AQUIFER CHARACTERIZATION RESULTING FROM GEOELECTRICAL MEASUREMENTS
IN ABRAKA, DELTA STATE, NIGERIA
BY
J. C. EGBAI
DEPARTMENT OF PHYSICS
DELTA STATE UNIVERSITY, ABRAKA, NIGERIA
Phone Number:+2348033822332
e-mail: jamesegbai@yahoo.com
ABSTRACT
Little was known about the subsurface geology of Abraka until 94 vertical electrical sounding using
Schlumberger array were made. These soundings provide information on the distribution of aquifers,
aquitards and the salinity of the groundwater. Several geophysical exploration techniques were applied to
determine the size of the lower and lateral boundaries of the aquifer system of Abraka. Seismic refraction
profiles were shot to determine precisely the geometry of the overburden sedimentary rocks. The maximum
electrode spacing (AB/2) was between 300 and 500m. The data obtained from VES were analysed by
partial curve matching and smoothening. The smoothed data were plugged into a computer for iteration,
where model parameters were obtained which gives the result of the resistivity, thickness, depth and
percentage error. To check the results of the geophysical and geohydrologic investigations, exploratory
drilling was conducted. The results reveal that the aquifer of the three campuses lies between 10m to 30m.
Keywords: Geoelectric section, equivalence, transmissivity, aquifer, vertical electrical sounding (VES).
INTRODUCTION
Abraka, a town in Delta State of Nigeria is located within the rainforest region. The water table of
this area is fairly low as evident by the difficulty in locating water in hand dug wells. It lies between
latitude 05o 46' and 05o 48' North of the equator and longitude 06o 05' and 06o 08' East. It is bounded on
the west by River Ethiope to the north by Obiaruku, on the east by Abbi and south by Abraka Inland. The
population of the area has increased tremendously because of the University. It has a total population of
about 250,000. The total land area is about 168.4km2 for Abraka and its environs. However, Abraka urban
where three campuses are located is about 37.32km2.
Abraka is in the Niger Delta region with a relatively flat terrain made up of low and average land
rising on the average of 26.48m elevation (Lagos datum) on the land and about 19.0m towards River
Ethiope. It experiences the equatorial hot and wet climate with almost uniform temperature throughout the
year. The relative humidity is consistently high, about 85% and annual rainfall which ranges from 25.4mm
to 457.2mm (Enger and Smith, 2004).
There exist spatial distribution of temperature in Abraka and its environ. The spatial distribution of
temperature showed that Abraka urban had 30o C while the rest areas had 28o C (Efe and Aruegodore,
2003). The reason for this difference is not unconnected with the rapid population increase of unplanned
1
buildings built close together, increased fumes from generators, motorbikes, vehicles and residential houses
where a lot of firewood are used for cooking.Abraka communities obtain water from the Ethiope River
about 500m to 2km from the town depending on the location. They practice subsistent farming.
The area under study is a hot/wet equatorial climate region that is characterized by two main
seasons, the wet season and dry season. The wet season begins from April and ends in September. During
this period, there is usually much rainfall and as a result there is an increase in the water table. The study
area has a direct recharge from rainfall. The rate of infiltration and percolation is also high and high stream
flow. The study area also acquires water directly from the spring where the river emerges from because of
much recharge and high recharge rate (Ako and Olorunfemi, 1989).
Slitcher (1933) demonstrated that if the conductivity within the earth is a function of depth only,
then measurement of the potential distribution on the surface of the earth will define the subsurface
distribution uniquely.
In theory, therefore, a resistivity sounding should uniquely define the conductivity depth function.
In practice, this is not the case. The earth’s conductivity usually varies in all three spatial directions and
even if it varied with depth only, the field data will never be perfect because of near-surface inhomogeneity
and instructional imprecision. The accuracy of field measurements is, in general 2 – 5%. It happens
