Journal of Water Resource and Protection, 2012, 4, 993-1000
http://dx.doi.org/10.4236/jwarp.2012.412115 Published Online December 2012 (http://www.SciRP.org/journal/jwarp)
Estimation of Aquifer Transmissivity Using Dar Zarrouk
Parameters Derived from Surface Resistivity
Measurements: A Case History from Parts of
Enugu Town (Nigeria)
Ahamefula U. Utom, Benard I. Odoh, Anthony U. Okoro
Department of Geological Sciences, Nnamdi Azikiwe University, Awka, Nigeria
Received September 2, 2012; revised October 6, 2012; accepted October 13, 2012
ABSTRACT
Many investigation techniques are commonly employed with the aim of estimating the spatial distribution of transmis-
sivity. Unfortunately, the conventional methods for the determination of hydraulic parameters such as pumping tests,
permeameter measurements and grain size analysis are invasive and relatively expensive. A geoelectric investigation
involving vertical electrical sounding was carried in parts of Enugu town, Enugu state, Nigeria. The survey was aimed
at extrapolating the result of pumping tests over an area. Using the Dar Zarrouk parameter, a β constant of 0.32 was
found to translate resistivity to transmissivity with clay content as the primary factor controlling the hydraulic conduc-
tivity. Results of the study show a strong correlation between aquifer transmissivity and longitudinal conductance (R2 =
0.82). Estimation of aquifer transmissivity values based on the results of the resistivity measurements also made it pos-
sible to demarcate area with good groundwater potential in parts of Enugu town, Nigeria.
Keywords: Resistivity; Transmissivity; Dar Zarrouk Parameters; Longitudinal Conductance; Pumping Tests
1. Introduction
As groundwater becomes more important as a source of
uncontaminated water, improved hydrogeological know-
ledge, new groundwater exploration technologies and
data processing methods must be efficient to facilitate
investigations and evaluation of groundwater resources
[1,2]. Many investigation techniques are commonly em-
ployed with the aim of estimating the spatial distribution
of aquifer parameters such as hydraulic conductivity,
transmissivity and aquifer depth [3]. Unfortunately, the
conventional methods for the determination of hydraulic
parameters such as pumping tests, permeameter mea-
surements and grain size analysis are invasive, relatively
expensive and either integrate over a largest volume of
data or provide information only to a small section of the
aquifer in the vicinity of the borehole [4,5]. According [6]
interpolating aquifer properties between boreholes is
often difficult with little or no data in which to base these
extrapolations. Therefore, in areas with few pumping test
information, the spatial distribution of aquifer properties
cannot be confidently calculated. The application of
surface resistivity method however, can provide useful
method for obtaining information on aquifer properties in
areas where pumping test data are sparse and subsurface
conditions area appropriate.
Surface resistivity techniques are a useful tool rou-
tinely used under a variety of field conditions and geo-
logical settings in hydrogeology, environmental geology
and geotechnical engineering [7,8,10-14]. Details on
effective sampling rate and high quality data require-
ments for high target definition in an area geometrically
constrained with complex subsurface conditions using
resistivity techniques are suggested in [16,17].
Geophysicists have realized that the integration of
aquifer parameters calculated from existing borehole
locations and subsurface resistivity parameters extracted
from resistivity measurements can be highly effective,
since a correlation between hydraulic and electrical
aquifer properties can be possible as both properties are
related to the pore space structure and heterogeneity [1,
18,19]. A number of outstanding papers and reports have
been published on the application of resistivity techni-
ques in evaluating the relationships between aquifer
electrical and hydraulic properties [5,20-24]. For this
purpose transformation of the aquifer resistivity distribu-
tion in terms of the aquifer Dar Zarrouk parameters
requires the application of physically consequential rela-
tion derived either theoretically or empirically [25,26].
C
opyright © 2012 SciRes. JWARP

A. U. UTOM ET AL. 994
The main thrust of this paper is therefore to use sur-
face resistivity sounding in extrapolating pumping test
results over an area, by estimating transmissivity from
resistivity data in parts of Enugu town, where inter-
mittent water supply and shortages are major problems of
the inhabitants.
2. Relationship between Transmissivity and
the Dar Zarrouk Parameters
Groundwater flow through an aquifer is not governed by
hydraulic conductivity, K alone, but the bulk parameter
transmissivity, defined as:
K
h

(1)
where h is the thickness of the aquifer. Attempts have
been made to relate hydraulic conductivity to resistivity
for specific aquifers, usually glacial deposits [e.g., 27-30].
Both direct and inverse relationships have been shown to
exist. [31,32] theoretically derived two equations using
Ohm’s law of current flow and Darcy’s law for fluid
flow in a medium as:

