Hydraulic characterization of the Adamawa-Cameroon aquifer using inverse slope method

Direct current (DC) geo-electrical methods stand out in the domain of groundwater prospection due to their accuracy and high efficiency in comparison with traditional methods of pumping tests (George et al. 2014, Umo et al. 2022a, 2022b). Several quantitative software programs and inversion techniques have been proposed and discussed for interpreting DC earth-resistivity measurements. Ghosh (1971) determined inverse filter coefficients for the computation of apparent resistivity standard curves for a horizontally stratified earth. Zohdy (1975, 1985) modified Dar–Zarrouk functions for automatic interpretation of Schlumberger vertical electrical sounding (VES) curves, and later, improved this technique by adding Wenner sounding curves. Koefoed (1976) presented progressive developments in the direct interpretation of the resistivity sounding. Geo-electrical DC methods have been used to investigate groundwater in the Pan-African context of Central Africa region (Aretouyap et al. 2015a, 2015b). Recently, geo-electrical resistivity technology has been deployed through VES and electrical resistivity tomography (ERT) to study shallow/intermediate depths of investigation for reasons bordering on hydrogeology, environment, archeology, engineering, and mining surveys (Ngako & JegouzoNzenti 1991; Ibanga & George 2016; Obiora et al. 2016; Thomas et al. 2020; George et al. 2021; Mohammed et al. 2021; Ekanem et al. 2022; Ikpe et al. 2022). The results assisted in solving both environmental and ecological problems in their respective study areas. Uwa et al. (2019) studied the geohydrodynamics of a coastal environment using VES data. However, it is important to assess the limitations of each technique regarding its suitability and assets (accuracy) in relation to different subsurface conditions for, each one is based on a separate approach and methodology (Asfahani 2016). For example, when Aretouyap et al. (2019, 2021) used the conventional curve matching method (CMM) to derive the hydro-parameters of the Adamawa Plateau watershed, it was found that the resolution of this method is so poor, such as thin layers buried at important depth are simply indistinguishable on the logarithmic plot. These CMM limitations encouraged the use of an alternative approach, namely the inverse slope method (ISM) for the interpretation of VES data. ISM was previously developed by Sanker Narayan & Ramanujachary (1967) and recently applied by Mohamed et al. (2014). Asfahani (2016) successfully applied the ISM program in exploration geophysics to characterize phosphatic layers in Al-Sharquieh mine in Syria. Recently, George et al. (2022) used both the ISM and the computer-aided iterative least-square inversion technique to delineate hydrogeological units. The outcomes of the research gave well-resolved depths, and thicknesses, in which the ISM parameters were more consistent with geological units than the least-square inversion technique. The ISM technique is simpler than CMM and has numerous qualitative and quantitative advantages. It allows for a distinctively resolved delineation of geologic layers, no matter how thin the layer is and can be used to interpret VES data collected with any electrodes array (Mohamed et al. 2014; George et al. 2022). The ISM technique is used herein to reinterpret VES data already investigated by Aretouyap et al. (2015a, 2015b) for groundwater and hydrogeological related purposes. Interestingly, the main objective of the present paper is to employ the ISM programming technique in testing the suitability and the applicability of the ISM in the Pan-African context. The method is also applied to overcome major interpretation difficulties (e.g., the eclipse of thinner layers and the sensibility to electrodes array in VES data collection), associated with traditional CMM as well as comparing the results obtained from ISM, CMM and programming inversion methods. By applying the geo-electrical results of ISM for hydrogeophysical and aquifer characterization through the integral interpolation protocol technique in the Pan-African context of Central Africa, alternative and reliable results, which overcome the principles of suppression and equivalence, can be avoided, mostly when constrained with ground truth data. The data for this research were collected in 2015 with the field campaign in Cameroon, while data interpretation was done using ISM in 2022.

The center of the plateau is marked by soft forms barely accented and swampy valleys, dotted with mountains or/and volcanic cones. At the east, there are massifs resulting from the former erosion and tectonic movements. In the west, the terrain is mountainous with hills. Volcanic inheritance covers the north, the east and the south parts of the area. One notes the presence of an assembly line which occupies an important part of the region, reaching altitudes of more than 2,240 m. There are also plains and basins (Toteu et al. 2000).

The geological history of the Adamawa-Cameroon region is marked by three major events (Toteu et al. 2000). These are (i) long period of continental erosion from Precambrian to Cretaceous, (ii) the onset of volcanism from Cretaceous to Quaternary and (iii) recurrent basement tectonics that explains the horst and graben structure of the Adamawa Plateau.

An investigation of superficial formations in the region has highlighted the Pan-African granite-gneiss bedrock, represented by Ordovician Granites, Gneisses and Pan-African Migmatites. The main geological formations encountered are basalts, trachytes and trachyphonolites based mostly on concordant calco-alkaline granites and discordant alkaline granites (Toteu et al. 2000).

