformed in many locations in the area (Etuk et al., 2008;
Benkhelil, 1982). In many locations the sandstones in the EAG form
ridges that averagely strike at N40°E and dip between 20° and 68°
a typical example is the OAASRS (Odigi and Amajor, 2009). The
shale within the EAG was reported by Okereke et al. (1998) as
having secondary properties like interconnected porosity, joint,
fracture and folds acquired as a result of the syndepositional defor-
mational episodes. These properties are significant and will play
vital roles in the transmission and storage of fluid. This property
of the IME introduces a slight geologic complexity in the litho-
stratigraphic architecture of the area at certain location especially
those areas around the geologic contacts. The Nkporo Formation
that Petters (1989) and some authors refer to as the Nkporo-Afikpo
Shale Province rest on the Post-Santonian hiatus and represent a
fossiliferous pro-deltaic facies of the Late Campanian–Early
Maastrichtian brackish marsh deposit that consists basically of
shale and sandstone lenses (Odigi, 2011).
Fig. 1. (A) Geologic map of the Nigerian sedimentary Basins showing the Lower Benue Trough LBT), Middle Benue Trough (MBT) and the Upper Benue Trough (UBT) (NGSA,
2006), (B) geologic map of the Ikom-Mamfe Embayment, (C) geologic map of Abi area showing the major geologic contacts, sedimentary variations, VES and borehole water
sample locations. Inset: Map of Cross River State (Redrawn from Ebong, 2012).
E.D. Ebong et al. / Journal of African Earth Sciences 96 (2014) 99–109 101

3. Materials and methods
The electrical resistivity survey involved a VES technique which
is based on measuring of the potentials between one pair of
electrodes (potential electrodes) due to a direct current being
transmitted between another pair of electrodes (current elec-
trodes). The survey was carried out in the area using the IGIS model
SSR-MP-ATS resistivity meter. Although the IGIS resistivity meter
can average up to 32 cycles of data, we usually truncate the cycling
process after four stacks if the displayed readings are well corre-
lated with standard deviation less than 5%. Four 50 cm length cylin-
drical steel stakes of 1.5 cm diameter was used as current and
potential electrodes, wires and crocodile clips were used to connect
the electrodes to the resistivity meter. Over thirty (30) sounding
were completed within the study area using the Schlumberger
configuration with electrode spacing (AB) ranging from 2 to
600 m and the potential electrode spacing (MN) ranged from
0.5 m to 20 m. The AB positions were selected at log scales and over
8 data sets made of four cross over points were acquired in each log
cycle. Generally, data quality was good especially the data set that
were acquired in the wet season but where contact resistance
problems were observed, water and salt solutions were used to wet
the electrode positions in order to lower the contact resistances.
Borehole water samples from twenty-eight (28) water wells
were collected and measured in situ to determine the aquifer water
electrical conductivity which was later converted to electrical
resistivity, total dissolved solids (TDS), pH and temperature values.
4. Data analysis
The measured earth resistances were multiplied by a geometric
factor resulting from the array used to obtain the apparent electri-
cal resistivity. The converted electrical resistivity values were man-
ually plotted in the field to check the data quality. Standard curve
smoothening techniques were applied to the data (Chakravarthi
et al., 2007; Bhattacharya and Patra, 1968). Qualitative interpreta-
tion of the smoothened curves was performed using master curves
and standard charts (Orellana and Moony, 1966) after which they
were subjected to computer modeling using the RESIST software
developed by Vender Velpen (1988). The software makes provision
for sounding data to be entered as apparent resistivities versus half
current electrode spacing (AB/2) for Schlumberger array. The input
parameters, resistivities and depths used for the starting model in
the inversion process were estimated from the manually inter-
preted field curves. Depth constraints were provided from litho-
logic logs from boreholes within the area obtained from the
Cross River State Rural Water Supply and Sanitation Agency
(RUWATSSA). During the inversion process, the apparent resistivi-
ties were compared with the synthetic values and a fit obtained
with minimal RMS error <5%. The inverse modeling produced a
model that best fits the data in a least squares sense using ridge
regression (Inman, 1975) after a couple of iterations that adjusted
the parameters to fit the starting model. The result of the inversion
provided inverted resistivity, thickness and depth of the geoelec-
tric layers for each VES station. Geophysical results generally are
Fig. 2. Correlation between lithologic logs and some of the 1D inverted resistivity models (A) Itigeve, (B) Mboti, (C) Emin Ekpongho and (D) Emikwo.

