A Hydrogeophysical Model of the Relationship between Geoelectric and Hydraulic Parameters, Central Jordan ()
1. Introduction
The development of groundwater resources and the regime of its activity largely depend on the porosity and permeability of water bearing formations. The porosity of rock is a measure of the amount of interstitial space that is capable of holding fluids and the permeability (hydraulic conductivity) of a rock is a quantitative measure of the case with which it will permit the passage of fluids through it under a hydraulic gradient. The determination of aquifer characteristics such as hydraulic conductivity and transmissivity is best made on the basis of data obtained from test pumping wells. These properties are important in determining the natural flow of water through an aquifer and its response to fluid extraction. This paper examines the influence of aquifer anisotropy on the relationship between hydraulic and geoelectrical parameters of aquifers that are needed to develop a hydrogeophysical model for an anisotropic aquifer in parts of central Jordan.
An alternative approach for estimating aquifer characteristics is the use of surface geoelectrical methods. Many investigators have studied the relationship between electric and hydraulic parameters of aquifers. Jones and Buford [1] measured the formation factor and intrinsic permeability of sand samples and found that as the grain size increase, the formation factor and intrinsic permeability also increases. A relation between the aquifer intrinsic permeability and formation factor was developed for a given porosity range [2]. The resistivity and the formation factor of an aquifer have been correlated with the permeability [3]. Empirical and semi-empirical relations between different aquifer parameters and the parameters obtained by geoelectrical soundings under different geological conditions have also been studied by others [4–13]. The analytical relations between aquifer transmissivity and Dar-Zarrouk parameters have been developed and various data sets tested [14,15]. An inverse relationship between porosity and hydraulic conductivity were used to explain the direct correlations between formation factor and hydraulic conductivity [16,17]. Here we present the Schlumberger sounding results in the area of central Jordan to define the aquifer geometry of the study area.
2. Geology and Hydrogeology
2.1. Geological Setting
Physiographically, the study area lies between latitude 31o 29.54¢ N to 31o 45.03¢ N and 35o 59.58¢ E to 36o 14.56¢ E, central Jordan (Figure 1). Jaser [18] has given the detailed geology of the area. Bedrock in the investigated area is of sedimentary origin and of Upper Cretaceous to recent age (Figure 1). The oldest outcrops in the area are the Amman Silicified Limestone (ASL) Formation (of Campanian age) of the Balqa Group. In the mapped area (Figure 1), the rock formation consists of
Figure 1. Geology map of the area (after Jaser [18]) and positions of geoelectrical soundings and wells.
Table 1. Stratigraphic column for the geology of northern Jordan (after Rimawi et al. [19]).
Table 2. Summary of results from computer modeling for all sounding stations.
limestone, chalk and chalky limestone. The overlying Al-Hisa Phosphorite (AHP) Formation, which belongs to the Balqa Group (Maestrichtian-Campanian in age) consists of limestone and phosphate with chalk and chalky marl units. These are overlain by sediments consisting of marl, chalk and chalky marl of the Muwaqqar Chalk-Marl (MCM) Formation belonging to the Balqa Group of Maestrichtian to Paleocene age. The overlying chalky limestone and chert of the Umm Rijam Chert-Limestone (URC) Formation (Eocene in age) belongs to Balqa Group. Surficial deposits are: marl, clay, sand and gravels of Holocene to Recent age.
2.2. Hydrogeology
Generally, the groundwater aquifers of Jordan are divided into three hydraulic complexes: Deep Sandstone Aquifer Complex, Upper Cretaceous Aquifer Complex, and Shallow Aquifer Complex (Table 1). Although this study is concentrated on the Upper Cretaceous Aquifers (namely B2/A7 aquifer), it is important to indicate the significant role of the Deep Sandstone Aquifer Complex where they occur in the adjacent highlands. They may contribute to the recharge of the Upper Cretaceous aquifers as upward leakage [19].
