https://orcid.org/0000-0003-3739-1757
ABSTRACT
The aim of this research was the application of geo-electrical technology in the determination of specific retention, specific yield, and storage-dependent drainability efficiency within a major coastal milieu in Nigeria. This improves on past work where expensive and time-intensive pumping tests were employed to determine specific retention and specific yield. In addition to the determination of these key aquifer geo-kinetic properties, other important aquifer characteristics such as aquifer potentiality, protectivity, and vulnerability to contamination within this major coastal system were determined. Geo-electrical technology employed Wenner and Schlumberger arrays to undertake Vertical Electrical Soundings (VES) and Electrical Resistivity Tomography (ERT) surveys and results obtained were constrained by ground truth from lithological logs. Results from the electrical resistivity surveys indicated that the lithological strata comprised motley topsoil, coarse sand, fine sand, and sandy clay. Measures of specific yield and specific retention were generated as secondary geo-electrical indices. Specific yield intersected with specific retention at 73% storage-dependent drainability efficiency (SDE), indicating that this percentage must be exceeded for optimal groundwater extraction from the rock matrix's pore spaces during pumping. Aquifer transmissivity measures indicated high aquifer potentiality; longitudinal conductance measures indicated poor aquifer protectivity implying increased vulnerability of the aquifer to contamination.
HIGHLIGHTS
Geo-electrical technology was employed to determine specific retention, specific yield, & storage-dependent drainability efficiency (SDE).
Specific yield intersected specific retention at 73% SDE.
Locations with SDE < 73% indicated non-optimal groundwater abstraction zones.
Optimal groundwater abstraction pore-space ratio was delineated.
Geo-electrical indices indicated high aquifer potentiality and vulnerability.
INTRODUCTION
Specific yield 
of an aquifer, otherwise termed gravity water porosity or effective porosity 
, (Liang et al. 2003) measures the volume of water released from a saturated rock (Freeze & Cherry 1979; Fetter 1994; Schwartz & Zhang 2003; Dietrich et al. 2018). Specific yield delineates the measure of water yielded when the porous medium is drained and represents the total amount of water available for abstraction (Lv et al. 2021). Specific yield is typically used in consonance with the specific retention 
to characterize the total porosity of a rock matrix (Reddy 2010). Total porosity therefore encompasses specific yield and specific retention. Given an unconfined aquifer, the specific retention 
is the fraction of water volume retained within a rock matrix to the total volume of the rock matrix (Bell 2004). Specific retention measures the amount of fluid retained within the groundwater reservoir due to adhesion and capillary forces (Healy & Cook 2002). Soil water retention curves, which indicate the empirical relationships between soil water and capillarity, are impacted by climatic conditions, soil water flow velocity, and porosity. Influences on specific yield and specific retention include regional geology, surface tension, fluid frictional forces, demand by plants for water, and depth to groundwater (Moench 1994; Logsdon et al. 2010; Machiwal & Jha 2015; Lv et al. 2021), which in turn impacts the storage-dependent drainability efficiency (SDE) of the aquifer.
To evaluate the specific yield and retention, several methodologies have been applied in past studies. These methodologies include pumping techniques, groundwater recharge techniques, rock matrix saturation techniques, laboratory drainage techniques, aquifer drainage techniques, slug testing techniques, rainwater-table response techniques, gravity surveys, water table fluctuation techniques, etc. (Neuman 1987; Todd & Mays 2004; Crosbie et al. 2005; Gehman et al. 2009; Yin et al. 2011; Fan et al. 2014; Lv et al. 2021). The process of acquiring specific yield and specific retention data using the above-mentioned techniques is typically multi-faceted, labor-intensive, expensive, time-consuming and complex, requiring series of expensive borehole and coring data (Healy & Cook 2002; George et al. 2011; Obianwu et al. 2011; Wang et al. 2014). Electrical resistivity technology, on the other hand, has been found to be an economically viable methodology for determination of aquifer geo-hydraulic parameters (Zohdy et al. 1974; Onu 2003; Samouëlian et al. 2005; Aweto 2011; Niwas & Celik 2012; Dietrich et al. 2018; Inim et al. 2020; George et al. 2022; Asfahani 2023a, 2023b; Ebong et al. 2023; Joshua et al. 2023; Udosen et al. 2023; Abro et al. 2024; George et al. 2024; Udosen et al. 2024a, 2024b). In geo-electrical investigations, current is inserted into the subsurface via electrodes and corresponding potentials are calculated. Groundwater comprises dissolved salts leading to an ionic conductivity which leads to the permeation of electrical current through it (George et al. 2017b). The implication therefore is that geo-resistivity technology provides an efficient methodology for characterizing aquifers to determine their hydrodynamic distribution. These aquifer hydrodynamic characteristics are influenced by the regional geology of the study area. The earth's surface acts as a conductor that allows the permeation of electric current due to the existence of moisture or water content in between its pore spaces (Zohdy 1989; Niwas et al. 2011; Ibuot et al. 2021). Geo-electrical technology enables the acquisition of data along extended profile lengths and gives spatial distributions of earth resistivity distribution, precluding the need for expensive and time-consuming borehole pumping tests (Ibuot & Obiora 2021; Ekanem et al. 2022; Okoroh & Ibuot 2022; Asfahani et al. 2023; Ekanem & Udosen 2023a, 2023b; Udosen et al. 2024c). The above advantages motivated the application of geo-electrical technology in this work for the characterization of lithological units to determine critical geo-kinetic properties. Measures of rock matrix resistivity provide valuable data on rock lithology and saturation. Rock matrix resistivity is dependent on rock water content, the amount of clay or other low-conductivity materials, the mineral content of the rock matrix, and the resistivity of water flowing within the pore spaces. Hard rocks with few or no pore spaces have high resistivities; clay geo-materials have low resistivities; ore bodies have high resistivities; igneous rocks have high resistivities; metamorphic rocks have moderate resistivities, and sedimentary rocks have low resistivities as a result of their capacity to retain large amounts of fluid. Saline water environments have high conductivities resulting from the existence of liquefied salts, and the occurrence of anomalous high resistivity zones within such environments indicates freshwater zones (Inim et al. 2020).