known to suffer from non-uniqueness problems that can be
reduced by a combination of results from several methods. To
reduce the ambiguity problem, geologic constrains and some bore-
hole lithologic data were used to constrain the vertical electrical
sounding data. The electrical resistivity derived 1-D inversion
models and their correlations with closest borehole lithologic logs
are shown in Fig. 2.
5. Geohydraulic parameter estimation
Geohydraulic properties are conventionally determined from
laboratory experiments performed on core samples and in the field
from pumping test results. With the availability of the bulk resis-
tivity of the aquifer layer measured from 30 evenly distributed
VES locations within the area and the in situ aquifer water resistiv-
ity measured from boreholes closest to the VES points, it was pos-
sible to estimate the apparent formation factor and afterwards the
hydraulic conductivity by applying the Salem (2001) equation. The
electrical resistivity of earth materials are known to vary with
changes in temperature, lithology, porosity, degree of saturation
and the resistivity of pore fluid. For a partially saturated aquifer
in which the pore fluid is the only medium of electrical conduction,
a quantitative relationship between some of these variables and
bulk resistivity (qb) can be expressed in terms of Archie’s equation
(Archie, 1942) as
qb ¼ a Á qw/Àm
Sn
ð1Þ
where qw is the resistivity of pore fluid measured directly from
borehole water samples, qb is the bulk resistivity of the rock, / is
the porosity of the rock (approximate volume of water filling the
pore space) and should be referred to as apparent porosity, a and
m are certain empirical constants that depend on the geologic for-
mation under investigation. The constant a is sometimes referred
to as tortuosity, whereas m (that is sometimes called the cementa-
tion index) and n are cementation and saturation exponents respec-
tively (Metwaly et al., 2006). The bulk resistivity values of geologic
formations are influenced by the type of rock and soils, porosity,
degree of saturation, nature of the saturating fluid and the diage-
netic cementation factor (Smith and Sjogren, 2006). For most rocks,
typical values of a and m have been observed to vary between 0.62–
2.45 and 1.08–2.15 respectively (Jackson et al., 1978).
The formation factor (F) is empirically related to the bulk resis-
tivity of the saturated geologic formation and the resistivity of the
infill pore fluid,
qb ¼ F Á qw ð2Þ
Archie also discovered from laboratory measured values of F
that, F is related to / of a saturated rock formation with perfectly
insulated grains by an empirical relation,
F ¼ a Á /Àm
ð3Þ
For formations that have the capacity to retain water, we may
combine Eqs. (2) and (3) such that,
qw ¼
qb
F
¼
qb
a/Àm ð4Þ
For a clay-free medium, the ratio of bulk resistivity to pore fluid
resistivity is known as the intrinsic formation factor, Fi. So the
Archie’s equation can be rearranged as
/ ¼ e
1
m lnðaÞþ1
m ln 1
Fi

ð5Þ
With the values of the coefficients a and m ideally determined,
porosity can be estimated using Eq. (5) (Soupios et al., 2007;
Aristodemou and Thomas-Betts, 2000). In reality, the validity of
Archie’s law is dependent on lots of factors including the extent
of saturation of the aquifer, composition of the saturating fluid
and the presence of extraneous sources of conductivity (e.g. clays,
shales, etc.) within the aquifer (Acworth and Jorstad, 2006; Okoyeh
et al., 2013). Under such influences, Archie’s law will break down.