Three main geological units are observed on the surface. Each type of those geological unit contains some VES locations. The largest formation, made up of granite contains the majority of VES points. Metamorphic Formations contain some pits such as P-11, P-34, P-36, etc. Pits P-28, P-29, etc. are located in volcano-sedimentary units.

In hydrological terms, 150–300 km wide, the Adamawa Plateau is called ‘the water tower of the region’ because it feeds three of the four major watersheds of the region, namely, the Lake Chad Basin, the Niger Basin in the North and the Sanaga Atlantic Basin in the south. Indeed, many rivers such as Mayo Deo, Mayo Banyo, Mbere, Vina (tributaries of the Logone), Mbam, Kim, Djerem and Lom (tributaries of the Sanaga) divert from this region. There are also many crater lakes including Tyson, Mbalang and Vina lakes resulting from a long volcanic history in the region (Nguetnkam et al. 2002). In addition to the existence of many lineaments in the region, this important hydrosphere may forecast the existence of aquifers located at interesting depths with significant thicknesses.

Geophysical survey reveals that the Pan-African belt was tectonically active, where many lineaments and faults occur (Cornacchia & Dars 1983; Dumont 1986; Robain et al. 1996; Toteu et al. 2004; Ngako et al. 2008; Njonfang et al. 2008). Those lineaments are supposed to constitute ‘highway’ for groundwater. Although groundwater productivity is directly linked to the bedrock alteration, there is no recent study aimed at locating and characterizing local aquifers. This situation justifies the interest of the present paper.

I is the intensity of the electrical current injected in the ground by electrodes A and B, and U_MN is the voltage potential between electrodes M and N.

The resistivity meter with the electrodes cables and other accessories is the main measuring equipment. The CMM is generally used to interpret the smoothened field curve to generate initial layer resistivities and thicknesses of the layers (Zohdy et al. 1974; George 2020). The initial layer indices are thereafter used as inputs in the computer-aided quantitative interpretation software program, which in this research is done by the use of a one-dimensional (1D) least-square forward modeling software program called WINRESIST (Vander Velpen & Sporry 1993; Udosen & George 2018). The program software made use of the input data to generate a theoretical model and then establishes a fit between the model and the measured field data to give the final 1D resistivity model curves. The goodness of fit is expressed in terms of the root-mean square error (RMSE) (Bandani 2011). The values of the measured apparent resistivity ρ_a depend on several factors such as true layers resistivities and thicknesses, and the electrode's location. The accuracy of their determination depends on the homogeneity of the substratum. For a heterogeneous medium, CMM interpretation does not provide enough accurate results.

However, some ambiguity problems can arise during the interpretation. A sample interpretation exercise must be carried out before each project in order to solve such encountered problems. If those ambiguity problems are too complex, further methods such as seismic and test wells are required (Asfahani 2007). Sometimes, the use of an alternative independent method is indispensable (Asfahani 2013).

The results of the CMM (Orellana & Mooney 1966) are used in the present paper for comparison with those obtained by ISM. For the CMM technique, an inverse technique programme fits thereafter both theoretical and field curves for each experimental VES (Zohdy 1985; Zohdy & Bisdorf 1989). This operation requires the double condition of accuracy in calculations and reasonable geological modeling. Furthermore, the medium is known as a one-dimensional model 1D (Dey & Morrison 1979). The 1D quantitative interpretation of the 50 VES by using both the CMM and the inversion software program of WinResist enabled the identification of hydrogeoelectrical characteristics of the Pan-African deposits (Aretouyap et al. 2015a, 2015b).

ISM can be used to obtain directly the resistivities and the thicknesses of subsurface layers from field data (Sanker Narayan & Ramanujachary 1967). Asfahani (2016) in an attempt to explore for sulfate minerals explained all the steps methodically used in ISM approach. The inverse resistivities for (AB/2)/ρ_a were plotted against the electrode separation (AB/2). The apparent resistivity of each can be obtained using the slope (m_i) in each segment using expression ⁠. Each line segment resulting from this graph represents a layer; and the intersection of the line segments, multiplied by a factor of 2/3, and corresponds to the depth of a particular layer. Concretely, let t₁… t_n be intersection points, then 2/3 ×t_i is equal to the depth of the i^th interface. Similarly, when (AB/2)/ρ_a is plotted versus AB/2, the slope gives the resistivity of the i^th layer except when the segment representing the high-resistivity layer shows a negative slope. In this case, the resistivity of the layer is taken as infinity (Asfahani 2016). The thickness of each layer is defined by the difference between the depths of two consecutive strata and at the point of intersection (George et al. 2022). The application of ISM is that it is possible to decipher thin layers even if they are buried at great depths. The work of Asfahani (2016) has been confirmed by George et al. (2022) and the result shows that ISM is more sensitive to CMM based on the closeness of results from ISM to ground truths. Based on the above analyses with ISM and CMM methods, the primary geo-electric indices (layer resistivity, layer thickness and depth) were determined as presented in Table 1. These parameters are used in characterizing the Pan- African aquifer systems. The layer resistivities realized showed high and low values, indicating the variations in the geological materials within the subsurface (Akpan et al. 2013; George et al. 2017; Ibuot et al. 2017).

