Modeling of groundwater yield by the electrical method case of the Triassic sandstone aquifer (Tataouine SouthEastern Tunisia)

The method of electrical resistivity has proven very effective in the evaluation of groundwater. This specialized technique uses Dar-Zarrouk (D-Z) parameters in the estimation of longitudinal unit conductance, transverse unit resistance, and longitudinal resistivity to examine the groundwater level, to distinguish the fresh, brackish, and saline water interface, and to assess the storage capacity of groundwater in the Triassic sandstone aquifer system in the Tataouine region (South-Eastern Tunisia). In this context, 23 vertical electrical soundings (VESs) were carried out in the Tataouine region using the Schlumberger con ﬁ guration with a current electrode with a maximum spacing of the current electrodes (AB) of 500 – 600 m. The results indicate that the study area consists of three types of aquifers: (i) silt/clay saline water ( < 20 Ω m), (ii) a mixture of sand and clay freshwater (20 – 40 Ω m), and (iii) sand freshwater (40 – 200 Ω m). These sand freshwater aquifers are characterized by low longitudinal unit conductance (0 – 2.8 S), high values of transverse unit resistance (more than 9,000 Ω m 2 ), and longitudinal resistivity (more than 35 Ω m) and are mainly concentrated in the north, south, and south-west regions of the study area. It should also be noted that the coef ﬁ cient of anisotropy ( λ ) overlaps and does not clearly differentiate the characteristics of the aquifers of fresh, brackish, and saline water. An interpretation of VESs can also determine the storage capacity of groundwater by determining yield index values. Groundwater supply for the entire study area was classi ﬁ ed as low yield, with a percentage of 13% and a maximum of 31% of the study area and 56% of moderate yield. Lastly, the real data from the drilling con ﬁ rm all these results presented previously. The ﬁ ndings suggest that D-Z parameters are useful for making a distinction of various aquifer zones.


INTRODUCTION
In the Tataouine region, the sandstone aquifer of Triassic at the below-to-medium level constituted the most precious resources in terms of quantity and quality, giving a rich inventory of drinking water to the principal urban communities of the locale and providing an abundant supply of drinking water to the main cities of the region (Smar, Kirchaou, Tataouine city, Ghomrassen, and Bir Lahmer).
Therefore, it becomes highly important to improve and preserve these resources. Geographically, the study area is region favor direct infiltration of runoff water into these sandstone units, thus forming an aquifer unit with freshwater. On the other hand, in the Bir Lahmer area, the lower aquifer is covered by a thick series of more or less waterproof monk clay, which delimits the runoff direct supply. Logs from wells entering the test holes indicate that the middle of the study area occupied by a thick series of clays is considered an area with no aquifer potential. Figure 3 (Duan a, b, ) accompanied by a succession of periods of drought.
Extreme climatic conditions (high temperature and extremely low precipitation) and increased water demand in arid zones could significantly affect water supply availability and water demand patterns (Duan & Kaoru ).
Therefore, it became necessary to evaluate these groundwater resources. The evaluation of the quality and quantity of hydraulic resources in the arid zone is carried out by several methods such as the statistic method of chemical analyses, the use of meteorological data (Kansoh et al. ), and salt concentrations (Obianyo ), but these methods are a bit expensive and time-consuming. In the same context, in an effort to provide more drinking water to the various regions, competent departments concentrated on digging many wells (but they were an expensive and time-consuming exercise). Apart from these disadvantages, the water in these wells is sometimes highly saline, making it unfit for both consumption and agricultural use. We, therefore, adopted an alternative method, which is a new geophysical method by electrical prospecting of D-Z parameters. This allows us first to assess the groundwater, then to determine the interface between fresh, brackish, and saline water, and finally to evaluate the storage capacity of groundwater in the Triassic sandstone aquifer system in the Tataouine region (South-Eastern Tunisia). The scope of this work was to assist the government agencies plan, develop, and manage groundwater resources in the Tataouine region in collaboration with the Tataouine Regional Agricultural Development Commissioner (RADC).
Our work is subdivided into five parts: First, from the apparent resistivities, a pseudo section is built, which provides a fairly clear picture of the variation in the apparent resistivities both laterally (depending on the profile) and vertically (in-depth). It highlights, especially by the contrasts of resistivities, the risks involved as well as the changes of facies. Then, we determine the ranges of resistivities of the resistance and conductor soils and identify the aquifer levels. This is done by a comparison of vertical electrical sounding (VES) interpretation and lithology, since it is considered a necessity for efficient use of electrical data in hydrogeological research (George et al. ). The changes in the resistivity of the grounds are linked to geological parameters such as the type of rock, porosity, and degree of saturation. Indeed, dry sand or gravel usually yields high resistivity, since their pore spaces lack water content for such materials. Usually, water aquifers of high resistivity are found in sand or gravel. On the other hand, the aquifers constitute altered rocks and the clayey materials present an average-to-low resistivity. Then, we use the parameters D-Z, that is, the longitudinal unitary conductance (Sc), the transverse unit resistance (Tr), and the longitudinal resistivity (ρl), to differentiate the zones of fresh, brackish, and saline water in the first step and to subsequently evaluate the groundwater yield index. Finally, we will confirm all these results by the real data of drilling ( Figure 4).
Several studies were carried out within this study area, most of them focusing on the determination of the hydrogeological characteristics (thickness, salinity, piezometric level, flow, transmissivity, etc.), geochemistry and geometric configuration, and the geographical delineation of each level, but none of them considered the aspect of determination of the interface between fresh and saltwater and then the evaluation of the storage capacity of groundwater. These two important aspects are our main focus.