;
hh
TRK forK

   (2)
1
lay content




;f
or
C
hh
TCK K   (3)
where, Th is the transmissivity, Kh is the hydraulic con-
ductivity, ρ is the electrical resistivity, R (·m2) is the
transverse unit resistance, C (–1) is the longitudinal unit
conductance of the aquifer and α and β are the constants
of proportionality.
The Dar Zarrouk Parameters (DZP) defined by the
longitudinal unit conductance in –1 (C, layer thickness
over resistivity) and transverse unit resistance in ·m2 (R,
layer thickness times resistivity) are also two of the most
important parameters in electrical prospecting [34,35].
Since Dar Zarrouk parameters are also bulk parameters,
taking the relationship between hydraulic conductivity
and resistivity a stage further leads to a relation between
transmissivity values estimated from pumping tests and
the Dar Zarrouk parameters from surface resistivity mea-
surement as shown in Equations (2) and (3). This mini-
mizes the problems arising from the non-uniqueness of
surface resistivity interpretation. While dealing with ba-
sic equations of direct current prospecting, [34] observed
that if one considers a geologic column built on a square
unit (Figure 1), R is the resistance to the lines of current
perpendicular to the strata, and, C is the conductance to
the lines of current parallel to the strata. These theoretical
relationships showing direct and inverse correlation be-
tween hydraulic conductivity and electrical resistivity has
been explained with respect to four basic assumptions
[5,6]:
Figure 1. Layered models showing transverse resistance
and longitudinal conductance [33].
1) In the case of a conducting basement, the hydraulic
conductivity is directly proportional to the electrical
resistivity: this applicable to Equation (1) (Figure 2);
2) In the case of a resistive basement, the hydraulic
conducting is inversely: this is applicable to Equation
(2) (Figure 2);
3) In the case of an unconsolidated, sandy, clay-free
aquifer, the hydraulic conductivity is directly related
to the porosity [36] and inversely related to the elec-
trical resistivity: this is applicable to Equation (1);
4) In the case of a clay-rich aquifer, the relationship be-
tween porosity breaks down in a more a complex
manner leaving clay content as the primary factor
controlling hydraulic conductivity: this is applicable
to Equation (2).
As a condition in sandy clay free hydrogeological en-
vironment, Kρ can be considered constant; in clay-rich
environment K/ρ should remain constant. The electrical
conductivity of the groundwater is expected not to vary
significantly throughout the aquifer as this would also
affect the measured resistivity. According to [5] some-
times this condition for using Equations (2) or (3) may be
difficult to meet. The authors further advised that it is
also essential that a priori hydraulic conductivity infor-
mation at least one point be known before using the
equations.
Using a representative average hydraulic conductivity
of 77.5 m/d [37] for 13 existing wells in the area, the
transmissivity in the study were estimated using Equation

A. U. UTOM ET AL. 995
Figure 2. Characteristic shapes of K- and H-type resistivity
curves [6].
(1). This average hydraulic conductivity values compared
favourably well with the work of [38] in the area. The
authors used the relation [39] for parallel flow within
each lithologic layer represented by point flow values:

1
m
Zii
i
K
bbk





 (4)
where, Ki is the hydraulic conductivity of each individual
layer of thickness, bi (ranging from 1 m to 60 m) with a
total number of 13 layers; b is the overall thickness of the
sequence (about 130 m). These hydraulic conductivity
values in the range of 10–5 - 10–2 m/s are characteristic of
a silty sand and clean sand aquifer [40].
Hence, in establishing the electrical nature of the base-
ment layer from resistivity sounding curves, we chose
Equation (3) to estimate the aquifer transmissivity from
the aquifer electrical parameters. This analogous and em-
pirical relationship can then assist in the estimation of
transmissivity using longitudinal conductance by surface
geoelectrical data, provided the aforementioned basic
assumptions are satisfied.
3. Site Information and Geoelectric Method
The Enugu area study site is located between latitudes
06˚22'N and 06˚27'N and longitudes 007˚25'E and
007˚30'E at about 5 km west of Enugu city and about 15
km near Akanu Ibiam International Airport at Enugu
North L.G.A in the southeastern Nigeria’s Enugu state.
The site area extent is approximately 84 km2.
The study area has three predominant and conformable
geologic formations (Figure 3): The Campanian Enugu
Shale, the Lower Maestrichtian Mamu Formation and the
Upper Maestrichtian Ajali Sandstone. Stratigraphically,
the Enugu Shale which overlies the Cross River Plain
east of the escarpment is overlain by the Mamu Forma-
tion which in turn is overlain by the Ajali Formation.
Hydrology and hydrogeology of the area is controlled by
topographic features. In the study area, the streams or
rivers, some of which appear fracture-controlled in their
flow path give rise to dendritic drainage pattern. The
topography and physiography affect the position and
shape of groundwater tables. The Enugu’s climate is
humid and humidity is high during rains. The average
annual precipitation in Enugu is estimated to be 2000
mm (79 in.) which arrives intermittently and becomes
very heavy during the rainy season. For the whole of
Enugu state, the mean daily temperature is 26.7˚C
(80.1˚F) [41]. The Sahara air mass, north-easterly dry
winds causes the dry season (October to March) as it
advances southwards while the Atlantic Ocean air mass
causes the rainy season (March to October) as it moves
northwards [42]. Water resources availability is also
limited due to the spatiotemporal variation of precipi-
tation. The area receives domestic water supply from
river reservoirs and the Ninth Mile Corner borehole
network. At present, it is a general practice that nearly
very single house built outside the municipal area drill a
groundwater well for its own domestic use. The wells are
generally drilled by local and small-scale contractors
where scientific data gathered are of secondary impor-
tance.
During this work, 19 geoelectrical soundings with a
maximum half current electrode separation of 150 m
have been used. The geoelectrical soundings were under-
taken within the study areas between July and August,
2011. The Schlumberger method was used to acquire the
soundings. The forms of the VES curves measured at the
studied locations are of different types, indicating
interplay between low and high resistivity layers (Figure
4). All resistivity soundings were invested using IPI2Win
software. This software performs an automated approxi-
mation of the initial resistivity model using the observed
data [43]. All resulting models produced a low RMS
relative error of the order of 3%. The starting model used
during the inversion of each of the measured VES loca-
tions were constrained according to obtained water table
of the nearest water and available drillers log information.
Five of the soundings closest to wells, where measured
aquifer properties were available gave estimate of the
Dar Zarrouk parameters (Table 1).