Aquifer's parameters investigated in this paper have been measured or computed punctually (especially on VES sites). Yet, an efficient and sustainable management of groundwater resources requires an accurate and continuous determination of hydrodynamic parameters. As opined by Varol et al. (2021), geostatistics is often useful in predicting, assessing and interpolating the distinct components of a system such as an aquifer system comprising resistivity, depth and thickness.

The technique applied herein is essentially based on the notions of semivariogram and Kriging according to Aretouyap et al. (2016).

In this equation, Var is the variance applied to the difference between two observations h(x) and h(x+r) separated by a distance r.

In this relation, represent the Kriging weights.

Determination of Kriging weights, which are needed to estimate a point defined by the linear estimator is explained in Aretouyap et al. (2014).

This approach is very important in the context of developing countries where data collected are generally sparse and irregular. One observes the following three steps, which aid efficiently in investigating the parameters such as exploratory data analysis, structural data analysis and prediction (interpolation).

Data consistency has been checked, outliers (strange values which are very high or very low compared to the dataset) removed and statistical distribution identified. Indeed, an optimal application of Kriging techniques requires normal data distribution. For this, the mean and the median values of the parameters to be estimated should be very similar.

The best semivariogram model (on the basis of cross validation) is selected to interpolate each parameter. Hence, various types of errors were computed and compared. Those are mean error (ME), mean square error (MSE), RMSE, average standard error (ASE) and root-mean square standardized error (RMSSE). ME 0 when predictions are unbiased. Unfortunately, this ME is strongly dependent upon the scale of the data, and usually is indifferent to the wrongness of semivariogram. Because of these weaknesses, ME is generally standardized by the MSE, being ideally equal to zero.

The above percentage ranges of parameters (aquifer resistivities) of model validation indicate that for NSOC between what is observed and what is alternatively calculated to be efficient, the calculated/modeled resistivity values should be close to the observed aquifer resistivities.

Figure 3 is extracted from Figure 2 to illustrate clearly the pits’ interpretation using ISM. The interpretation of VESs P-9, P-13, P-14 and P-23 with ISM shows a good agreement with the available lithological description of those points. These ISM results are compared with the true lithological description. One can observe that both the ISM results and lithological logs have exactly the same number of layers with respective thicknesses slightly different. It is observed for all the interpreted pits that the last segment is characterized by a very low slope, equivalent to a very high resistivity (>2,500 Ω m). This high-resistive layer corresponds to the bedrock, made of granite. It also observed some differences in terms of layer numbers and resistivities, thicknesses and depths between the ISM results and those obtained using CMM (Aretouyap et al. 2015a, 2015b). Table 1 compares the Pan-African aquifer characteristics obtained from both CMM and ISM methods.

The qualitative interpretation of P-15 reveals three main layers: clay, cracking granite and granite arranged downward. The quantitative interpretation allowed for the respective delineation of resistivities as 502, 11 and 2,531 Ω m, and their respective thicknesses as 6 m, 15 m and infinite.

The clay resistivity for this pit VES P-15 is very high, and may be higher for the following pits. These high values are due to the nonpure character of the clay. In fact, this is a mixture of clay and laterite (Koita et al. 2013). The VES P-42 exhibits four layers with the clay (748 Ω m, 16 m) at the top and the granitic bedrock (5,217 Ω m) at the bottom. Intermediary layers are basalt (104 Ω m, 33 m) and ferruginous clay (3 Ω m, 17 m).

All of the 50 pits have been interpreted similarly by using ISM, where the local Pan-African aquifer made up of the upper weathering portion of the granitic basement has been characterized as shown in Table 2.

For some pits, the number of layers obtained from both interpretations (CMM and ISM) are different. CMM does not split some thinner layers, where those thin layers are detected by ISM. Furthermore, significant differences are observed in layers thicknesses and resistivities for the aquifer. For P-1 for example, CMM interpretation provides 565 Ω m resistivity, 40 m thickness and 18.4 depths while ISM interpretation provides, respectively, 320 Ω m, 42.1 m and 21 m for the same parameters as shown and compared in Table 1. Such differences are observed for almost all other VES points. Given the importance of aquifer resistivity and thickness in groundwater productivity and management (Asfahani 2007; Aretouyap et al. 2015a, 2015b), these dissimilarities observed from different techniques demonstrate the necessity of using and comparing both methods in the context of accurate interpretation and efficient water resources management. The high standard deviation noticed in the table is due to the heterogeneous nature of the geologic units serving as aquifers. This hinges on the fact that aquifer systems in the Pan-African region are made of suites of intercalations of geologic units, which give a dynamic range of the primary geo-electric indices. However, the efficacy of the model is validated by the use of NSOC, which checks for the consistency between the universal model (CMM) and the alternative model (ISM). The NSOC gave 87.93% as the correlative optimization between the CMM and ISM using Equation (13). The value of NSOC according to Yao et al. (2007), suggests that the model is satisfactory.