MATERIALS AND METHODS
VESs were performed at the Tataouine region with Schlumberger configuration, as shown in Figure 1. The maximum current spacing of the electrodes (AB) was maintained between 400 and 500 m (AB/2 ¼ 200-250 m). The unit measured is the apparent resistivity, and ρ is plotted on the bilogarithmic paper as a function of AB/2 in meters, resulting in a VES curve, using IpI2Win software (IpI2Winv.2.1Usersguide 2001).
Both a qualitative and a quantitative interpretation of the VES curve was done, and the qualitative analysis involved a visual examination of the pseudo sections and the sounding curves. Although the soundings were also quantitatively interpreted, the findings were interpreted in terms of geoelectric parameters (i.e., resistivity and thickness of the layer). Subsequently, the geoelectric parameters were combined into single variables, in other words, known as the Dar-Zarrouk (D-Z) parameters (Mailet ).
However, in the present study, based on the parameters of D-Z (longitudinal unit conductance Sc, transverse unit resistance Tr, and longitudinal resistivity ρl) we delineated the interface of fresh, brackish, and saline waters; in the second stage, we relied on the coefficient of anisotropy (λ) and total transverse resistance (Tr), i.e., (λ*Tr) to calculate the groundwater supply index value, which proved very useful for determining and assessing groundwater supply.
The groundwater yield index was used for validating the groundwater supply throughout the study area.

Pseudo section
The pseudo section is a qualitative approach that shows the lateral and vertical variance of the apparent resistivity. The locations of the profiles are shown in Figure 1.
The pseudo section following profile I ( Figure 5) shows the presence of four highly resistant anomalies over 100 Ωm. The first is at the base of VES 13, and the second is semideep (þ50 m deep) located below SEV 9. These two anomalies reflect the sandstone unity of Inferior Trias. The third anomaly is located below SEV 2, 21, and 18 and is rooted in depth, while the fourth anomaly is superficial and is located at the level of SEV 6, 12, and 1 and does not attack the 50 m depth. These two last anomalies are stuck to the sandstone unit of the Middle Triassic.
Note also that a conductive anomaly located in the middle of the profile shows that the terrain is dominated by clay. The rest of the profile is occupied by average resistivity attributed to clay-sandy or sand-clay soil. We note a slight discontinuity in the lithology accompanied by two fairly contrasting resistivities which reflect that the area is affected by three faults, the first located between VES 9 and VES 14, the second between VES 2 and VES 21, and the third located between VES 21 and VES 18.
The pseudo section following profiles II and III (Figure 6(a) and 6(b)) are of direction E-W that shows the same pace; a resistant anomaly extends almost over the entire profile; it shows the sandstone terrain. There are also clayey-sandstone lenses whose resistivities do not exceed 70 Ωm for profile II and 40 Ωm for profile III.