Most regional groundwater reserves are archived in sedimentary units that require effective geological and geophysical methods for their characterization. The assessment of such groundwater systems can be characterized via geo-electrical technology to evaluate aquifer potentiality, aquifer protectivity and aquifer vulnerability to toxicants (Niwas & Singhal 1985; Udosen 2022; Udosen et al. 2024d, 2024e) Such characterization requires comprehensive knowledge of critical geo-hydraulic parameters such as permeability, porosity, tortuosity, hydraulic conductivity, etc. Whereas permeability defines the ease of groundwater flow via saturated pore spaces, porosity defines the fraction of voids within a given soil volume as a ratio of the entire rock matrix volume and is influenced by void quantity and geometry. Rock porosity <5% is considered poor, porosity gamut of 5–20% is considered medium, and porosity >20% is considered good. Primary porosity is generated during rock deposition and tends to increase indefinitely as long as deposition continues, generating isotropy within sandstones. Secondary porosity, on the other hand, arises after rock deposition and is due to the fissures and cracks within the rock matrix. Secondary porosity fluctuates with time and generates anisotropy in carbonate rocks. Within the voids and pore spaces of a porous rock's matrix reside groundwater and soil moisture which influence the rate of contamination dispersal within the subterranean water resources, hence the higher the rate of groundwater transmissivity, the faster the rate of toxicant percolation into the aquifer system. Pore-space characterization is also critical in the determination of aquifer hydrokinetic properties (George et al. 2017a; Udosen & George 2018b), which are strongly influenced by pore nature, geometry, extent, size, degree of saturation, and interconnectivity. When rock matrices comprise uniform grain/sediments, measures of porosity are dependent on the nature of grain packing within the rock matrix (Mazáč et al. 1985).
The region in question, Ikot Abasi, Nigeria, comprises a major aquifer system. It has an unconfined aquifer system with no impermeable overburden geo-materials. The water table is the uppermost aquifer boundary within this aquifer system; hence this aquifer system is prone to contamination from surface and near-surface toxicants. Groundwater within this unconfined aquifer system is also prone to fluctuations in water levels, which in turn impacts groundwater yield in wells that have the unconfined aquifer as its fount. A confined aquifer system, on the other hand, would comprise permeable saturated rocks enclosed on both sides by impermeable geo-materials such as clay, making such aquifer systems less prone to contaminator percolation. With an increasing population due to the establishment of Federal Government tertiary institutions and other key industrial facilities in the region, groundwater resources in the region have become extremely vulnerable. The region has high levels of corrosivity (Ibanga & George 2016), indicative of the existence of toxic chemicals that have leached into subterranean water resources. It was therefore critical to assess its water reservoirs to obtain information about their hydrokinetic properties, the aquifer potentiality and the aquifer's susceptibility to contamination. This would aid in policymaking to preclude health-related problems arising from the permeation of pollutants into the subterranean water sources. The results obtained would give vital information on groundwater potability and natural aquifer protectivity as several ecosystems in the region are dependent on aquifer resources. Further, it would inform on locations of safe groundwater reservoirs, channels of contamination flow, and zones of optimal groundwater abstraction. This information would be useful in the development of action plans to enhance groundwater sustainability.
The aim of this work, therefore, was the employment of geo-electrical technology in the determination of key aquifer geo-kinetic properties such as specific retention, specific yield and storage-dependent drainability efficiency (SDE). This improves on past work where expensive and time-intensive techniques such as pumping tests, aquifer recharge techniques, evapotranspiration analysis from groundwater, magnetic resonance soundings, volume-balance techniques, rainfall–water table response techniques, type-curve techniques; laboratory drainage experiments, water table fluctuation analysis, and slug tests were used to generate measures of specific yield and specific retention in a bid to estimate the groundwater reserves within an aquifer (Nwankwor et al. 1984; Crosbie et al. 2005; Kollet & Zlotnik 2005; Loheide et al. 2005; Schilling & Kiniry 2007; Malama 2011; Yin et al. 2011; Vouillamoz et al. 2014; Gribovszki 2018; Lv et al. 2021). In this work, key hydrokinetic parameters were generated via geo-resistivity technology, an efficient and efficient modality, the goal being to delineate zones of optimal and sub-optimal groundwater abstraction. Via measures of specific yield 
and specific retention 
one could generate measures of the storage-dependent efficiency (SDE) to determine locations of efficient aquifer extraction. Further, geo-electrical technology was employed to generate measures of aquifer potentiality, aquifer protectivity and aquifer vulnerability to contamination via the use of primary and secondary geo-electrical index-based parameters. Past work has generated evidence that hydrogeological units can be effectively characterized via geo-electrical technology.