therefore, that a number of earth models may give rise to soundings which are practically coincident; they
agree within experimental error and are said to be electrically equivalent.
Suppression on the other hand, is a consequence of the inability of a surface method, such as the
resistivity method, to resolve subsurface detail (Evjen, 1938). Many geoelectrical rock units, either because
of their thickness or poor contrast with surrounding formations, will not be resolved by the resistivity
method. Their existence will not be manifested on sounding curves and they will be ignored during
interpretation.
In anticipating whether a given layer will be resolved or suppressed on a field sounding the concept
of relative thickness is very useful (Flathe, 1955a). This is defined as the ratio of layer thickness to depth of
cover. Any layer less than 0.1 will not be resolved, regardless of resistivity contrasts, and the resolution of
layers with values between 0.1 and 1.0 depends entirely on resistivity contrasts. If a 2m layer can be
resolved at a depth of 10m, then a similar layer would need to be 20m thick in order to be detected at 100m
depth.
In a layered earth defined by thickness hi i  1 ,2 ,3    n  1 and resistivities
 i i  1,2    n , equivalence occurs in layers having a small relative thickness. The thickness of such a
layer is sufficient to escape suppression but insufficient for unique resolution. Instead, the resistivity
method is able to resolve the thickness-resistivity product of a thin resistive layer.
The first type, t-equivalence, holds in layer if  i   i  1 ; it holds for both K-type and Q-type
sequences defined by
K :  i 1   i   i 1
Q :  i 1   i   i  1
The second type, S-equivalence, holds in layer i if  i   i  1 ; it holds for both H- and A-type
sequences defined by
2
H :  i 1   i   i  1
A :  i 1   i   i 1
Koefoed (1969) recognized two problems in multilayer sections where two or more layers exist
beneath an equivalent layer.
(i)
It is not known how the lower layers affect equivalence.
(ii)
It is not known how the interpretation of lower layers is affected by variations in the thickness
and resistivity of the equivalent layer.
Zohdy (1970c) emphasized that if a layer is adjusted for equivalence, the change in thickness
distributed between the upper and lower boundaries of the layer should be considered. It is usually assumed
that the upper boundary is unaffected. He noted that equivalence is not a property of the resolving power of
an electrode array but also depends on the domain of comparison; for example, two models which give
coincident kernel curves may not give coincident apparent resistivity curves because of poorer resolution in
the kernel domain. These problems are difficult to solve without the use of computers. By means of a
program, it is possible to evaluate equivalence for any given sounding curve regardless of the thickness,
resistivity or number of layers in the section. The procedure automatically adjusts each boundary to give
the best least-squares fit to the sounding curve.
Equivalence is probably the most severe limitation of the resistivity method. In estimating the depth
to the base of the equivalent layer, gross errors can be expected in the absence of geologic or other control
measures. All other boundaries are, however, only slightly affected by the presence of an equivalent layer
within the section.
The quantitative interpretation of vertical electrical sounding curves is hampered by the well known
principle of equivalence which means that many different layered models may produce practically the same
resistive curve. To select the model that best represents the true conditions of the subsurface additional
hydrogeologic information is needed.
To check the results of the geophysical and geohydrologic investigations, exploratory drilling was
conducted. Three boreholes drilled within the area of exploration were used to correlate the result of
vertical electrical survey.
Further work on resistivity sounding could be seen from the work of Okwueze (1996), Chukwurah
(1998), Egbai and Asokhia (1998), Emenike (2000) and Oyedele (2001)
THEORY
Power
I
V
C1
C2
P1
0
P2
r1
r2
r3
3
r4
Fig. 1: Schlumberger Electrode Configuration
C 1C 2 are the current electrodes
P1 P2 are the potential electrodes
r1 , r2 , r3 and r4 are the distance between the electrodes.
Difference in potential between P1 and P2 is
V 
I
2
 1 1   1 1  
       
