Geostatistical Correlation of Aquifer Potentials in Abia State, South-Eastern Nigeria

doi:10.4236/ijg.2011.24057

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International Journal of Geosciences, 2011, 2, 541-548

doi:10.4236/ijg.2011.24057 Published Online November 2011 (http://www.SciRP.org/journal/ijg)

541

Geostatistical Correlation of Aquifer Potentials in

Abia State, South-Eastern Nigeria

Magnus Uzoma Igboekwe1*, Cyril Ngozi Nwankwo2

1Department of Physi cs, Michael Okpara University of Agriculture, Umudike, Nigeria

2Department of Physi cs, University of Port Harcourt, Port Harcourt, Nigeria

E-mail:{igboekwemu, cyrilnn}@yahoo.com

Received February 7, 2011; revised August 16, 2011; accept ed September 28, 2011

Abstract

In this paper, a collection of statistical correlation methods is used in the study of aquifer potentials in Abia

State of south-eastern Nigeria. The Physiology, geomorphology and hydrogeology of the area are first pre-

sented. Sixty-six Vertical Electrical Sounding (VES) data sets are used to determine the aquifer. Demo-

graphic studies are then carried out in 220 communities in order to determine the relationship between popu-

lation size on one hand and a unit draw-down of wells due to groundwater abstraction on the other. The rela-

tionship between geological Formation, aquifer potentials and depth of boreholes are then calculated using

Pearson’s correlation matrix. Results show that the mean population of persons appears to be higher in

Bende-Ameki Formation (of Eocene-Oligocene age) and the late Tetiary-Early Quaternary Coastal Plain

Sands, than in the Cretaceous shale Formation of Asata Nkporo. The mean population of persons sitting on

these Formations is 31,200, 18,370 and 5400 respectively. Furthermore, it is observed that a population in-

crease of about 50 persons in a community in Abia State is accompanied by a unit volume (1 m3) draw-down

of wells due to groundwater abstraction. It is therefore concluded that population size is positively correlated

with groundwater abstraction, aquifer potentials and geological Formation favouring aquifer in Abia State.

Keywords: Geostatistics, Pearson’s Correlation, Groundwater, Krigging, Aquifer, Bende-Ameki Formation,

Coastal Plain Sands.

1. Introduction

With the creation of Abia state in 1991 in south-eastern

part of Nigeria and the consequent increase in population

density in the cities [1], there arose a corresponding in-

crease in demand for potable water for the teaming popu-

lation. There has been scarcity of improved water schemes

before and even after the creation of the state. Many of

the boreholes drilled at different places in these cities

have become abortive or dried up because of heavy

draw-down by the teaming population.

The result of the draw-down or out right failure of the

wells as well as inadequacy of water supply from im-

proved schemes is the consumption of poor drinking

water by the people [2]. It therefore has become neces-

sary to study the geostastitical correlation of aquifer po-

tentials in the state in order to determine the relationship

between population size and a unit draw-down of water

boreholes due to groundwater abstraction. This paper is

therefore aimed at finding the correlationship in popula-

tion size, groundwater abstraction, aquifer potentials (or

geological Formation favouring aquifer) and depth of

boreholes.

Physiography, geomorphology, geology and hydro-

geology: Abia state is located between lat 4˚49.30'N -

6˚02'N and between long 7˚08'E - 8°04'E in the south-

eastern part of Nigeria (Figure 1). It has an area of about

5833.77 km2, which is roughly 9% of Nigeria’s land

mass. It is bounded in the north by Enugu state, in the

south by River state, in the east by Cross River and

Akwa Ibom states and in the west by Imo state.

Population: Using the 1991 census figures, Abia state

has a population of 2,293,978 inhabitants [3], residing in

both the rural and urban areas in the state. This is about

393 inhabitants per square km on the average, which is

about 3.5 times the mean population in Nigeria. While

some parts like Ngwa is below the average, Umuahia and

Aba are each above the mean population density with

about 2000 inhabitants per square km respectively.

Climate: Abia State enjoys an equatorial climate con-

M. U. IGBOEKWE ET AL.

542

Figure 1. Geographic location and geologic map of Abia State.

sisting mainly of two major seasons: Rainy season, (Mar-

ch-October) and Dry season (November-February) each

year. The north east trade wind from Sahara Desert and

the southerly humid marine air mass from the Atlantic

Ocean cause the seasonal variation in the climate of Abia

state. The number of sunshine hours in the state is 3600

hours per year.