GEOLOGY OF THE STUDY AREA
Map indicating location of the study area.
The study area is located within the Coastal Plain Sands of the Niger Delta's Benin Formation. The Benin Formation, deposited during the Tertiary–Quaternary age, forms the major hydrogeological unit in the region (Avbovbo 1978). The Benin Formation overlies the Agbada Formation (the oil-bearing formation in the Niger Delta region) and the shaly Akata Formation, in that sequence (Avbovbo 1978; Stacher 1995). The Benin Formation is linked to arenite and minor argillite intercalations found at increasing depths of burial (Short & Stäuble 1967; Petters et al. 1989). The Formation comprises fine to coarse-grained arenites and gravels interbedded with argillites and lignite, leading to the creation of multiple aquifer systems (Reijers & Petters 1987; Udosen et al. 2024e, 2024f). The Benin Formation also comprises fluvial sediments, rock, sands and sediments with clay intercalations, all intertwined with one another (Short & Stäuble 1967; Avbovbo 1978). The alluvial units present in parts of the Benin Formation comprise lagoonal and tidal arenites. The alluvial sands within the Benin Formation range in grain size from extremely fine to coarse, and the light grey argillites that give these sands their distinctive appearance are rather small and sporadically located. Due to gravitational forces, these alluvial sediments are frequently found near dipping heights. Green shrubbery, trees, and forests comprise the main vegetation in the region, leading to intensive agricultural activities. The potentiality of groundwater is high in areas with sandy formations. The structure of the hydrogeological units, their flow dynamics, and the arrangement of littoral sequences impact groundwater reserves in the region.
METHOD
to generate values of apparent electrical resistance 
The geometric factor G of Schlumberger array was given by
was then multiplied by the geometric factor G to generate measures of apparent resistivity
as ordinate against half the current electrode spacing (AB/2) as abscissa, sounding curves were generated which illustrated the variation of subsurface apparent resistivity as a function of ground depth. Data smoothening on these sounding curves was undertaken via the elimination of anomalous data points that deviated pointedly from the curve's prevailing orientation. Data generated from these curves were then quantitively analyzed with a least squares inversion software WINRESIST (Vander Velpen & Sporry 1993) which served as a 1D iterative reconstruction algorithm that aimed to reduce the difference between the theoretical values generated from the software and the field data generated from fieldwork (Udosen et al. 2011; Udosen & Potthast 2018, 2019). The final inversion curves generated by WINRESIST gave measures of the primary geo-electrical indices which included geo-layer resistivity, thickness and depth, as well as the root mean square error, which indicated by how much the field data varied from the theoretical inversion model.
generated by the terrameter was then multiplied by Wenner's geometric factor G to generate measures of apparent resistivity
= apparent resistivity of data obtained from Wenner array, and 
= apparent resistance obtained from the terrameter. To generate resistivity tomograms delineating subsurface resistivity distribution for the 2D ERT surveys, the least-square iterative reconstruction software RES2DINV (Loke & Barker 1996) was applied. Geo-resistivity imaging is an ill-posed problem having challenges of unstable solutions and non-uniqueness (Loke & Dahlin 2002; Udosen et al. 2013a, 2013b), hence it required iterative reconstruction schemes (e.g. Loke & Barker 1996; Udosen & George 2018a) that addressed the non-linear and ill-posed problem of electrical resistivity (Tripp et al. 1984; Loke et al. 2001). The ERT models generated from the RES2DINV reconstruction software delineated the spatial distribution of subsurface resistivity with depth. Zones of low subsurface resistivity (high conductivity) were indicative of argillitic-prone strata. Arenaceous zones, on the other hand, were indicated by high resistivities. In both VES and ERT surveys, necessary survey precautions were undertaken to ensure the acquisition of accurate data. These precautions included ensuring an equidistant electrode spread, ensuring the injection of at least half the electrode into the subsurface to guarantee good electrode-ground contact, ensuring that the electrode spread was a straight line, and avoiding locations of known buried pipes, electrical cables, and other installations when laying out the survey lines.
(which defines the ratio of hydraulic head to fluid flow distance). The negative sign, which is often ignored in practical situations, implies that groundwater flows from a region of increasing hydraulic gradient to a region of decreasing hydraulic gradient. VES are influenced by both rock resistance and mineral content of water within the pore spaces. Consequently, resistivity measures of the saturated rock matrix will be dependent on the resistivity of the water within the pore spaces 
and the resistivity of aquifer bulk matrix 
. The formation factor indicated the relationship between these parameters via:
resistivity of saturated groundwater reservoir, 
resistivity of void space water, a = co-efficient of void space saturation (otherwise termed the tortuosity co-efficient), 
and m = co-efficient of cementation. The value of the co-efficient of void space saturation ‘a‘ depended on the nature of the pore spaces. For example, ‘a‘ is less than 1 in intergranular porosity and has a value of 1 in fracture porosity. The co-efficient of cementation ‘m‘ was also dependent on the lithology of subsurface strata within the study area. For example, m is typically less than 2 in rocks with a low degree of compaction, and it is equal to 2 in rocks with a high degree of compaction. In this work, a = 0.5245 and m = 1.5432 (George et al. 2011).