 r1 r2   r3 r4  
(1)
where   resistivity of the layer.
If there exist distortion of potential at a plane interface between two media there will also be distortion in
current passing from one medium of one resistivity into another, the equipotential also will be distorted
(Telford, et al, 1990). The potential field could be determined by solving Laplacian’s equation for the
appropriate bounding conditions or by direct integration. Employing electrical images, the potential
problem could be solved since current density, like light ray intensity decreases with the inverse square of
distance from the point source.
If  1 is resistivity in a medium separated by adjacent medium  2 by a plane boundary and k and
1  k are respectively reflection and transmission coefficients then the potential P in the first medium is
I1  1 k 
  
4  r1 r2 
V
and the second media P 1 is
V1 
I 2
4
 1 k 


 r3 
Applying the boundary conditions, V  V 1 at the interface when r1  r2  r3
Thus
  1
1 1  k
or k  2

2 1  k
 2  1
(2)
where k  1
The potential due to the third image P' ' ' , 4Z below ground, will be further reduced, as will that of
its image 4 Z above the ground.
I 1  kxk kxkxk  I 1  2 k 2 




V

2  r2
r2  2  r2 
The resultant total potential at P can be expressed as an infinite series of the form
 1 2k 2k 2

2k m







   

r2
rm
 r r1

m  integer
V
I 1
2
(3)
4
where
r1 
r
rm 
r
2
2

r
 2Z  , r2 
2
 2mZ 
2
2

 4Z  ,
2

The series can be written in compact form
I
V  1
2
I
 1
2r


1
  2

m1
r
km
2
r 2  2 mZ 









2V
1
 2V

I  1 1   1 1    I
       
 r1 r2   r3 r4  

(4)



km
1  2 
2 
1  2 mZ r  
m 1

Rearranging equations 1 and 4, we obtain

P

(5)
where P has to do with the electrode geometry.
By measuring V and I and knowing the electrode configuration, the resistivity  is obtained. The
resistivity is constant for homogeneous and isotropic medium. In inhomogeneous medium, different
measurements give rise to different resistivity. The measured quantity is known as apparent resistivity,  a .
Equation (4) relates the potential of a single electrode for the resistivity of the upper layer in terms
of the electrode spacing, the depth to the interface and the resistivity contrast between the two beds. If this
expression is put in the apparent resistivity form which would be measured by four electrode system and
using equations 1, 2, 3, 4 and 5, the potential of P1 with respect to the current electrodes C1 and C 2
becomes
V1 

1
I1 

2


2 
m 1
 r1

km


r22  4m 2 Z 2 


km
 
1


2
r12  4m 2 Z 2   r2 
m 1
while for P2 we have
V2 
I 1
2


1
  2 
m 1
 
 r3
km
r32  4 m 2 Z 2




 
1


2
 


m 1
 
 r4
km
r42  4 m 2 Z 2






 
Thus, the measured potential difference between P1 and P2 will be
V  V1  V2

I 1
2

 1 1   1 1 

        2  k m 

m 1
 r1 r2   r3 r4 


1

r  4m 2 Z 2

2
2

(6)
 

 
In the case of Schlumberger spread, r1  r4  L  l , r2  r3  L  l . The potential then becomes
1

2
r3  4 m 2 Z 2

1

r  4m 2 Z 2
2
1

1
2
r4  4 m 2 Z 2


5


 2  2   4  k m
 L  l L  l 
m 1


1


1
2
2 2 
L  l  1  2 mZ  L  l 

I
V  1
2

1
L  l 1  2 mZ 2 L  l 2  2
1


I 1 2 l   L  l  
km
km
 Ll 


1



 L2  l 2   l  m 1 1  2 mZ 2  L  l 2 1 2  l  m 1 1  2 mZ 2  L  l 2 1 2 


If L  l , the terms within the square brackets can be simplified by using the relation



1
L  l 
 2 mZ 
2
2

1

 L  l 
1
 2 mZ 
2
2
2

1

2

2l

L2 1  2 mZ L
2

3

2
Then the potential becomes
 I 2 l

I 1 2 l 
  1 2 1  2 D31
1

2

3
2
L2 
L
2 
m  1 1  2 mZ L 


The exact expression of apparent resistivity is
V 




km
 L l  

 l  m 1 1  2 mZ 2  L  l 2
 a   1 1  



  1 1  Ds 

1
2

 Ll  


 l  m 1 1  2 mZ 2  L  l 2



1
(7)
2


Approximately, we have


km

 a  1 1  2
2
m 1

1  2mZ L 



  1 1  2 Ds1 
3
2 

(8)