In order to account for the influence of these factors on bulk resis-
tivity of saturated aquifers, Archie’s law has been modified by the
introduction of some corrective terms. The Waxman–Smits model
is one of the modified forms of Archie’s law and was considered in
this study since it can empirically relate apparent and intrinsic for-
mation factors, Fa and Fi respectively after taking into account the
shale effects. A good number of such models are currently in use
and majority of them are either shale-fraction or cation exchange
models with concepts derived from parallel conductors (Waxman
and Smits, 1968; Patnode and Wyllie, 1950). The Waxman–Smiths
model relates the apparent and intrinsic formation factors as
Fa ¼ Fið1 þ BQvqwÞÀ1
ð6Þ
where the BQv is related to the effect of surface conduction mainly
due to clay. Waxman and Smits (1968) used two parameters; the
first is Qv which is the cation exchange capacity (CEC) per unit pore
volume of the rock (Worthington, 1993). It is defined as cation con-
centration (Butler and Knight, 1998) and reflects a specific surface
area, which is a constant for a particular rock. It describes also the
number of cations available for conduction that are loosely attached
to the negatively charged clay surfaces within the formation. The
ions, which can range in concentration from 0 to $1.0 meq/ml are
in addition to those in the bulk pore fluid. The second parameter,
B is the equivalent ionic conductance of clay exchange cations
(mho cm2
/meq) as function of 1/qw (specific conductivity of the
equilibrating electrolyte solution) (mho/cm). This parameter is
called the equivalent electrical conductance, which describes how
easily the cations can move along the clay surface (Butler and
Knight, 1998). Re-writing Eq. (6), we obtain a linear relationship
between 1/Fa and qw of the form
1
Fa
¼
1
Fi
þ
BQv
Fi

qw ð7Þ
where 1
Fi
is the intercept of a fitted straight line and BQv
Fi
is the slope
(Aristodemou and Thomas-Betts, 2000; Huntley, 1986). Fa was com-
puted from the ratio of the bulk electrical resistivities qb derived
from 1-D inversion of resistivity data and the measured fluid elec-
trical resistivities qw, obtained from boreholes closest to the VES
points.
An empirical relationship developed by Salem (2001) was used
to estimate the hydraulic conductivity, K from Fa values
K ¼ 7:7 Â 10À6
Á F2:09
a m=s ð8Þ
Hence, the transmissivity (T) expressed in m2
/s or m2
/day was
estimated from
T ¼ K Á h ð9Þ
where h is the thickness of the aquifers in meters (m). The use of
apparent formation factor in the estimation of the transmissivity
helps in eliminating the effect of changes in water resistivity but
utilizes the information on these changes in its computation
(K’Orowe et al., 2011). Hydraulic conductivity and transmissivity
generally give a measure of the ability of an aquifer to transmit
water over a unit thickness for hydraulic conductivity and over
the entire saturated thickness (Massoud et al., 2010).
In theory, stratified conductors are known to possess certain
fundamental parameters that are significant in both interpretation
and understanding of the geoelectric layer (Braga et al., 2006).
These parameters are related to different combinations of q and
h for each geoelectric layer in the model (Batte et al., 2010;
Singh et al., 2004). Such parameters include the DZP that consist

of the longitudinal conductance (S) and the transverse resistance
(TR). S is the ratio of h of the individual geoelectric layer to its
corresponding q value (Sinha et al., 2009; Gowd, 2004).
S ¼
XN
i¼1
hi
qi
ð10Þ
This parameter is used to quantitatively assess the properties of
a thin conducting layer. Studies have shown that hydraulic conduc-
tance has an inverse relationship with electrical resistivity values,
thus high groundwater potential aquifers are usually characterised
by high conductance values (Kumar et al., 2001). TR of a geoelectric
layer is defined as the product of h and its corresponding q (Chang
et al., 2011; Mele et al., 2010).
TR ¼
XN
i¼1
hi Ã qi ð11Þ
These parameters are based on the consideration of a column of
unit square cross-sectional area (m2
) cut out of a group of layers of
infinite lateral extent (Khalil, 2009; Ayolabi et al., 2010).
6. Results and discussion
The results of the geohydraulic parameters and the DZP as esti-
mated from 1-D electrical resistivity inversion and hydrogeologic
measurements of borehole water sample are shown in Tables 1
and 2. Table 3 shows a comparison of VES-hydrogeological
measurements, lithologic and pumping test data. The Surfer 11
contouring software from Golden Software Inc., USA was used to
produce the aquifer thickness map, longitudinal unit conductance
and hydraulic conductivity maps. The Inverse Distance Weighting
(IDW) was considered as the gridding method as a result of the
failure of other gridding methods such as the ordinary kriging
method, basically, due to its inherent over-extrapolation into areas
where no data exist. The IDW method is based on the assumption
that the predicted value of an unsampled point is the weighted
average of the observed values within its vicinity, and the weights
are inversely related to the distances between the predicted value
and the observed values (Lu and Wong, 2008). The choice of the
IDW was based on its ability to utilise only the proximity factor,
unlike the ordinary kriging in which the predicted value takes into
consideration the proximity of the observed data locations and the
general spatial variability as predicted by the variogram and so will
depend on the outcome of the variogram. The inverse-distance
weight which incorporates a constant power or a distance-decay
parameter that tends to adjust the diminishing strength of the pre-
dicted value relative to the observed with respect to increasing dis-
tance can also be referred to as the Inverse distance to a power (Lu
and Wong, 2008).