, a = co-efficient of void space saturation, F = formation factor, and m = co-efficient of cementation.
(otherwise termed the co-efficient of permeability) expresses the volume of water flowing within a given time under a given hydraulic gradient via a cross-sectional area at a right angle to the trajectory of fluid percolation. Hydraulic conductivity depended on the geo-hydraulic characteristics of the aquifer and the viscosity of the fluid flowing through it and defined the rock matrix's ability to transmit fluid. Hydraulic conductivity flow in directions parallel to the rock matrix's horizontal layering is typically more uniform and less turbulent than hydraulic conductivity in directions at right angles to the matrix's horizontal layering. The determination of hydraulic conductivity
was via the employment of the Kozeny-Carman-Bear equation
(1,000 kg/m3), 
= dynamic viscosity of water (0.0014 kg/ms, according to Fetter (1994)), dm = mean grain size (0.000348 m), g = acceleration due to gravity (9.8 m/s2), and 
.
of the aquifer system was computed as
= density of water, 
= dynamic viscosity of water, and g = acceleration due to gravity. Permeability 
measures were transformed to millidarcy (mD) via multiplication by 1.01325 × 1012. Different values of permeability determined the diverse characterization of water-bearing formations. These water-bearing formations included aquifers (saturated formations with high water yield), aquicludes (saturated formations with low water yield even under normal hydraulic gradients), aquitards (groundwater reservoirs with low permeability and consequently low transmissivity), and aquifuges (groundwater reservoirs with nil permeability and nil transmissivity). Permeability differed from porosity in that whereas porosity measured a rock's ability to retain fluids, permeability measured the ease of fluid flow within the rock matrix. Rock permeability was influenced by the interconnectivity between the rock's pore space, implying that the greater the interconnectivity between the pore spaces, the greater the permeability. Permeability influenced hydraulic conductivity; hence, a water-bearing formation with high permeability would have a high hydraulic conductivity, and vice versa. Coarse sands and gravels have higher permeability than fine/medium-grained arenites and argillites. The surface tensional forces that retained fluids within pore spaces in fine/medium-grained arenites and argillites were the reason for the reduced permeability in such geo-materials. Consequently, fine/medium-grained arenites and argillites have poor pore-space interconnectivity, high water retention and reduced specific yield (Meinzer 1923; Johnson 1967).
= water resistivity, 
= aquifer bulk resistivity, 
= resistivity of saturated aquifer (given that 
), 
= resistivity of the unsaturated vadose zone overlying the uppermost unconfined aquifer (Frohlich & Kelly 1988; Tizro et al. 2012). Parameter n defined a cementation co-efficient similar to m, and had a value of 2. Computation of specific retention of the aquifer 
was via the empirical formulation
and 
= specific yield of the aquifer (Lv et al. 2021). The storage-dependent drainability efficiency (SDE) co-efficient 
, which defined the aquifer's specific yield as a ratio of the aquifer's specific retention was computed via:
was computed. Tortuosity expressed the quotient of the total span of fluid flow to its straight-line distance and was estimated quantitatively as
, F = formation factor.
was generated from values of hydraulic conductivity 
such that
(in mhos). Via groundwater protectivity studies, one could identify zones prone to contamination, and this information would aid in the monitoring and regulation of groundwater resources within such zones (Braga et al. 2006). In locations where protective layers are thin, pollutants percolate into the aquifer system causing irreparable damage to the groundwater reservoir (Omosuyi 2010). Such pollutants could emanate from anthropogenic activities leading to the percolation of pesticides, fertilizers, and fumigants via the vadose zone into subterranean water resources. The study area was considered vulnerable to contamination as a result of its land-use practices. It was therefore critical that information of aquifer protectivity be determined. Longitudinal conductance (i.e., conductance through the rock matrix surface area parallel to the bedding planes of the rock matrix) was given as
= overburden geo-layer resistivity, i = number of overburden layers, and h = overburden thickness. According to Oladapo et al. (2004), longitudinal conductance value range of > 10 (mhos) indicated excellent aquifer protective capacity, 5–10 (mhos) indicated good aquifer protective capacity, 0.2–0.69 (mhos) indicated moderate aquifer protective capacity, 0.1–0.19 (mhos) indicated weak aquifer protective capacity, and less than < 0.1(mhos) indicated poor aquifer protective capacity. The nature of the lithology overlying the aquifer system was a determinant of the aquifer's protectivity; hence via measures of longitudinal conductance 
, one could determine the extent of aquifer vulnerability to contamination.RESULTS AND DISCUSSION
(a)–(d) Representative 1D inversion curves obtained from vertical electrical sounding surveys.