Analyses of D-Z parameters
A qualitative and a quantitative interpretation of the VES curve was done, and the result of the qualitative  Regarding our study area, Table 1 shows the resistivity ranges of the various formations after interpreting the layer parameters and then comparing them with the lithological logs. A remarkable difference is revealed for the resistivity value range of the study area (Table 1) and that of Table 2: for clay with saline water and clay with freshwater sand. A slight variation in sand, clay, and salinity can alter the values of resistivity, causing uncertainty in interpretation. This uncertainty will make differentiating between fresh and saline aquifers a difficult task. In such a case, an effective method for analyzing and interpreting the data is required to obtain a viable solution for delineating the aquifers of fresh, brackish, and saline water. An analysis of the D-Z parameters (Sc, Tr, and ρl) provides a simple and useful method for understanding the geophysical character of the fresh, brackish, and saline aquifers. These parameters are validated in Table 3.

D-Z Parameters (methods of estimation)
For a horizontal, homogeneous, and isotropic layer, two basic parameters are defined: the layer resistivity (ρi) and the layer thickness (hi) for its h layer (i ¼ 1 for the surface layer). The integration of this parameter into single variables, in other words, is known as Dar-Zarrouk parameters. Mailet in 1974 was the first to introduce the concept of these parameters, which is used as the basis for determining aquifer properties (Niwas & Singhal ). (1) Transverse resistance Tr ¼ h ▪ ρ The unit of Tr is Ohm meter square (Ω-m²).
(2) For n layers, where ρ is the resistivity calculated in ohm meters (Ωm), h is the thickness consecrated in meters (m), and I is the number of layers.
ρl ¼ H=Sc ρt ¼ Tr=H Clay with saline water 3-6 Sand 100 where H is the depth of the bottom-most geoelectric layer. The

Longitudinal unit conductance (Sc)
Typically, longitudinal conductance (Sc; Equation (3)) is used to define the potential target areas of groundwater.
Based on resistivity data from 23 sounding stations, the contour map of the Sc value was established with a contour  Figure 9, which indicates that a marked variation in the variety of Sc values also shows large differences in the magnitudes of saline, brackish, and fresh groundwater. The range of Sc values for saline water in the graph is 7.5-34.88 S, the range for brackish water is 3-7.5 S, and the range for freshwater is 0.5-2.8 S. So, the categorization of the three zones becomes uncomplicated.
Transverse unit resistance (Tr) Figure 10 presents the transverse unit resistance map, Tr, in 23 sounding stations with an interval of 3,000 Ωm 2 . Once again, it furnishes a remarkable distinction between the three regions of the saline, brackish, and fresh aquifers.
It can also be noticed from the map that the contours of saltwater brackish and those of freshwater have a distinct region and are not similar.  3, 5, 7, 9, 10, 11, 13, 15, 18, 19, 21, 22, and 23, which clearly indicate a noticeable difference in the behavior of these aquifers.
The same figure exposes a range of values for the transverse longitudinal (Tr) of saline water, oscillating between 3,000 and 5,317.6 Ωm 2 and between 6,356 and 7,947.3 Ωm 2 and those for brackish water and freshwater aquifers extending from 10,025.12 to 47,746.3 Ωm 2 .

Longitudinal resistivity (ρl)
The ρl has also been used to distinguish between saline, brackish, and freshwater. The 10 m contour interval map is plotted for all values, as shown in Figure 12. These represent very simple, visible, and widely differing ranges in three different regions for the saline, brackish, and freshwater aquifers based on the widths that these have achieved. For the saline water aquifer, the ρl is <15 Ωm; for the brackish water aquifer, it is from 15 to 35 Ωm; and for the freshwater aquifer, it is up to 35 Ωm. A graph of ρl values for the soundings belonging to the saline (VES 4,6,8,14,and 20), brackish (VES 1,11,12,16,17,18,and 19), and freshwater (VES 2,3,5,7,9,10,13,15,21,22,and 23) groups is shown in Figure 13.