6.1. Determination of hydraulic conductivity and transmissivity from
VES and hydrogeologic measurements
The estimated hydraulic conductivity (Ke) values (Table 1)
within the area under investigation were found to be within the
range 1.4 Â 10À5
–1.0 Â 10À4
m/s (1.25–9.04 m/day). The lower
values of Ke observed in some locations, could be due to the
influence of clay minerals in the aquifer rock matrix which tends
to lower the values of resistivity will invariably lower the values
Table 1
Estimates of geohydraulic parameters and the Dar Zarrouk parameters from electrical resistivity VES data.
Location Coordinates in degrees Bulk
Resistivity
(Ohm-m)
Aquifer
water
resistivity (Ohm-m)
Aquifer
thickness
(m)
Longitudinal
unit
conductance
(S)
Transverse
unit
resistance
Apparent
formation
factor (Fa)
1/Fa Hydraulic
conductivity
Transmissivity
Longitude Latitude (m/s) (m/day) (m2
/s) (m2
/day)
Adadama 8.098 5.941 52.8 31.83 20.0 0.38 1056.0 1.66 0.60 2.2EÀ05 1.92 4.4EÀ04 38.32
Adadama2 8.084 5.935 20.8 15.39 30.6 1.47 636.5 1.35 0.74 1.4EÀ05 1.25 4.4EÀ04 38.21
Emin Ekpongho 8.089 5.937 52.2 31.83 21.9 0.42 1143.2 1.64 0.61 2.2EÀ05 1.87 4.7EÀ04 40.97
Ngoli 8.085 5.931 23.7 15.39 10.3 0.43 244.1 1.54 0.65 1.9EÀ05 1.64 2.0EÀ04 16.89
Emikwo 8.099 5.925 263.0 98.45 16.4 0.06 4313.2 2.67 0.37 6.0EÀ05 5.19 9.8EÀ04 85.06
Ebasekpa 8.097 5.929 135.8 98.45 62.9 0.46 8541.8 1.38 0.72 1.5EÀ05 1.30 9.5EÀ04 81.95
CSCS Adadama 8.083 5.931 44.8 31.83 32.7 0.73 1465.0 1.41 0.71 1.6EÀ05 1.36 5.1EÀ04 44.44
Itabongho 8.083 5.929 246.4 98.45 4.3 0.02 1059.5 2.50 0.40 5.2EÀ05 4.53 2.3EÀ04 19.46
Agbara 8.012 5.996 21.5 11.64 10.8 0.50 232.2 1.85 0.54 2.8EÀ05 2.40 3.0EÀ04 25.91
Mgarabe 8.021 5.994 62.7 29.15 16.2 0.26 1015.7 2.15 0.46 3.8EÀ05 3.30 6.2EÀ04 53.42
Akarefor 8.027 5.995 122.7 58.45 35.2 0.29 4319.0 2.10 0.48 3.6EÀ05 3.13 1.3EÀ03 110.31
Anong Ezege 8.045 5.992 56.5 21.15 4.3 0.08 243.0 2.67 0.37 6.0EÀ05 5.19 2.6EÀ04 22.30
Akpoha 8.016 5.991 97.6 47.07 14.0 0.14 1366.4 2.07 0.48 3.5EÀ05 3.05 4.9EÀ04 42.76
Emin Ekpon 8.02 5.928 60.2 35.03 33.3 0.55 2004.7 1.72 0.58 2.4EÀ05 2.06 8.0EÀ04 68.70
Egboronyi 8.037 5.945 86.3 35.03 14.4 0.17 1242.7 2.46 0.41 5.1EÀ05 4.38 7.3EÀ04 63.06
Itigeve 8.047 5.902 98.5 37.10 19.8 0.20 1950.3 2.65 0.38 5.9EÀ05 5.12 1.2EÀ03 101.38
Anong Bahomono 8.036 5.869 62.6 22.92 16.0 0.26 1001.6 2.73 0.37 6.3EÀ05 5.43 1.0EÀ03 86.94
Ediba 8.029 5.863 72.2 – – – – – – – – – –
Usumutong 8.012 5.837 338.2 97.05 36.1 0.11 12209.0 3.48 0.29 1.0EÀ04 9.04 3.8EÀ03 326.34
Egbezum 7.965 5.848 66.2 – – – – – – – – – –
Anoikpata 7.965 5.849 415.5 173.48 6.7 0.02 2783.9 2.40 0.42 4.8EÀ05 4.13 3.2EÀ04 27.66
Afafanyi 7.994 5.884 602.7 217.05 51.3 0.09 30918.5 2.78 0.36 6.5EÀ05 5.62 3.3EÀ03 288.49