(a)–(d) Representative 1D inversion curves obtained from vertical electrical sounding surveys.
(a)–(e) 2D inversion tomograms obtained from electrical resistivity tomography surveys.
(a)–(e) 2D inversion tomograms obtained from electrical resistivity tomography surveys.
, bulk conductivity 
, water resistivity 
, formation factor 
, porosity 
, hydraulic conductivity 
, and permeability 
. Figures 4(a) and (b) illustrated the iso-parametric maps indicating the spatial variation of bulk resistivity and water resistivity respectively. These two maps correlated proportionally with each other, indicating high values of bulk resistivity and water resistivity in the north-eastern sections of the study area. The southern section of these iso-parametric maps, on the other hand, indicated reduced values of bulk resistivity and water resistivity. Figures 5(a) and (b) illustrated the iso-parametric maps indicating the geographical variation of formation factor and porosity. The map for formation factor correlated inversely with the map for porosity, indicating that locations of high formation factor were locations of low porosity, and vice versa. Figure 5(a) also indicated the immense diversity in formation factor values at varying sounding stations, illustrating that the formation factor was highly sensitive to measures of porosity and lithological strata within the geological formation. The study area was observed to have good porosity as indicated by its porosity values >20%. Total porosity within the region was dependent on the distribution of soil grains, geometry of the grains/pore spaces, and interconnectivity between pore spacings. The mean value of grain size in the region was 0.000348 m, indicating the presence of coastal plain arenites intercalations with argillites, a prominent feature of geo-layers within the Benin Formation. Figures 6(a) and (b) illustrated the iso-parametric maps indicating the spatial distribution of hydraulic conductivity (m/s) and permeability (mD) respectively. Hydraulic conductivity and permeability correlated proportionally with one another, and increments in both parameters were observed from the north-east toward the south. Large values of hydraulic conductivity and permeability indicated ease of fluid flow and high transmissivity, whereas low/moderate values indicated low/moderate ease of fluid flow. Summary of measured hydrokinetic parameters obtained for this aquifer system at different VES stations: (i) site elevation, (ii) bulk aquifer resistivity 
, (iii) bulk aquifer conductivity 
, (iv) water resistivity 
, (v) formation factor 
, (vi) porosity 
, (vii) hydraulic conductivity 
, and (viii) permeability 
| VES No | Longitude (°) | Latitude (°) | Elevation (m) | Bulk resistivity  (Ωm) | Bulk conductivity  (Ωm)−1 | Water resistivity  (Ωm) | Formation factor F | Porosity  | Hydraulic conductivity  (m/s) | Permeability  (mD) |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 15 | 115 | 0.008696 | 20.28655 | 5.6687805 | 0.21382 | 7.44843E-05 | 10781.9 |
| 2 | 7.60866667 | 4.61011111 | 9 | 229.7 | 0.004354 | 26.91277 | 8.534982 | 0.16401 | 2.97296E-05 | 4303.45 |
| 3 | 7.60963889 | 4.60055556 | 9 | 69 | 0.014493 | 17.62913 | 3.9139765 | 0.27183 | 0.000178413 | 25825.9 |
| 4 | 7.60363889 | 4.60666667 | 7 | 68.5 | 0.014599 | 17.60025 | 3.8919913 | 0.27283 | 0.000180871 | 26181.7 |
| 5 | 7.60519444 | 4.60305556 | 9 | 51.4 | 0.019455 | 16.61238 | 3.0940784 | 0.31656 | 0.000319873 | 46302.8 |
| 6 | 7.60519444 | 4.58638889 | 9 | 72.1 | 0.01387 | 17.80822 | 4.0486928 | 0.26594 | 0.000164379 | 23794.4 |
| 7 | 7.60575 | 4.601222222 | 7 | 111.5 | 0.008681 | 20.2981 | 5.6754069 | 0.21366 | 7.42848E-05 | 10,753 |
| 8 | 7.61141667 | 4.59266667 | 9 | 59.9 | 0.016694 | 17.10342 | 3.5022229 | 0.29214 | 0.000234342 | 33921.7 |
| 9 | 7.61252778 | 4.59227778 | 3 | 63.5 | 0.015748 | 17.3114 | 3.6681042 | 0.28351 | 0.000209048 | 30260.4 |
| 10 | 7.60836111 | 4.58955556 | 14 | 50.5 | 0.019802 | 16.56039 | 3.049446 | 0.31956 | 0.000331942 | 48049.7 |
| VES No | Longitude (°) | Latitude (°) | Elevation (m) | Bulk resistivity (Ωm) | Bulk conductivity (Ωm)−1 | Water resistivity (Ωm) | Formation factor F | Porosity | Hydraulic conductivity (m/s) | Permeability (mD) |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 15 | 115 | 0.008696 | 20.28655 | 5.6687805 | 0.21382 | 7.44843E-05 | 10781.9 |
| 2 | 7.60866667 | 4.61011111 | 9 | 229.7 | 0.004354 | 26.91277 | 8.534982 | 0.16401 | 2.97296E-05 | 4303.45 |
| 3 | 7.60963889 | 4.60055556 | 9 | 69 | 0.014493 | 17.62913 | 3.9139765 | 0.27183 | 0.000178413 | 25825.9 |
