VES data recording and interpretation

A vertical electrical sounding (VES) with Schlumberger configurationis conducted in the region in order to locate and characterize the aquifers in the study region. With this technique, the electrical resistivity variations are expressed as a function of depth. Fifty vertical electrical soundings (VES) including 14 with available water samples have been conducted in the region using the Terrameter ABEMSAS-1000 with a spacing of current electrodes (AB) varying from 2 to 600 m.

In the present research, the curve matching technique is used to set structural parameters (^{Orellana and Mooney, 1966}). Then, an inverse technique algorithm developed by ^{Zohdy (1989)} and ^{Zohdy and Bisdorf (1989)} fits both theoretical and field curves for each experimental. ^{Dey and Morrison (1979)} mentioned the possibility of considering and assuming the medium to be as a one-dimensional model (1D). The geological conditions in the study area were favorable and allowed us to assume and apply the 1D model. The 1D quantitative interpretation of the 50 VES has already enabled the identification of geoelectrical characteristics of the Pan-African deposits (^{Arétouyap et al., 2015}).

Hydraulic conductivity estimation

This section is the main core of the survey. The hydraulic conductivity is estimated by using the approach proposed by ^{Asfahani (2016)}, which consists of the seven steps reminded below.

Determination of the water resistivity ρ _w

14 experimental VES measurements are carried out in the vicinity of available water samples (boreholes in function). Values of water conductivity (σ_W) from those 14 available water samples are measured, their water resistivity (ρ _w) values are thereafter deduced by using equation 1.

Hence, the factor formation (F) used in Archie's law becomes a function of both σ_W and (ρ _w).

Those 14VESs have been quantitatively interpretedusing curve matching method (as illustrated in Figure 2), where the resulting resistivity (ρ _rock ) and thickness (h) values are shown in Table 1.

Figure 2 An illustration of CMM interpretation of VES measurements. 

Determination of the formation factor

The formation factor (F) used in Archie's law (^{Worthington, 1993}) is computed as the ratio of ρrock and ρ-W (Equation 2).

In this Equation (2), ρ _rock represents the saturated aquifer resistivity estimated from the quantitative interpretation (using curve matching method as illustrated above) of VES, and ρ-W is the average pore fluid resistivity for the 14 reference VES. Water resistivity ρ_W is obtained through converting water conductivity σ_W since the conductivity is the inverse of the resistivity (see Equation 1).

Computation of the corresponding hydraulic conductivity

The formation factor F obtained previously using VES method is related to the hydraulic conductivity (^{Salem, 1999}) as expressed by equation 3.

Estimation of the transverse resistance and the transmissivity for the 14 experimental VES

The transverse resistance TR and the transmissivity T for the interpreted 14 VES are computed using Equations 4 and 5.

where K- is the average value of hydraulic conductivity of the available 14 water samples shown in Table 1.

Expressing the MTR as a function of TR

The modified transverse resistance (MTR) is expressed by Equation 6 (^{Niwas and Singhal, 1985}).

Where ρ-W is the average water resistivity of the available fourteen water samples shown in Table 1, and ρ_w is the water resistivity at the location of the VES point (Table 1). Knowing ρ-W and ρ_w, MTR for the 14 VES points is plotted versus TR (Figure 3).

Figure 3 MTR expressed as a function of TR for a suitable empirical relationship purpose. 

This plot enabled to establish an empirical relationship between both parameters (equation 7).

With R ² = 0.8447

Equation 9 will be used to extrapolate MTR values at the remaining VES points where no water sample exists.

Expressing T as a function of MTR

The transmissivity T is expressed as a function of the modified transverse resistance MTR (Equation 8) thanks to the plot (Figure 4).

Figure 4 T expressed as a function of MTR in order to establish an empirical relationship between both parameters. 

With R ² = 0.7688

Equation 10 will be used to extrapolate T values at the remaining 36 VES points where no water sample exists.

Extrapolation of T in the whole region

In order to estimate MTR values in the remaining 36 VES points without water sample, the formula established in equation (7) is applied. Equation 8 is thereafter used to compute K values in those VES without water sample. In other terms, since the transverse resistance of each point is known (as the product of rock resistivity by its thickness as expressed by earlier Equation 5) from VES interpretation, the empirical relationship established in Equation 7 enables us to obtain the modified transverse resistance as the product of the transverse resistance by 0.8518 plus 1005.6. Finally, the transmissivity of each point is obtained as the product of the modified transverse resistance by 5 × 10^-4 plus 3.2951. This methodology takes into account the geological context of the study area as exposed in Section 3.

Hydrogeophysical parameters of 14 reference VES

Fourteen VES were conducted near existing boreholes with available water samples. Interpretation of those VES enabled to compute rock resistivity (ρ_rock) and aquifer thickness (h) at those points. The corresponding transverse resistance (TR), modified transverse resistance (MTR), formation factor (F) and hydraulic conductivity (K) are thereafter computed since the expression of water resistivity (ρ_w) is known. These parameters are represented in Table 1.

Those 14 reference boreholes have an average value of water resistivity ρ-w=3.0Ω.m and an average value of hydraulic conductivity K-=0.29m/day. Those average values have been used respectively to compute MTR and T. Geophysical and hydrogeological parameters of those 14 reference VES points are summarized in Table 2.