Abeugo 8.004 5.879 843.4 332.40 22.0 0.03 18554.8 2.54 0.39 5.4EÀ05 4.66 1.2EÀ03 102.46
Ilike 8.159 5.94 62.7 31.74 16.2 0.26 1015.7 1.98 0.51 3.2EÀ05 2.76 5.2EÀ04 44.71
Mboti 8.16 5.943 50.0 35.03 32.8 0.66 1640.0 1.43 0.70 1.6EÀ05 1.40 5.3EÀ04 45.91
Egada 8.161 5.944 73.2 35.03 16.3 0.22 1193.2 2.09 0.48 3.6EÀ05 3.10 5.9EÀ04 50.60
Ikpal-Ekori Rd 8.115 5.934 380.0 166.64 41.90 0.11 15922.0 2.28 0.44 4.3EÀ05 3.73 1.8EÀ03 156.12
Lehangha 8.149 5.957 32.8 15.10 8.5 0.26 278.8 2.17 0.46 3.9EÀ05 3.37 3.3EÀ04 28.61
Ebijikara 7.969 5.819 363.6 141.90 43.4 0.12 15780.2 2.56 0.39 5.5EÀ05 4.75 2.4EÀ03 206.33
Ebom-Adim Rd 7.97 5.805 183.0 81.90 15.3 0.08 2799.9 2.23 0.45 4.1EÀ05 3.57 6.3EÀ04 54.63
Maximum 1.47 30918.51 3.48 0.74 1.0EÀ04 9.04 3.8EÀ03 326.34
Minimum 0.02 232.20 1.35 0.29 1.4EÀ05 1.25 2.0EÀ04 16.89
Average 0.30 4818.96 2.16 0.49 4.1EÀ05 3.54 9.4EÀ04 81.14

of hydraulic conductivity in those areas where they exist (Heigold
et al., 1979). The northeastern and northwestern areas were notable
portions with low Ke within the study area. Some of such locations
include Agbara, Adadama, Lehangha, Egada and some portions in
Egboronyi with Ke values ranging from 1.5 Â 10À5
to 4.5 Â 10À5
m/s (1.3–3.89 m/day) (see Fig. 3). Geologically, these locations fall
within the Nkporo Formation that predominantly consists of the
Nkporo Shale. This shale layer is highly fractured in some locations
and constitutes aquifer horizons in areas where the volume of such
fractures can accommodate water (Akpan et al., 2013). Usually, the
groundwater yield in such areas is marginal except along areas with
high fracture density. Higher values of Ke were observed in the
southern portion of the study area, which is predominantly com-
posed of sandstone units of the Asu River and sandstone lenses of
the Eze-Aku Formations. Afafanyi and its environs are typical loca-
tions of the sandstone-based aquifer horizon having Ke values
4.5 Â 10À5
m/s (3.89 m/day) and increased to $1.0 Â 10À4
m/s
(9.04 m/day) around Usumutong. The estimated values of transmis-
sivity (Te) and Ke were observed to be directly proportional such
that Ke increases with Te suggesting that h is almost constant. This
progressive increase in both parameters has been attributed to
the influence of hydraulic and electric anisotropies, mineral and
lithologic variation, pore shape and size, sizes of grains and pore
connectivity (Salem, 1999). In Fig. 4, the northern portion where
fractured and deformed shale aquifers are dominant, Te values
were observed to be $2.0 Â 10À4
m2
/s ($16.89 m2
/day) and
increased to 1.0 Â 10À3
m2
/s (90 m2
/day) in the southern por-
tions where sandstones aquifers are dominant.