| 4 | 7.60363889 | 4.60666667 | 7 | 68.5 | 0.014599 | 17.60025 | 3.8919913 | 0.27283 | 0.000180871 | 26181.7 |
| 5 | 7.60519444 | 4.60305556 | 9 | 51.4 | 0.019455 | 16.61238 | 3.0940784 | 0.31656 | 0.000319873 | 46302.8 |
| 6 | 7.60519444 | 4.58638889 | 9 | 72.1 | 0.01387 | 17.80822 | 4.0486928 | 0.26594 | 0.000164379 | 23794.4 |
| 7 | 7.60575 | 4.601222222 | 7 | 111.5 | 0.008681 | 20.2981 | 5.6754069 | 0.21366 | 7.42848E-05 | 10,753 |
| 8 | 7.61141667 | 4.59266667 | 9 | 59.9 | 0.016694 | 17.10342 | 3.5022229 | 0.29214 | 0.000234342 | 33921.7 |
| 9 | 7.61252778 | 4.59227778 | 3 | 63.5 | 0.015748 | 17.3114 | 3.6681042 | 0.28351 | 0.000209048 | 30260.4 |
| 10 | 7.60836111 | 4.58955556 | 14 | 50.5 | 0.019802 | 16.56039 | 3.049446 | 0.31956 | 0.000331942 | 48049.7 |
Iso-parametric maps illustrating the spatial distribution of (a) bulk resistivity and (b) water resistivity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) bulk resistivity and (b) water resistivity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) formation factor and (b) porosity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) formation factor and (b) porosity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) hydraulic conductivity and (b) permeability within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) hydraulic conductivity and (b) permeability within the study area.
(m/s) and 
permeability (mD) against porosity 
, with hydraulic conductivity varying directly as permeability. The empirical formulae relating hydraulic conductivity 
with porosity 
was
, implying a good model fit. The formulae relating permeability 
with porosity 
was
, implying a good model fit. 
Regression curves of aquifer hydraulic conductivity 
(m/s) and permeability 
(mD) against porosity 
.
Regression curves of aquifer hydraulic conductivity (m/s) and permeability (mD) against porosity .
unsaturated resistivity 
, specific yield 
, specific retention 
, storage-dependent drainability efficiency (SDE), and tortuosity (τ). Figures 8(a) and (b) illustrated the iso-parametric maps of saturated resistivity 
and unsaturated resistivity 
zones in the region. The figures indicated that the extent of pore-space saturation impacted the geo-resistivity of the subsurface geo-layers. The saturated zone within the aquifer (Figure 8(a)) indicated ease of current penetration, with the zone having a generally low resistivity distribution (high conductivity) which was indicative of the presence of permeable sedimentary groundwater reservoirs. The unsaturated resistivity zone (Figure 8(b)), on the other hand, indicated immense heterogeneity within the unsaturated vadose or aeration zone. When Figure 8(b) was correlated with the electrical resistivity tomograms in Figure 3 and the interpretations of vertical electrical sounding data, it corroborated that the topsoil comprised motley geo-materials that generated high lateral and vertical heterogeneity within the subsurface resistivity distribution. Summary of more hydrokinetic parameters obtained for this aquifer system at different VES stations: (i) saturated resistivity 
(ii) unsaturated resistivity 
, (iii) specific yield 
, (iv) specific retention 
and (v) storage-dependent drainability efficiency (SDE) and (vi) tortuosity 
| VES No | Longitude (°) | Latitude (°) | Saturated resistivity  (Ωm) | Unsaturated resistivity  (Ωm) | Specific yield ( ) | Specific retention ( ) | Storage-dependent drainability efficiency SDE (%) | Tortuosity  |
|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 94.7135 | 907.8 | 0.131572 | 0.082245 | 61.53469 | 1.10095 |
| 2 | 7.60866667 | 4.61011111 | 202.787 | 1254.8 | 0.079061 | 0.084949 | 48.20484 | 1.18314 |
| 3 | 7.60963889 | 4.60055556 | 51.3709 | 641.2 | 0.213498 | 0.058335 | 78.54007 | 1.03148 |
| 4 | 7.60363889 | 4.60666667 | 50.8998 | 736.4 | 0.216353 | 0.056474 | 79.30041 | 1.03046 |
| 5 | 7.60519444 | 4.60305556 | 34.7876 | 55.2 | 0.211965 | 0.1046 | 66.95794 | 0.98969 |
| 6 | 7.60519444 | 4.58638889 | 54.2918 | 236.5 | 0.188179 | 0.077757 | 70.76099 | 1.03764 |
| 7 | 7.60575 | 4.601222222 | 94.9019 | 654.2 | 0.128562 | 0.085093 | 60.17268 | 1.10117 |
| 8 | 7.61141667 | 4.59266667 | 42.7966 | 280.4 | 0.239239 | 0.052898 | 81.89268 | 1.0115 |
| 9 | 7.61252778 | 4.59227778 | 46.1886 | 119 | 0.195762 | 0.087744 | 69.05042 | 1.01977 |
| 10 | 7.60836111 | 4.58955556 | 33.9396 | 185.7 | 0.287328 | 0.032232 | 89.91372 | 0.98716 |