where
km
 L l  
Ds  

 l  m 1 1  2 mZ 2  L  l 2


Ds1  
m 1
km
1  2mZ
L
2

3

1
2
km
 Ll  


 l  m1 1  2 mZ 2  L  l 2


1
2
2
This result can be obtained by integrating equation (4) with respect to r , multiplying result by 2
(two current electrodes) and applying equation (5) to get  a
METHODOLOGY
The resistivity measurements are normally made by injecting current into the ground through two
current electrodes ( C1 and C 2 as shown in figure 1), and measuring the resulting voltage difference at two
potential electrodes ( P1 and P2 ). From the current (I) and ( V ) values, an apparent resistivity  a  value is
calculated. In this method, the centre point of the electrode array remains fixed, but the spacing between
the electrodes is increased to obtain more information about the deeper sections of the subsurface.
6
Other geophysical exploration techniques were adopted to determine the size and boundaries of the
aquifer system at Abraka. Two seismic refraction methods were shot to determine the boundaries of aquifer
at Abraka. The main exploration method adopted was the vertical electrical sounding (VES). This was used
to distinguish between sandy, loamy and clayey layers which enables the delination of fresh and saline
water-bearing zones. 94 VES using Schlumberger configuration were used. The maximum electrode
spacing AB/2 was between 300 and 500m. The geophysical instrument used was the Abem Terrameter
SAS 1000B with inbuilt booster for more injection of current into the subsurface. The three University
Campuses were used for the survey. Campus 2 is very close to River Ethiope, Campus 1 is about 1km from
the river while Campus 3 is about 2km from River Ethiope.
RESULT AND DISCUSSION
The determination of the nature of the hydrogeology of Abraka and its environs as regards the
aquifer and its boundaries, a look at the shapes of the field curves and apparent resistivity ranges were
carried out. The curves are classified into five groups (A through E). Each group represents specific
geologic or hydrogeologic conditions.
Locations 1 and 2 are for Campus 2, with location 3 for Campus 1 while locations 4 and 5 are for
Campus 3 with their various curves as shown in figure 2 – 6.
Table 1: Summary of results of model paramenters obtained from computer iteration
VES
No. of
Layers
A
(Campus2)
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
1
2
3
4
5
B
(Campus2)
C
(Campus1)
D
(Campus3)
E (Campus3)
Resistivity of
various
Layers (Ωm)
712.10
1893.00
151.50
1166.30
597.40
1121.80
6357.8
138.90
10375.4
282.70
367.20
4055.60
1523.40
8009.60
250.70
405.70
1516.70
2066.6
1613.5
1768.2
2264.0
27226.8
4008.0
755.7
Thickness
(m)
Depth
(m)
1.1
2.8
3.0
28.5
1.1
3.9
6.9
35.4
1.2
2.4
1.8
64.4
1.2
3.5
5.4
69.8
0.9
2.2
7.1
33.3
0.9
3.0
10.1
43.4
1.1
1.0
7.6
1.1
2.1
9.7
1.0
2.3
2.6
49.1
1.0
3.3
5.8
55.0
7
RMS %
Error
3.6
7.4
4.3
5.9
2.6
Lithology
Fine grain sand
White pebbles
Fine sand
Medium grain sand
Clayey sand
Fine grain sand
White pebble
Fine sand
Medium grain sand
Clayey sand
Clayey sand
Medium grain sand
Fine sand
Medium grain sand
Clayey sand
Clayey sand
Medium grain sand
Fine sand
Clayey sand
Clayey sand
Medium grain sand
Clayey sand
Fine sand
Curves
KHK
KHK
KK
AQ
AQ
A close look at the various curves show that Campus 2 of locations A and B are mainly of KHK
curves with low resistivity at the surface. The second layer has a very high resistivity followed by a low
resistivity. The aquifer is located within the third layer. At low depth, the resistivities are relatively high.
In Campus 1, the shape is similar to that of Campus 3, where all resistivities are low at the first
layer followed by a second layer of very high resistivities. In Campus 1, the aquifer is located at the third
layer while in Campus 3, the actual aquifer is found in the fourth layer. Comparing these curves with those
of Campus 2 leads to the conclusion that the curve of Campus 1 represents a zone of transition.
The groundwater is generally found at depths between 10 and 30m, the high resistivities of the top
layers will correspond to the unsaturated zone. The intermediate values will then represent the aquifer with
high fresh water. In campus 3, the aquifer is lower and is found in the fourth layer.
Fig. 2:
8
Fig. 3:
Fig. 4:
9
Fig. 5:
Fig. 6:
EQUIVALENCE
The quantitative interpretation of VES curves is hampered by the well known principles of
equivalence, which means that many different layered models may produce practically the same resistivity
curve (Overmeeren, 1989).
Two examples of equivalence from Abraka are shown in curves C and D. The values from the
model parameters show that both curves have lower resistivities for the first layer followed by very high
resistivities at the second and third layers. They are characterized by clayey sand, medium grain sand and
fine sand with very little difference in their respective resistivities and thickness.
10
Another example of equivalence is also shown in curves D and E. The curves are of the same shape.
The two areas have the same lithology from borehole data.
The result has shown that the low resistivity value of Campus 2 reveals that there are traces of
saline water close to the river. Figure 7 shows the geoelectric section from borehole data
The results of the drilling show that some layers were so small that they could not be resolved on
the resistivity curves at deeper layers of 30m and below on the subsurface.
The result of the seismic refraction method at Abraka shows that Abraka area has velocity ranging
between 300m/s – 460m/s for the first layer and 400m/s – 510m/s for the second layer. The velocities
which are directly related to the soil and rock type is the range of dry silt, sand, loose gravel, loamy, loose
rock and moist fine-grained topsoil. From the geology of the area, it can be deduced that the first layer is
fine-grained topsoil. Since the other layers are close to the aquifer, it can be medium grained sand or fine
sand.
GEOPHYSICAL WELL LOGGING
The results of vertical electrical sounding and seismic refraction survey were compared by carrying
out exploratory drilling in the three campuses. The three boreholes were drilled within the areas of VES
and seismic refraction survey. Borehole 1 drilled in Campus 1, a site of geoelectric boundary, was drilled to
ascertain the abruptness of the transition. It also confirmed the presence of saline water in Campus 2.
The borehole data results show that the three campuses are characterized by fine grain sand, clay,
medium grain sand and pebbles.
Table 2: Summary of aquifer electrical properties of all VES.
VES
No.
Resistivity
 a (Ωm)
Thickness
(m)
1
151.5
3
2
138.9
1.8
3
1523.40
7.1
4
1516.7
1.0
5
2264.0
2.3
Conductivity
(Ωm)-1 (σ)
3
6.60 X 10
7.2 X 10 3
6.56 X 10 3
6.59 X 104
4.42 X 104
Longitudinal
Conductance
(S)
Transmissivity
Tr 
ks