Topography: South of Abia state is low lying. The

south-eastern part is about 122 m above sea level. The

average elevation in the entire state is about 152 m above

mean sea level.

Geology: There are two principal geological Forma-

tions in the state namely Bende-Ameki and the Coastal

Plain Sands otherwise known as Benin Formation. The

Bende-Ameki Formation of Eocene to Oligocene age

consists of medium–coarse-grained white sand stones,

(Figure 1). The late Tetiary-Early Quaternary Benin

Formation is the most predominant [4] and completely

overlies the Bende-Ameki Formation with a south west-

ward dip. The Formation is about 200m thick [5]. The

lithology is unconsolidated fine-medium-coarse-grained

cross bedded sands occasionally pebbly with localized

clay and shale [6].

Hydrogeology: The two principal geological Forma-

tions have a comparative groundwater regime. They both

have reliable groundwater that can sustain regional bore-

hole production. The Bende-Ameki Formation has less

groundwater when compared to the Benin Formation.

The numerous lenticular sand bodies within the Bende-

Ameki Formation are not extensive and constitute minor

aquifer with narrow zones of sub-artesian condition.

Specific capacities are in the range of 3 - 6 m3 per meter

per hour, [1,7]. On the other hand, the high permeability

of Benin Formation, the overlying lateritic earth, and the

weathered top of this Formation as well as the underlying

clay shale member of Bende-Ameki series provide the

hydrogeological condition favouring the aquifer forma-

tion in the area.

Drainage: Abia state is drained by five important riv-

ers namely: Imo, Esu, Akpoha, Igu and Aba River. The

drainage is however dominated by two main rivers: the

Imo River on the west and Cross-River on the east.

Rainfall: The rainfall duration in the state can be clas-

sified into the wet and the dry seasons. Abia state enjoys

a copious rainfall during rainy (monsoon) season. The

mean monthly rainfall during this season [4] is 335 mm

and falls to 65 mm during the dry season. The annual

rainfall is between 2000 mm and 2250 mm south of Abia

and between 1250 and 2000 mm north-east of Abia.

There are about 240 rain days towards the north of

M. U. IGBOEKWE ET AL.

543

Ovim-Abriba axis and about 255 rain days south of it.

2. Methods and Results

Geostatistics is a collection of statistical methods, which

are traditionally used in geo-sciences. These methods

describe special auto correlation among sample data.

They are recently adopted in ecology and appear to be

very useful in this new area. Geostastitical analysis ap-

plications provide sophisticated interpolation techniques,

which can search for and identify data anomalies, then

analyze the data for statistical trends. This analysis pro-

vides extreme flexibility. It allows the explorationist to

cross-validate the data quantitatively evaluating the ac-

curacy of geological model and predictions. Geostatisti-

cal and geospatial GIS processing in combination pro-

vide a very powerful exploration tool for identifying,

evaluating and preventing geospatial relationship that

could otherwise have gone unnoticed [8]. Using both

geospatial and geostastitical analysis, we can test whether

the distribution of water bore-holes show a close spatial

relationship to one, two, or all three sets of geologic and

demographic parameters that would be expected by

chance. If this correlation is statistically strong, we can

then use the model to make spatial predictions on the

aquifer potential of the study area.

The following steps are involved in geostatistical ana-

lysis: estimation of correlogram, estimation of parame-

ters of the correlogram model, estimation of the surface

(map) using point krigging and estimation of mean value

using block krigging.

The Pearson’s product-moment correlation coefficient

(



) expresses the degree of correlation between the

variables x and y with expected values Ux and Uy and

standard deviation



and



defined as





 

Cov ,

xy xy xy

yEXxYy



 



 (1)

where E is the expected value operator and Cov means

covariance. Since



xEx



,



222

xExE x



 (2)

and likewise for Y, we may also write

,22 22

() ()()

()() ()()

XY EXY EXEY

EXEXEYEY









(3)

The correlation is defined only if both the standard

deviations are finite and both of them are nonzero. It is

noteworthy here that it is a corollary of the Cauchy-

Schwarz inequality that the correlation cannot exceed 1

in absolute value. Also, correlation is 1 in the case of an

increasing linear relationship, –1 in the case of a de-

creasing linear relationship, and some value in between

in all other cases, indicating the degree of linear de-

pendence between the variables. The closer the coeffi-

cient is to –1 or 1, the stronger the correlation between

the variables. If variables are independent then the cor-

relation is 0 but the converse is not true because the cor-

relation coefficient detects only linear dependencies be-

tween two variables.