Hydrogeophysical parameters of 36 remaining VES without available water sample

MTR ant T at the 36 VES points without available water samples are obtained using the established empirical Equations 7 and 8. The resulting MTR, T, and K values enable to approximately characterize the Pan-African aquifer. Those values are presented and compared with previous results (^{Arétouyap et al., 2015}) as shown in Table 3. Significant changes between those results are visible in hydraulic conductivity and transmissivity values. This difference attests the necessity and the advantage of using this alternative approach, where salinity variations from place to place are taken into consideration.

For each VES point presented in Table 3, the K* value of the hydraulic conductivity can be obtained as a ratio of the transmissivity T to the saturated thickness h obtained at that point. The spatial distribution of h is shown in Figure 5, where its values range from 6 to 84 m, with an average of 32 m.

Figure 5 Thematic map of the Pan-African thickness. 

The spatial distribution of the transverse resistance (TR) shown in Figure 6 reveals that TR values range from 330 to 22600 Ω.m² with an average value of 7021 Ω.m².

Figure 6 Thematic map of the Pan-African transverse resistance. 

The distributions of the modified transverse resistance (MTR), transmissivity (T) and hydraulic conductivity (K) are also shown respectively in Figures 7, 8 and 9, and summarized in Table 4. Many similitudes are observed between TR distribution (Figure 6) and MTR distribution (Figure 8). Respective minimum and maximum values are located in the same regions. However, one can observe a minor dissimilarity in the variation rate and direction. This change can be explained by several factors as electric anisotropy, mineralogical variation, hydraulic anisotropy and lithological disparity. Furthermore, since the local aquifer results from the bedrock alteration/weathering, it is possible to have many mini aquifers confined in unconnected aquitards.

Figure 7 Thematic map of the Pan-African modified transverse resistance MTR. 

Figure 8 Thematic map of the Pan-African transmissivity. 

Figure9. Thematic map of the Pan-African hydraulic conductivity. 

The transmissivity distribution shown in Figure 9 exhibits the existence of a poor-transmissive zone in the eastern part of the study area. Transmissivity values are low in this area contrary to the west and the center, where values can reach 17 m²/day. The presence of sedimentary formations can explain the easy spread of water in horizontal direction unlike the western area, covered by surficial granite.

However, it is important to note that hydraulic conductivity K varies in the opposite sense to transmissivity. Indeed, higher K values are observed eastward while lower ones are observed westward (Figures 8 and 9). This distribution can also be explained by the geological and lithological setting as in transmissivity distribution. On the other hand, the inverse proportion between hydraulic conductivity (derived from vertical flow) and transmissivity (derived from horizontal) can be due to the presence of vertical faults and lineaments in the region.

Transmissivity and hydraulic conductivity of the Pan-African aquifer are determined through the proposed alternative approach (^{Asfahani, 2016}). However, the application of this approach recommends the respect of three fundamental principles:

The first two rules are followed. In addition, the results obtained are compared with those of ^{Arétouyap et al. (2015)}. This comparison shows a fairly good agreement between the values of the aquifer thickness and a slight agreement regarding the values of hydraulic conductivity and transmissivity (Figure 10). Those differences are due to the basis of the analysis method. In the previous study, ^{Arétouyap et al. (2015)} used an empirical linear relationship between K_σ and the resistance R of the aquifer, where K and σ represent the hydraulic conductivity and the electrical conductivity of the aquifer respectively. Yet in the present investigation, the aquifer hydraulic conductivity is the ratio of the transmissivity to the saturated thickness. Note that transmissivity values are derived from modified transverse resistance computed thanks to an empirical relationship between MTR and T. Furthermore, the present study has increased the number of reference boreholes, top to 14.

Figure 10 Comparison between aquifer parameters obtained respectively from former approach and newer one. 

Validation of the approach

The equation used to determine hydrodynamic parameters from this approach isan empirical relationship (Table 3). In order to assess its reliability, the values of transmissivity obtained experimentally from pumping tests and those computed analytically using equation 8, as shown in Table 5, we compared.

This comparison shows an absolute random ranging from 0.003 to 1.576 with an average value of 0.38, which is bearable. Thus, this method that has already been proven inthe Quaternary and Paleogene aquifers in the semi-arid Khanasser valley region of Northern Syria (^{Asfahani, 2016}) can also be used in the Pan-African context.

Further conditions on the approach

Since VES results are highly influenced by electrical noise, land use and other economic activities such as agriculture, livestock, tannery etc., measurements may be carried out in locations far away from any electrical line from several anthropogenic activity centers. K values are generally influenced. In order to mitigate such negative impacts, VES measurements may be calibrated and their 1D quantitative interpretation must necessarily reflect the aquifer lithology. This is the case of VES measurements presented in the present study. Geostatistical analysis largely contributes in assuming that VES data are not influenced by electrical noise.

Contamination is another technical concern. The methodology proposed by ^{Asfahani (2016)} and applied in this paper is entirely based on water resistivity. Any contamination of that water may affect and modify its resistivity, and by consequence will affect the K values. This methodology must therefore be applied in a proper area, without any contamination influence. If this is not the case, the contamination factor and its influence on water resistivity must be calibrated and moved away. Fortunately, our study area is free of any relevant contamination.