A. U. UTOM ET AL. 996
Figure 3. Physiographic and geologic map of the study also showing the location of the six VES points.
Table 1. Aquifer parameters and resistivity at six sites in parts of Enugu town (Nigeria).
VES Name Aquifer Thickness
(m)
Aquifer
Resistivity
(·m)
Longitudinal Conductance
(–1)
Measured
Transmissivity
(m2/d)
Modeled
Transmissivity
(m2/d)
R1 9.0 527 0.017 696 470
R2 2.1 55 0.038 162 105
R3 6.6 354 0.019 511 525
R4 8.2 364 0.023 635 636
R5 2.1 68 0.031 162 857
R6 3.9 127 0.031 302 858
4. Calculating the Aquifer Transmissivity highlights the applicability of the geoelectric sounding to
the study area, giving a β value of 0.32. This relationship
could be attributed to the influence of hydraulic and
electrical anisotropy as well as the variations in the
geology, grain size, as well as shape of pore channels.
The transmissivity value at each of the 19 VES locations
was then calculated using the longitudinal conductance
from the resistivity survey.
The understudied aquifer system consists of fine grained,
clayey-silty sand materials. Transmissivity of the studied
aquifer is therefore assumed to be controlled by the
thickness of the specific layer and the presence of
fine/clay particles. Also, assuming that the longitudinal
conductance is the dominant parameter, Equation (3) was
used to calculate the transmissivity. The constant, β was
calculated using a linear regression taken between
transmissivity and longitudinal conductance for the six
locations where both data were available (Figure 5). The
negative but strong statistical correlation between aquifer
transmissivity and longitudinal conductance (R2 = 0.82)
Figure 6 shows the transmissivity distribution over the
entire study area. It is clear that the highest transmissivity
values are mostly on the northwestern part of the area
and some parts in the southeastern part, identifying zones
of high water bearing potential. Although details about
he tectonic structure have not been defined in this study, t

A. U. UTOM ET AL. 997
(a) (b)
(c) (d)
(e) (f)
Figure 4. Resistivity soundings and inter pre t ation at the six sites. Locations are shown in Figure 3.
it could be hypothesized that the disturbed nature of the
fracture zones in the Enugu area ay be acting as boun-
daries between the same hydrolithological units and
define the place the where aquifer parameter varies.
5. Conclusion
A rapid, simple relatively inexpensive and liable method
of estimating the transmissivity distribution has been
demonstrated in the Enugu area. The results of the study
show useful estimation of the transmissivity and can be
recommended when siting exploratory boreholes or as an
initial input to a groundwater flow odel. Hydraulic con-
ctivity information known at one point can be used to
extrapolate the transmissivity over the area, which de-
nds on the aquifer thickness and hydraulic conducvity.
Using Equation (3), it was necessary to establish a
working relationship between transmissivity and the Dar
Zarrouk parameter (longitudinal onductance) from which
the value of β, was computed in the field for further
modeling of the transmissivity values from the VES
measurements. Effective application of this method like all

A. U. UTOM ET AL. 998
Figure 5. Longitudinal conductance and transmissivity at
six sites in parts of Enugu town (Nigeria).
Figure 6. Contour map of the study area with transmissivity
and physiography.
geophysical tool, however require a fair knowledge of the
study site’s geology and hydrogeogeology, which was
taken into account. This technique employing the rela-
tionship between transmissivity and Dar Zarrouk para-
meters is well-founded and has been successfully applied
by [5,6,29,44]. This technique could also assist in iden-
tifying parts of the aquifer with best potential yields and
produce realistic ground water models especially in the
Enugu area where small shallow aquifer are being in-
creasingly developed for domestic water supply.
6. Acknowledgements
This paper is based on fieldwork by Ahamefula Utom
carried out as part of the M.Sc. degree course in Applied
Geophysics at the Nnamdi Azikiwe University (NAU),
Nigeria. AAPG/Alexander & Geraldine Wanek Grants-
in-Aid and SEG Foundation Project of Merit Grant is
acknowledged for financial support. Two anonymous
reviewers and Prof. Boniface C. E. Egboka (NAU) are
thanked for their helpful and invaluable comments on
this manuscript.
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