Based on the lithology log data of 23 wells from the study area, we divide the area into two distinct hydraulic units: Hydraulic unit-1 towards the northern and central parts comprised of almost sorted material (mainly limestone) with low uniformity coefficient and another unit comprising of unsorted materials (limestone and chert) with relatively high uniformity coefficient occurring towards the southern parts (Hydraulic unit-2) (Figure 1).
3. Field Studies
Surface resistivity methods have been used in groundwater research for many years. Earth resistivities are related to important geologic parameters of the subsurface including types of rocks and soils, porosity, and degree of saturation. The detailed description of this method is available in [20]. In general, the resistivity method involves measuring the electrical resistivity of earth materials by introducing an electrical current into the ground and monitoring the potential field developed by the current. The most commonly used electrode configuration for geoelectrical soundings, and the one used in this field survey, is the Schlumberger array. Four electrodes (two current A and B and two potential M and N) are placed along a straight line on the land surface such that the outside (current) electrode distance (AB) is equal to or greater than five times the inside (potential) electrode distance (MN). Vertical sounding, in Schlumberger array, were performed by keeping the electrode array centered over a field station while increasing the spacing between the current electrodes, thus increasing the depth of investigation.
The potential difference (rV) and the electrical current (I) are measured for each electrode spacing and the apparent resistivity (ra) is calculated by the equation:
(1)
where
(2)
is the geometrical factor that depends on the electrode arrangement for the Schlumberger array.
An integrated approach of hydrogeological and geoelectrical soundings surveys has been used to study the relationship between the geoelectric and hydraulic parameters in the central part of Jordan. Data from 23 deep wells are available, on which pumping tests have been conducted. The pumping test data were analyzed and the aquifer hydraulic parameters (hydraulic conductivity, transmissivity and water resistivity) have been evaluated by Water Authority of Jordan in 2006. The geophysical field work in this study included recording of 23 vertical electrical soundings (VES) carried out in the fall of 2006. The VES were recorded up to a maximum electrode separation of 2000 m. The VES soundings were conducted with the help of Iris Syscal R2 resistivity instrument in the close vicinity of deep wells as shown in Figure 1.
A preliminary interpretation of the sounding curves using partial curve matching [21] provides the initial estimates of the resistivities and thickness (layer parameters) of the various geoelectric layers. The layer parameters derived from the graphical curve matching were then used to interpret the sounding data in terms of the final layer parameters through a 1-D inversion technique (RESIX-IP, Interpex Limited, Golden, Co., USA). Inversion analyses of the sounding curves have been made with an average fitting error of about 5%. Quantitative interpretation of geoelectrical sounding curves is complicated due to the well known principle of equivalence [22]. Data from the two boreholes (CD1245 and CD1232, Figure 1) was used to minimize the choice of equivalent models, by fixing thicknesses and depths to certain levels and allowing the adjustment of resistivity. Correlation between VES interpretation at stations 8 and 19 and borehole lithology determines the electrical characteristics of the rock units with depth (Figure 2). Table 2 presents the results of interpretation of the VES stations.
Figure 3 is a typical sounding data plot and best-fit four-layer model for one selected sounding data. On the left, Figure 2 shows the Schlumberger apparent resistivity curve with data (points) superimposed on the best match 1-D inversion (solid line). On the right the figures shows the interpreted results in terms of resistivity and
Figure 2. Comparison of interpreted VES field curves and nearby test-hole logs for two selected sites.
Figure 3. Typical electrical resistivity sounding data and best-fit four layer model interpretation for VES11.
depth together with the allowable range of equivalence (dashed lines). The result of the 1-D inversion of Figure 2 (right) shows a thin topsoil layer about 1 m thick, below which is a 30 m band of chalk and marl representing the upper of the MCM formation with a resistivity value of about 15 Wm. The third unit has higher resistivity values (23 Wm) and considerably thick (about 200 m). This layer represents the lower of the MCM formation. The fourth unit has resistivity values of 60 Wm, representing the saturated zone.
4. Hydraulic Parameters Versus Geoelectric
Figure 4 shows an analogy between the electrical current flow and groundwater flow in layered media. If the flow of electric current is parallel to the geological layering and hydraulic flow [20], the average horizontal hydraulic conductivity (Kh) is given as (3):