A correlation between two variables is diluted in the

presence of measurement error around estimates of one

or both variables in which case disattenuation provide a

more accurate coefficient.

If we have a series of n measurements of X and Y

written as x1 and y1 where 1, 2, ... n, then the Pearson

product-moment correlation coefficient can be used to

estimate the correlation of x and y. In this case Pearson

coefficient is also known as “sample correlation coeffi-

cient”. In such case, Pearson correlation coefficient is

written as:



 

xy xy

iii i

ii ii

xy nxy

rnss

nxyx y

nxx nyy















 

(4)







xy xy

xy y

rnss







(5)

where

and y are the sample means of X and Y.

and

S are the sample standard deviation of X and Y

and the sum is from i = 1 to n of population correlation.

We may rewrite the equation thus.



 

xy xy

iii i

ii ii

xy nxy

rnss

nxyx y

nxx nyy















 

(6)

Here the absolute value of the sample correlation must

be less than or equal to 1.

The square of the sample correlation coefficient,

which is also known as the coefficient of determination,

is the fraction of the variance in yi that is accounted for

by a linear fit of xi to yi This is written

 (7)

where 2

Sy is the square of the error of a linear re-

gression of xi on yi by the equation y = a + bx:



xyi i

Syabx

n



 (8)

M. U. IGBOEKWE ET AL.

544

and 2

S is just the variance of y:



Syy

n



 (9)

Since the sample correlation coefficient is symmetric

in xi and yi, Gayen, [9] was able to get the same value for

a fit of yi to xi:

 (10)

This equation also gives an intuitive idea of the corre-

lation coefficient for higher dimensions. Just as the

above sample correlation coefficient is the fraction of

variance accounted for by the fit of a 1-dimensional lin-

ear sub manifold to a set of 2-dimensional vectors (xi, yi),

so we can define a correlation coefficient for a fit of an

m-dimensional linear manifold to a set of n-dimensional

vectors. For example, if we fit a plane z = a + bx + cy to

a set of data (xi, yi, zi) then the correlation coefficient of z

to x and y is

Sxy

 (11)

This form expresses the method of simple linear re-

gression. In this method, X is the vector of independent

variables xi and Y of the dependent variables, yi and a

simple linear relationship between X and Y is sought

through a least squares method on the estimate of y:







(12)

Then, the equation of the least-squares line can be de-

rived to be of the form



iii i

nxyx y

YYX X

nx x



 





 (13)

This equation can be rearranged in the form.

 

YYX X

 (14)

where r has the familiar form mentioned in Equation (4)

above.

The Correlation matrix of n random variables X1, …,

Xn is the n × n matrix whose i, j entry is Corr(Xi, Xj ). If

the measures of correlation used are product-moment

coefficients, the correlation matrix is the same as the

covariance matrix of the standardized random variables

Xi/SD(Xi) for i = 1, …, n. Consequently, it is necessarily

a positive-semidefinite matrix. The correlation matrix is

symmetric because the correlation between Xi and Xj is

the same as the correlation between Xi and Xj.

An example of a correlation matrix is of the form:

1231

123

245

3246

4356

YYYY

Yxxx

Yx xx

Yxx x

Yxxx

(15)

3. Data Acquisition

Sixty-six (66) VES sounding data sets were collected

throughout Abia state using the ABEM SAS 4000 Ter-

rameter and analyzed using the Resist software [10].

Figure 2 shows a sample geoelectrical section along AA/

for the results of seven geoelectric soundings namely:

VES # 8, 7, 9, 1, 10, 4, 5 conducted in the southern part

of Umuahia of Abia state (a sedimentary area with the

prolific Coastal Plain Sands—geologic Formation—fa-

vouring good aquifer). It begins from Umuobia Olokoro

(point A) and ends at Amizi Oloko (point A′). This sec-

tion shows the presence of four (sometimes interrupted)

geoelectric layers namely the top soil, underlain by

brown-reddish laterite. Other layers lying immediately

below the laterite are the fine-medium-coarse-grained

sands (the aquiferous zone) and lastly the conductive

(clay) layer. The litholog of a borehole at Michael Ok-

para University of Agriculture, Umudike (Figure 4)

shows these lithologic units much more distinctly.