6.2. Correlation between transmissivity and transverse unit resistance
The correlation of the Te (m2
/day) and TR ( X-m2
) (Fig. 5)
revealed a direct relationship with a correlation coefficient,
R2
= 0.65 such that
Table 2
Hydrogeologic measurements of electrical conductivity, TDS, pH and temperature from borehole water sample.
Borehole No. Coordinates in degrees Measured conductivity
corrected to 25 °C (lS/cm)
TDS (mg/l) pH Temprature (°C)
Longitude Latitude
BH1 8.019 5.830 504.96 338.32 4.5 27
BH2 8.019 5.828 467.52 313.24 3.8 27
BH3 8.016 5.831 478.08 320.31 4.8 27
BH4 8.006 5.843 130.66 87.54 3.2 28
BH5 7.991 5.888 21.12 14.15 1.4 27
BH6 8.020 5.887 103.04 69.04 3.6 29
BH7 8.018 5.886 30.08 20.15 1.9 28
BH8 8.021 5.984 608.18 407.48 4.3 28
BH9 8.021 5.985 667.40 447.16 5.2 28
BH10 8.020 5.985 472.82 316.79 3.6 28
BH11 8.017 5.988 733.20 491.24 3.5 28
BH12 8.018 5.988 164.50 110.22 1.2 28
BH13 8.013 5.992 203.04 136.04 3.4 28
BH14 8.014 5.994 212.44 142.34 2.1 28
BH15 8.016 5.993 171.08 114.62 1.5 28
BH16 8.016 5.987 89.30 59.83 2.6 28
BH17 8.037 5.947 396.68 265.78 3.6 28
BH18 8.088 5.928 728.14 487.85 4.3 26
BH19 8.089 5.927 649.44 435.13 5.1 31
BH20 8.081 5.930 688.94 461.59 4.8 26
BH21 8.082 5.925 314.16 210.49 3.9 24
BH22 8.099 5.929 31.28 20.96 2.3 29
BH23 8.115 5.934 664.24 445.04 1.7 29
BH24 8.117 5.935 439.76 294.64 3.4 29
BH25 8.117 5.936 150.06 100.54 2.4 34
BH26 8.145 5.937 19.20 12.86 1.8 27
BH27 8.158 5.940 931.00 623.77 3.1 26
BH28 8.160 5.944 285.48 191.27 3.8 36
WHO (2006) 500 7.5
Table 3
Comparison of VES-hydrogeological measurements, lithologic and pumping test data.
Location Aquifer thickness (m) Hydraulic Conductivity (m/day) Transmissivity (m2
/day)
VES Litho-log Estimated Pumping test Estimated Pumping Test
CSCS Adadama 32.7 25.5 1.4 2.0 44.4 51.0
Emikwo 16.4 27.0 5.2 3.7 85.1 99.7
Mboti 32.8 15.3 1.4 3.2 45.9 49.0
Lehangha 5.8 7.3 3.4 3.4 28.6 25.0
Mgarabe 14.0 15.0 3.3 4.5 53.4 67.8
Agbara 10.8 8.6 2.4 4.4 22.9 37.8
Enong Ezege 4.3 8.0 5.2 4.0 22.3 32.1
Egboronyi 14.4 11.0 4.4 4.5 53.1 49.5
Egada 16.3 21.0 3.1 3.0 50.6 63.4
Maximum 32.8 27.0 5.2 4.5 85.1 99.7
Minimum 4.3 7.3 1.4 2.0 22.3 25.0
Average 16.4 15.4 3.3 3.6 45.1 52.8
Correlation coefficient 0.63 0.54 0.94

TR ¼ 7:51 Á T1:38
e ð12Þ
From the correlation of the Te and TR, increase in Te will results
in considerable increase in TR which is indicative of a continuous
fluid flow potential across the entire area (Salem, 2001). Areas such
as Ngoli, where the original sedimentary successions have been
altered by paleotectonic activities may not yield the same result
(Odigi, 2011; Odigi and Amajor, 2009).
