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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) Copyright © 2011 SciRes. 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. Copyright © 2011 SciRes. IJG 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. Copyright © 2011 SciRes. IJG 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 ( x y ) expresses the degree of correlation between the variables x and y with expected values Ux and Uy and standard deviation x and x defined as Cov , xy xy xy x 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: 22 22 1 ii xy xy iii i ii ii xy nxy rnss nxyx y nxx nyy (4) 1 ii xy xy x xy y rnss (5) where x and y are the sample means of X and Y. x S and y 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. 22 22 1 ii 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 2 2 2 1x xy y Sy rS (7) where 2 x Sy is the square of the error of a linear re- gression of xi on yi by the equation y = a + bx: 2 2 1 1 1 n xyi i i Syabx n (8) M. U. IGBOEKWE ET AL. Copyright © 2011 SciRes. IJG 544 and 2 x S is just the variance of y: 2 2 1 1 1 n yi i 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: 2 2 2 1 x y xy y S rS (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 2 2 2 1z z Sxy rS (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: YX (12) Then, the equation of the least-squares line can be de- rived to be of the form 2 2 iii i ii nxyx y YYX X nx x (13) This equation can be rearranged in the form. y x rs YYX X s (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 1 1 1 1 i i 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 The distribution of mean population by some background characteristics is shown on Table 1. As the Table shows, M. U. IGBOEKWE ET AL. Copyright © 2011 SciRes. IJG 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. Copyright © 2011 SciRes. IJG 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. Copyright © 2011 SciRes. IJG 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. Copyright © 2011 SciRes. IJG 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. |