| VES No | Longitude (°) | Latitude (°) | Saturated resistivity (Ωm) | Unsaturated resistivity (Ωm) | Specific yield () | Specific retention () | Storage-dependent drainability efficiency SDE (%) | Tortuosity |
|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 94.7135 | 907.8 | 0.131572 | 0.082245 | 61.53469 | 1.10095 |
| 2 | 7.60866667 | 4.61011111 | 202.787 | 1254.8 | 0.079061 | 0.084949 | 48.20484 | 1.18314 |
| 3 | 7.60963889 | 4.60055556 | 51.3709 | 641.2 | 0.213498 | 0.058335 | 78.54007 | 1.03148 |
| 4 | 7.60363889 | 4.60666667 | 50.8998 | 736.4 | 0.216353 | 0.056474 | 79.30041 | 1.03046 |
| 5 | 7.60519444 | 4.60305556 | 34.7876 | 55.2 | 0.211965 | 0.1046 | 66.95794 | 0.98969 |
| 6 | 7.60519444 | 4.58638889 | 54.2918 | 236.5 | 0.188179 | 0.077757 | 70.76099 | 1.03764 |
| 7 | 7.60575 | 4.601222222 | 94.9019 | 654.2 | 0.128562 | 0.085093 | 60.17268 | 1.10117 |
| 8 | 7.61141667 | 4.59266667 | 42.7966 | 280.4 | 0.239239 | 0.052898 | 81.89268 | 1.0115 |
| 9 | 7.61252778 | 4.59227778 | 46.1886 | 119 | 0.195762 | 0.087744 | 69.05042 | 1.01977 |
| 10 | 7.60836111 | 4.58955556 | 33.9396 | 185.7 | 0.287328 | 0.032232 | 89.91372 | 0.98716 |
Iso-parametric maps illustrating the spatial distribution of (a) saturated resistivity zone and (b) unsaturated resistivity zone within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) saturated resistivity zone and (b) unsaturated resistivity zone within the study area.
with SDE co-efficient 
was determined as
with SDE co-efficient 
was determined as
Iso-parametric maps illustrating the spatial distribution of (a) aquifer-specific yield capacity and (b) aquifer-specific retention capacity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) aquifer-specific yield capacity and (b) aquifer-specific retention capacity within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) tortuosity and (b) storage-dependent drainage efficiency within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) tortuosity and (b) storage-dependent drainage efficiency within the study area.
Regression curves of aquifer-specific yield 
and aquifer-specific retention 
against aquifer storage-dependent drainability efficiency.
Regression curves of aquifer-specific yield and aquifer-specific retention against aquifer storage-dependent drainability efficiency.
values varied between 0.01 and 2.53 mhos with seven out of ten stations having longitudinal conductance values ranging from 0.01–0.17 mhos, indicating poor to weak aquifer protectivity. The very low measures of longitudinal conductance illustrated in Table 5 indicated high vulnerability of the aquifer to contamination and consequently poor aquifer protectivity. The problem of poor aquifer protectivity was attributed to the highly permeable overburden and the negligible argillitic zones that would serve to preclude contaminant percolation. The trend of low longitudinal conductance measures (Figure 12(b)) indicated that subterranean water resources in the region were extremely vulnerable to toxicants due to the weak aquifer protective capacity. Such vulnerable water resources would require intensive monitoring to preclude the aggravation of contaminant percolation into subterranean water resources. Aquifer potential rating based on the values of aquifer transmissivity (Gheorghe 1978)
| Transmissivity (m2/day) | Aquifer potential capacity |
|---|---|
| >500 | High |
| 50–500 | Moderate |
| 5–50 | Low |
| 0.5–5 | Very low |
| <0.5 | Negligible |
| Transmissivity (m2/day) | Aquifer potential capacity |
|---|---|
| >500 | High |
| 50–500 | Moderate |
| 5–50 | Low |
| 0.5–5 | Very low |
| <0.5 | Negligible |
Aquifer protective rating based on the values of overburden longitudinal conductance (Oladapo et al. 2004)
| Longitudinal conductance (mhos) | Aquifer protective capacity |
|---|---|
| >10 | Excellent |
| 5–10 | Very good |
| 0.7–4.49 | Good |
| 0.2–0.69 | Moderate |
| 0.1–0.19 | Weak |
| <0.1 | Poor |
| Longitudinal conductance (mhos) | Aquifer protective capacity |
|---|---|
| >10 | Excellent |
| 5–10 | Very good |
| 0.7–4.49 | Good |
| 0.2–0.69 | Moderate |
| 0.1–0.19 | Weak |
| <0.1 | Poor |
Summary of aquifer potentiality and protectivity capacity measures
| VES No | Longitude (°) | Latitude (°) | Aquifer bulk resistivity ρa (Ωm) | Thickness of aquifer (m) | Transverse resistance (Ωm2) | Longitudinal conductance (mhos) | Aquifer protective rating | Transmissivity (m2/day) | Aquifer potentiality rating |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 115 | 97.8 | 12809.1 | 0.056745014 | Poor | 629.387 | High |