These structural changes resulted in the alternate sequences of
sands, shales which are fracture in some areas and clays (Okereke
et al., 1998; Raju and Reddy, 1998). For the fractured shale aqui-
fers, low values of TR and Te were observed except in locations with
high fracture density and considerable thickness. In such cases, the
observed values of Te were taken to be the sum of individual trans-
missivity contributions from all fractures within the aquifer interval.
Where an aquifer interval contains a single fracture, then Te is sim-
ply equal to the transmissivity of that fracture. Lithologic data from
boreholes drilled around Akpoha, Adadama, Mboti and Lehangha
indicate a fractured shale aquifer within these areas, which corre-
lated strongly with the VES derived subsurface models of these
areas (see Fig. 2). Variations in the values of Te and TR in the area
were attributed to the heterogeneous and anisotropic nature of
the aquifer systems in the area (Akpan et al., 2013). These varia-
tions were in conformity with variations in the measured physical
parameters of water samples. For instance, EC was observed to
vary from 19.2 to 931.0 lS/cm, temperature between 24 and
34 °C, TDS between 12.86 and 623.77 mg/l and pH varying from
1.2 to 5.1 (see Table 2).
6.3. Longitudinal unit conductance and aquifer thickness
The longitudinal unit conductance map (Fig. 6) shows that areas
dominated by aquifers with lower values of S ($0.2 XÀ1
), resistivity
values are relatively high when compared to their corresponding
thickness. Also, these areas were observed to have higher values
of Te compared to other areas having similar values of thickness
with lower resistivity values. Thus, Te tends to decrease with
increased value of S especially in locations where clayey
materials were present within the rock matrix in the aquifers.
Locations where relatively high resistivity values and aquifer
thicknesses which translate to areas with higher Te values include
Afafanyi, Usumutong Ikpalegwa and adjoining areas with values
ranging from 340–600 Xm, 36–51 m and 1.81–3.77 Â 10À3
m2
/s
(156–326 m2
/day) respectively. Locations that have considerable
thickness ($10–32 m), lower resistivity values (20–53 Xm) and
higher values of S (P0.5 XÀ1
) but with low Te values (1.85–5.09
m2
/s) (16–44 m2
/day) include Adadama and adjoining areas where
the Nkporo Shale Formation dominates (Table 1, Figs. 6 and 7). In
any case, the DZP are diagnostic of Te, since Te is influenced by the
aquifer formation resistivity and thickness.
Fig. 3. Hydraulic conductivity map.
Fig. 6. Longitudinal unit conductance map.
Fig. 4. Transmissivity map.
Fig. 5. Relationship between the transmissivity and the transverse resistance for
the area.

6.4. Correlation between the inverse apparent formation factor and
fluid resistivity
The formation factor is known to be a function of the bulk resis-
tivity, pore-water or aquifer water resistivity, porosity and cemen-
tation factor such that an increase in the formation factor resulting
from a considerable increase in the bulk resistivity over the pore-
water resistivity will correspond to a decrease in porosity (Salem,
1999). Fig. 8 shows a graph of inverse apparent formation factor
(1/Fa) against fluid resistivity (qw). By applying the least squares
best fit to the data, the values of 1/Fi and BQv were deduced.
1
Fa
¼ 0:7146 À 0:0047qw ð13Þ
Comparing Eqs. (13) and (7), a value of 1/Fi for the area was
observed to be 0.7146. Also, the product of BQv and the inverse
of Fi is equal to the slope ($0.0047) thus yield the effect of clay con-
ductivity to be $0.0066 mho. The slope shows that the influence of
clay on the aquifer horizon is relatively small and can be ignored.
Equation (13) is an empirical model that carries with it, the correc-
tive factor for clay conductance within the aquifer horizon. It is
suitable for the determination of apparent formation factor in
aquifer horizons whose conductivity is a sum of fluid and shale
conductivities. Salem (2001) and Huntley (1987) have observed
similar apparent formation factor-water resistivity relationship in
shale contaminated aquifers. It may give erroneous results in aqui-
fers with highly resistive mineral grains and conducting pore fluid
(Kirsch and Yaramanci, 2009).