2
0.0198
(m /day)
30
0.01296
18
4.6576 X 10 3
6.59 X 10 3
1.0166 X 10 3
71
10
23
The result reveals that Campus 1 (Loc. C) has the highest aquifer transmissivity of 71m 2/day while
location D (Campus 3) has the lowest aquifer transmissivity of 10m2/day. Hence location C has been
characterized, having good groundwater potential and as such any good water project in the University
should be concentrated in Campus 1.
CONCLUSION
Vertical electrical soundings, so far, has been regarded as the best geophysical exploration
techniques to obtain qualitative and quantitative information on groundwater salinity and delineate between
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vertical distribution of permeable sandy layers and permeable clayey horizons. The VES survey enables us
to demarcate aquifer system, its boundaries and transition zone as well as equivalence that existed in
certain locations. The problem of equivalence is very paramount in geophysical exploration by VES
method but however, borehole drilling and logging have proved to be the best methods for ascertaining the
correctness of geophysical data and interpretation of VES. Location 3 (Campus 1) has the highest aquifer
thickness and transmissivity and has been demarcated as having good groundwater potential and as such
any groundwater project by the University should be sited in Campus 1.
ACKNOWLEDGEMENT
I wish to express my profound gratitude to all my final year Physics undergraduate students
(2007/2008 session) for their cooperation during the field work where the data was collected for the
research. My wife is highly acknowledged for her encouragement.
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