| 2 | 7.60866667 | 4.61011111 | 229.7 | 76.5 | 3975.92 | 0.011884739 | Poor | 196.5 | Moderate |
| 3 | 7.60963889 | 4.60055556 | 69 | 111.4 | 11137.35 | 0.172012671 | Weak | 1717.22 | High |
| 4 | 7.60363889 | 4.60666667 | 68.5 | 83.9 | 19001.32 | 0.040690599 | Poor | 1311.13 | High |
| 5 | 7.60519444 | 4.60305556 | 51.4 | 80.8 | 8082.77 | 0.094818095 | Poor | 2233.07 | High |
| 6 | 7.60519444 | 4.58638889 | 72.1 | 39.2 | 18,036 | 0.07693054 | Poor | 556.732 | High |
| 7 | 7.60575 | 4.601222222 | 111.5 | 23.8 | 17870.7 | 0.169458803 | Weak | 152.753 | Moderate |
| 8 | 7.61141667 | 4.59266667 | 59.9 | 20.3 | 884.68 | 2.532117779 | Good | 411.016 | Moderate |
| 9 | 7.61252778 | 4.59227778 | 63.5 | 103.3 | 824.6 | 0.697603486 | Moderate | 1865.78 | High |
| 10 | 7.60836111 | 4.58955556 | 50.5 | 78.3 | 1020.3 | 2.012219266 | Good | 2245.63 | High |
| VES No | Longitude (°) | Latitude (°) | Aquifer bulk resistivity ρa (Ωm) | Thickness of aquifer (m) | Transverse resistance (Ωm2) | Longitudinal conductance (mhos) | Aquifer protective rating | Transmissivity (m2/day) | Aquifer potentiality rating |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 7.60869444 | 4.61472222 | 115 | 97.8 | 12809.1 | 0.056745014 | Poor | 629.387 | High |
| 2 | 7.60866667 | 4.61011111 | 229.7 | 76.5 | 3975.92 | 0.011884739 | Poor | 196.5 | Moderate |
| 3 | 7.60963889 | 4.60055556 | 69 | 111.4 | 11137.35 | 0.172012671 | Weak | 1717.22 | High |
| 4 | 7.60363889 | 4.60666667 | 68.5 | 83.9 | 19001.32 | 0.040690599 | Poor | 1311.13 | High |
| 5 | 7.60519444 | 4.60305556 | 51.4 | 80.8 | 8082.77 | 0.094818095 | Poor | 2233.07 | High |
| 6 | 7.60519444 | 4.58638889 | 72.1 | 39.2 | 18,036 | 0.07693054 | Poor | 556.732 | High |
| 7 | 7.60575 | 4.601222222 | 111.5 | 23.8 | 17870.7 | 0.169458803 | Weak | 152.753 | Moderate |
| 8 | 7.61141667 | 4.59266667 | 59.9 | 20.3 | 884.68 | 2.532117779 | Good | 411.016 | Moderate |
| 9 | 7.61252778 | 4.59227778 | 63.5 | 103.3 | 824.6 | 0.697603486 | Moderate | 1865.78 | High |
| 10 | 7.60836111 | 4.58955556 | 50.5 | 78.3 | 1020.3 | 2.012219266 | Good | 2245.63 | High |
Iso-parametric maps illustrating the spatial distribution of (a) transmissivity and (b) longitudinal conductance within the study area.
Iso-parametric maps illustrating the spatial distribution of (a) transmissivity and (b) longitudinal conductance within the study area.
CONCLUSION
Geo-electrical data was used to characterize the unconfined groundwater reservoir system within a significant littoral system in Southern Nigeria, the overall goal being to generate measures of specific yield, specific retention and storage-dependent drainability efficiency (SDE). Locations with SDE >73% indicated regions with efficient groundwater abstraction resulting from the optimal release of groundwater via the pore spaces. Spatial distribution of other geo-hydraulic parameters within the geo-stratigraphic units in the region were also delineated using the primary and secondary geo-electrical indices, and aquifer potentiality, aquifer protectivity, and aquifer vulnerability to contamination were assessed. The geo-electrical surveys were undertaken via VES and ERT surveys, and inversion results indicated that the lithological strata comprised motley topsoil, coarse sand, fine sand, and sandy clay, in that sequence. Variations within the lithological strata were attributed to bioturbating activities, subsurface heterogeneity, and sand–clay intercalations. Via characterization of the aquifer geo-hydraulic parameters, pore-space characteristics were analyzed and employed to generate information on groundwater abstraction efficiency from the aquifer during pumping. In addition, measures of aquifer transmissivity delineated the aquifer as having high potentiality, while measures of Dar-Zarrouk parameters delineated the aquifer as having low protectivity and a consequent high vulnerability to toxicants. Characterization of this aquifer system will aid subterranean water management and conservation in the region, a critical step to preventing pollutant percolation into the water reservoirs. The hydrogeological units from which groundwater is abstracted have been delineated to be vulnerable to contaminants, hence percolation of leachates and other organic and inorganic contaminants could cause irreparable damage to the aquifer system.
COMPETING INTERESTS STATEMENTS
The authors have no competing interests to declare that are relevant to the content of this article.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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