From the measured aquifer water resistivity (see Table 1), the
groundwater system within the area is fit for domestic and indus-
trial uses, except in some communities such as Lehangha, Ilike,
Adadama2, Ngoli, Agbara, CSCS Adadama and Mboti where the
fluid and bulk resistivities were observed to vary between 15.10–
35.03 Xm and 650 Xm respectively. In these areas, the groundwa-
ter was inferred to be marginally fit. The low resistivities observed
for the water-bearing aquifer zones in the northeastern axis of the
study area, could be due to the nature of the deteriorating quality
of the underground water system as observed from the hydrogeo-
logic measurements and the fractured shale system that tends to
dominate the aquifer systems in these areas.
From Fig. 9, the bulk resistivity cut-off was pegged at 50 Xm,
which is above the 48 Xm that Buggs and Lloyd (1976) used in
their aquifer classification scheme. Thus, aquifers with bulk resis-
tivity below 50 Xm were considered to brackish water while those
above were attributed to be fresh water aquifers.
7. Conclusion
With the aid of the bulk resistivity of the subsurface formations
derived from the 1-D electrical resistivity inversion, measured
groundwater resistivities and the apparent formation factor, the
estimation of hydraulic conductivity using the empirical relation-
ship established by Salem (2001) was possible. The estimated
hydraulic conductivity paved the way for the determination of
estimated transmissivity. The result of Ke and Te represents two dis-
tinct aquifer domains. The first domain comprises fractured shale
aquifers that are dominant in the northeastern axis of the study
area. The fractured shale aquifers have relatively low bulk resistivity
(645 Xm), hydraulic conductivity (62.0 Â 10À5
m/s or 61.7 m/day)
and transmissivity (65.2 Â 10À4
m2
/s or 645 m2
/day). The
second group consists of sandy aquifers that have higher values of
bulk resistivity ($100–800 Xm), hydraulic conductivity ($4.0 Â
10À5
–1.0 Â 10À4
m/s or $3.46–9.04 m/day) and transmissivity
($6.94 Â 10À4
–3.81 Â 10À3
m2
/s or $60–330 m2
/day). Generally,
the observed Te values for the entire area ranged between
2.0 Â 10À04
–3.8 Â 10À03
m2
/s or 16.89–326.34 m2
/day ($9.4 Â
10À04
m2
/s or $81.14 m2
/day on average). The DZP estimated for
any aquifer horizon has the tendency of influencing the value of
the estimated transmissivity, which in turn depends on the aquifer
thickness. The ranges of result observed correlated well with results
from pumping test from 9 boreholes within the area. The results in
Table 3 showed a comparison between the aquifer thickness as
estimated from VES and those derived from lithologic data, the
estimated hydraulic conductivity and transmissivity and those
from available pumping test data closest to the VES points with cor-
relation coefficients of h = 0.63, K = 0.54 and T = 0.94 respectively.
Fig. 7. Aquifer thickness map.
Fig. 8. Inverse apparent formation factor versus aquifer water resistivity plot to
determine the intrinsic formation factor.
Fig. 9. Bulk resistivity versus aquifer resistivity plot showing the cut-off resistivity
for fit and marginal fit groundwater.

Usually, uncertainties are inevitable in any geophysically deter-
mined result, but to a greater extent the values gotten from this
work were in the neighbourhood of those gotten from pumping test
experiments and other previous reports within the area to a reason-
able degree. The results of the in situ measurements of aquifer water
EC (19.2–931.0 lS/cm), temperature (24–34 °C), TDS (12.86–623.77
mg/l) and pH (1.2–5.1) is an indication that the groundwater system
within the area is fit for both domestic and agricultural purposes.
Although the approach used in this work cannot reliably replace
the conventional pumping test technique due to the inherent ambi-
guities associated with its results, it can provide an estimate of the
aquifer parameters, which can serve as an initial guide for a more
detailed hydrogeologic investigation in the area.
Acknowledgements
The authors are grateful to Late Prof. E.W. Mbipom for all the
support and encouragement that he had showered on them during
the field data acquisition and analyses that led to the successful
completion of this work. We thank the Cross River State Rural
Water Supply and Sanitation Agency (RUWATSSA) for freely releas-
ing the borehole information used in this study. We also wish to
acknowledge with thanks all the suggestions and comments from
the anonymous reviewers.
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