Coefficient of anisotropy (λ)
Anisotropy is the result of alternating layers of clay and fine sand, according to Flathe (), while Frohlich () indicates that anisotropy is the impact of the intercalation of   Unlike other parameters such as Sc, Tr, and ρl, the anisotropy contour map ( Figure 14) is not able to distinguish between the three water groups. Figure 15 shows great overlap and does not easily distinguish between the saline, brackish, and freshwater characteristics. The ambiguity of these characteristics can be explained by the irregularity in the proportion of clay and sand. So, we should infer that it is not possible to distinguish the three groups of water aquifers based on anisotropy (λ).

Significance and use of D-Z parameters
Through the research mentioned above, the behavior of Sc, Tr, and ρl with respect to the saline, brackish, and freshwater aquifers was evidently proved. Table 2 illustrates the different resistance levels for understanding subsurface layers in groundwater aquifer systems. With the exception of the ranges of 30-150 Ωm for freshwater areas, which also overlap with sandstone ranges with clay layers (20-40 Ωm), we find that the ranges for different geoelectric layers are very similar and display no wide variation and have overlapping characteristics. Therefore, they establish an ambiguous and speculative condition. In fact, it is difficult to set specific resistance values for fresh, brackish, and saline groundwater because they depend on various factors that are beyond the scope of this article, but the present uncertainties in the demonstration of resistance data can be greatly reduced if the geophysical parameter is clear and easy to identify, supporting the interpretation.
This reduction in uncertainty is based on the D-Z parameters as they provide very good accuracy. They indicate obvious, clear, and widely large ranges for the saline, brackish, and freshwater aquifers, as summarized in Table 4. In addition, it can be noted that the graphic presentations (Figures 9, 11, and 13) and the contour maps of Sc, Tr, and ρl (Figures 8, 10, and 12) agree with the distinction between the three types of aquifers, brackish, saline, and freshwater, for the entire study area. If these parameters are implemented consistently and correctly, the ambiguity generated by the interpretation of the resistivity data may be minimized. Therefore, in any virgin area, the above-illustrated techniques must be performed and useful and applicable ranges of Sc, Tr, and ρl must be defined for that area. This helps regional authorities to select     Finally, this study is of vital importance for this aquifer, as it helps reduce the margin of error when researching and exploring areas of high yield and good quality. It also reduces the uncertainty resulting from the interpretation of the resistivity data. Therefore, researchers like us can apply this study to other regions whose groundwater experiences ambiguities in the distribution of fresh, brackish, and saline water. However, the limitation of this study is its unsuitability to areas with complex geological settings.

CONCLUSION
In order to obtain a knowledge of the geoelectric characteristics of the subsurface sequence, aquifer geometry, and fresh, brackish, and saline water, a geoelectric investigation of groundwater potential was performed around Tataouine and Bir Lahmer, South-Eastern Tunisia. We also suggested a detailed method of combining all parameters that are significant for determining groundwater potential. This article confirms some of the results of the previous study and exposes further details and a clear demonstration of the distinction of the three groups of aquifers from evaluations of the parameters of D-Z, i.e., Sc, Tr, and ρl. We concluded the following from this study: one can deduce that the North and South-East parts of the study region are characterized by a low value of Sc <2.8 S, and values of Tr range between 9,000 and 44,000 Ωm² and ρl >35 Ωm, and this zone reflects fresh groundwater. The rest of the study area is occupied by brackish to saline water. Thus, the D-Z parameter allows an easy distinction between the three groups of aquifers (fresh, brackish, and saline water). In addition, the value of the groundwater production capacity index less than 13,088 G.W.Y.I. implies a low or extremely low yield, that between 15,196 and 28,206 G.W.Y.I. implies a moderate yield, while a value of 30,000 G.W.Y.I. and above represents a high yield. These yield values are validated by the drilling data.
The interpretation of these parameters is considered to be  an easy task, can be efficiently done, and is not a time-consuming affair. It also helps the competent departments to choose less salty areas for drilling wells in order to augment water resources in the region.