Figure 6 shows the distribution of the Pan-African aquifer resistivity deduced from the ISM interpretation of the 50 pits. Minimum values are observed in the northeast part of the region above VES location P-4 and maximum values are observed in the southwest part where is located P-20. Given that the local Pan-African aquifer is almost made up of a weathered portion of the granitic bedrock, minimum values of the aquifer resistivity correspond to a more cracked basement while maximum resistivity values correspond to a less fractured basement portion. One can also observe that the northeast part of the region is covered with volcano-sedimentary formations (see Figure 1). Other geological and geothermal factors as age and temperature can explain these maximum and minimum values. The resistivity map divides the area into two zones: a high-resistive zone in the southwest and a low-resistive zone in the northeast. Groundwater therefore may flow from the northeast (where is concentrated the recharge area) to the southwest.

Figure 6 shows the distribution of the saturated Pan-African aquifer thickness h deduced from the use of the 50 VES points interpreted by ISM. The minimum thickness is observed northward above VES P-4 point and the maximum eastward at VES P-6. The aquifer formations correspond with the low-resistivity layers. Higher aquifer thickness is observed in the eastern part of the study area.

Attentive analysis of Figures 5 and 6 insinuates that aquifer depth and resistivity vary inversely. Indeed, the highest depth values are observed south-eastward while the highest resistivity values are observed north-westward. This situation has an advantage and inconvenience. Having in mind that more productive aquifers in terms of flow or recharge are less resistive, citizens can drill productive hand-made wells in the region. However, because of the shallow location of these wells, they are very vulnerable to pollution, quality alteration and climate variability. ISM allows for precise determination of the hydraulic parameters such as resistivity, thickness and depth of the aquifer. These parameters are very useful in the integrated and sustainable management of groundwater resources. Their importance is also due to the potential environmental impacts they can generate in case of poor control. Such impacts can be wetland desiccation and especially structural damage as in London and Birmingham (Biwas 1992).

Comparatively, the reliability of the method can be seen in the coefficients of determination and correlation coefficients (R) for the aquifer resistivity and depth in Figures 7 and 8. The CMM-ISM plot for aquifer resistivity gave while the CMM-ISM plot for depth gave ⁠. The correlations indicate strong relation in resistivity and depth between CMM and ISM, which implies the uniqueness of the method.

The application of the ISM in the present paper for interpreting VES data demonstrated the suitability of this method in the Pan-African context of groundwater purpose. Based on the goodness of fit, the method, which can avoid the principle of suppression and equivalence, has the capacity to overcome to quantitatively interpret geo-electrical units better than the CMM. ISM is simpler than CMM and has numerous qualitative and quantitative advantages. It allowed for the unique determination of all geologic layers. Even thinner layers can be determined with ease using ISM methods. ISM can be used to interpret VES data collected with any electrodes array (Asfahani 2013; Aretouyap et al. 2022; George et al. 2022). Its application has allowed for the characterization and derivation of the hydrogeophysical parameters of the Pan-African aquifer in the Adamawa region through the integrated protocol of interpolation technique, which can be useful for further groundwater modeling and assessment. The PAA resistivity values obtained by applying this ISM are in the range of 20–900 Ω m with a mean of 241 Ω m and a standard deviation of 228 Ω m. The aquifer thickness ranged from 2 to 90 m, with an average of 33 m and a standard deviation of 21 m. The high standard deviation is symptomatic of the high variability in the primary geo-electric indices, caused by variation in sand grains and depth of burial of aquifer systems. This economically exploitable aquifer is globally located at 37 m. The NSOC proposed by Yao et al. (2007) indicates that the model percentage is 87.93% reflecting that the chosen model is satisfactory. The correlation of CMM with the new technique (ISM) from the graphical analysis showed correlation coefficient is greater than 80% in resistivity and depth determination of the economic aquifers. These results enhance the understanding of the uneven Pan-African terrain and may be taken into account when planning groundwater management in the context of sustainable development. It is envisaged to identify the VES database in the region for future hydrogeophysical investigations.

The authors are very thankful to the anonymous reviewers who helped them to improve this article. They are also very thankful to the managing editor, Maryam Shabani, who handled the manuscript.

All relevant data are available on request.

The authors declare there is no conflict.