A typical sounding curve obtained at Abia state Uni-

versity Uturu (ABSU) is also shown in Figure 3. It is

from such curves as this and the corresponding layer

parameters that the geoelectrical sections are developed.

Sequel to the above resistivity survey, demographic

studies on two hundred and twenty (220) towns and vil-

lages in Abia state were then carried out. The communi-

ties were grouped into eight study zones and data were

collected under the following headings: population, ex-

isting water schemes, possible depth of bore-hole, geo-

logical formation and aquifer potentials. The Vertical

Electrical Sounding (VES) points were used to determine

the aquifer while demographic figures were used to de-

termine the statistical parameters. Of the 220 communi-

ties surveyed, 162 of them enjoy good aquifer potential

i.e. almost three quarters (74%) have substantial aquifers.

Similarly 158 i.e. 72% of the communities sit on Coastal

Plain Sands (or Benin Formation). The findings are

summarized in Table 1.

4. Discussion of Results

The distribution of mean population by some background

characteristics is shown on Table 1. As the Table shows,

M. U. IGBOEKWE ET AL.

545

Figure 2. Geoelectrical section along section AA (showing good aquifer formation).

Figure 3. Computer modeled curve of VES B5.

the mean population is higher in places with good and

moderate (or fair) aquifer potentials i.e. the places with

difficult potentials appear to be less conducive for habi-

tation.

On geological formation, the mean population appears

to be highest for Bende-Ameki with about 31,200 per-

sons, followed by the Coastal Plain Sands. Asata Nkporo

on the other hand has the lowest mean population of

about 5400 persons. Ordinarily, population is usually

linked with surface water. However, population is linked

with aquifer in this case to show that there are many

streams which feed the aquifer in the areas with high

M. U. IGBOEKWE ET AL.

546

Figure 4. Litholog of a borehole at M.O. University, Umudike.

mean population.

The correlation matrix showing the relationship among

the population, aquifer potential, geological Formation

and depth is shown in Table 2.

From the table, it is obvious that geological formation

is positively correlated with the depth of a well and aq-

uifer potential. On the other hand, population appears to

be negatively correlated with depth.

To test the significance of the relationship between

population on one hand and depth, geological formation

and aquifer potential on the other, a multiple regression

analysis was conducted.

M. U. IGBOEKWE ET AL.

547

Table 1. Mean population by some background char ac ter i stics.

NO. OF COMMUNITIES MEAN POPULATION % POPULATION % COMMUNITIES

AQUIFER POTENTIAL

GOOD 162 18,552 81 73.6

FAIR 1 13,000 1 0.4

MODERATE 8 28,875 6 4

DIFFICULT 49 9143 12 22

GEOLOGICAL FORMATION

COASTAL PLAIN SANDS 158 18,370 79 72

LOWER COAL MEASURES 34 9765 9 15

UPPER COAL MEASURES 9 10,111 2 4

ASATA MKPORO 5 5400 0.7 2.3

BENDE-AMAEKI 10 31,200 8.4 5

IMO SHALE 1 8000 0.2 0.4

AGWU NDIABOR 2 7500 0.4 0.9

AJALI 1 10,000 0.3 0.4

POSSIBLE DEPTH (M)

60 93 20,194 53 42

65 - 130 27 11,296 8.6 12

140 17 18,588 9.0 8

150 36 17,139 17.4 16

160 - 230 23 9229 6.0 11

240 13 8115 3.0 6

250 - 260 11 9818 3.0 5

Table 2. Correlation matrix of population and some back-

ground characteristics.

Population Depth Geo. Form Aquifer Pot.

Population 1 –0.217 –0.043 –0.116

Depth –0.217 1 0.510 0.588

Geo. Form –0.043 0.510 1 0.757

Aquifer Pot. –0.116 0.588 0.757 1

Results of the analysis show that population is signifi-

cantly related only to the depth of a well. This is the

general trend shown by the Equations (1)-(15). Hence the

regression equation is given by

Yi = 22561 – 49.8Xi (16)

where Yi = Population and Xi = Depth.

This indicates that on the average, an increase of about

50 persons in the population of a community in Abia

State is accompanied by a decrease of about one metre

depth of water in a well.

It should be noted that for wells of uniform diameter,

the depth is directly proportional to the volume of

groundwater contained. Therefore, a population increase

of about 50 persons in a community in Abia State is ac-

companied by a unit volume (1 m3) draw-down of wells

due to groundwater abstraction.

Generally, the aquifer in Abia state is the prolific

Coastal Plain Sands and depth to boreholes range from

60 m to 100 m in Aba, Obingwa and Ukwa Local Gov-

ernment Areas and from 140 to 250 m around Umuahia,

Isialangwa and Ikwauno Local Government Areas.

5. Conclusions

The relationships between geological Formation, aquifer

potentials and depth to water boreholes have been calcu-

lated in this work using Pearson’s correlation matrix.

Results from resistivity soundings show that most parts

of Abia state are blessed with good aquifer potentials.

Demographic studies conducted here also show that the

mean population appears to be higher in places with

good and moderate aquifer potentials than in those with

difficult ones. That is to say, the mean population ap-

pears to be higher in Bende-Ameki Formation of Eocene

to Oligocene age and the late Tetiary-Early Quaternary

Benin Formation, than in the Cretaceous shale Formation

of Asata Nkporo. The mean population of persons sitting

on these Formations is 31,200, 18,370 and 5400 respec-

tively. It is further observed that a population increase of

about 50 persons in a community in Abia State is ac-

companied by a unit volume (1 m3) draw-down of wells

due to groundwater abstraction. It is therefore concluded

M. U. IGBOEKWE ET AL.

548

that population size is positively correlated with ground-

water abstraction, aquifer potentials and geological For-

mation favouring aquifer in Abia State.

6. References

[1] M. U. Igboekwe, “Geoelectrical Exploration for Ground-

water Potentials in Abia State, Nigeria,” Ph.D. Dissertion,

Michael Okpara University of Agiruclture, Umudike,

2005, p. 131.

[2] M. U. Igboekwe, V. V. S Gurunadha Rao, and E. E. Ok-

wueze, “Groundwater Flow Modeling of Kwa Ibo River

Watershed, South-Eastern Nigeria,” Hydrological Proc-

esses, Vol. 22, No. 10, 2008, pp. 1523-1531.

doi:10.1002/hyp.6530

[3] NPC (National Population Commission of Nigeria,) “Na-

tional Population Commission Census Figures for Abia

State, Nigeria,” Abuja, 1991.

[4] P. D. C. Mbonu, J. O. Ebeniro, C. O. Ofoegbu and A. S.

Ekine, “Geoelectric Sounding for the Determination of

Aquifer Characteristics in Parts of the Umuahia Area of

Nigeria,” Geophysics, Vol. 56 , No. 2, 1991, pp. 284-291.

doi:10.1190/1.1443042

[5] Ebilah-Salmon and Partners in Association with Esokay

Ltd., Abia State Rural Water Supply Project, Feasibility

Report and Preliminary Engineering Design Report, 1993,

p. 183.

[6] M. U. Igboekwe, E. E. Okwueze and C. S. Okereke, “De-

lineation of Potential Aquifer Zones from Geoelectric

Soundings in Kwa Ibo River Watershed, South-Eastern,

Nigeria,” Journal of Engineering and Applied Sciences,

Vol. 1, No. 4, 2006, pp. 410-421.

[7] Ebilah-Salmon and Partners. “Investigation of the Exist-

ing Water Supply Facilities within the University Com-

plex. Geophysical Report and Recommendations for Re-

activation and Future Exploitation for Potable Water

Supply, Federal University of Agriculture, Umudike,

1994, p. 25.

[8] J. L. Rogers and W. A. Nicewander, “Thirteen Ways to

Look at the Correlation Coefficient,” The American Stat-

istician, Vol. 42, 1988, pp. 59-66. doi:10.2307/2685263

[9] A. K. Gayen, “The Frequency Distribution of the Prod-

uct- Moment Correlation Coefficient in Random Samples

of Any Size Drawn from Non-Normal Universes,” Bio-

metrica, Vol. 38, No. 1-2, 1951, pp. 219-247.

[10] D. L. B. Jupp and K. Vozoff, “Stable Interative Methods

for Inversion of Geophysical Data,” Geophysical Journal

of the Royal Astronomical Society, Vol. 24, No. 3, pp.

957-976.