Application of Three Electrical Resistivity Arrays to Evaluate Resolution Capacity of Fractured Zones at Apatara Farms, Iwo, Osun State, Nigeria

The study applied three different electrical resistivity arrays (Wenner, dipole-dipole, and Pole-dipole) based on their resolution capacity to delineate fractured zones at Apatara Farm in Iwo, Osun State, Nigeria. Theoretical apparent resistivity data were computed for each model and contaminated with 5% Gaussian noise as a further concession to real field conditions. The simulated results revealed that the Wenner array gave the least error in trying to reconstruct the true model when the fractured zone is placed near the subsurface. However, when the fractured zone is placed at a depth beyond 5 m, the Dipole-Dipole array gave a better resolution than Pole-Dipole and Wenner array in decreasing order of resolution. The study further revealed that the Wenner array is less susceptible to edge effect at shallow depth while Dipole-dipole is more susceptible to edge effect at deeper depth followed by the Pole-dipole array. 2D electrical resistivity field measurements were carried out to confirm the results of the numerical simulation in the same field using the same parameters. The inverted resistivity images showed that the fractured zones are well delineated by the Dipole-dipole and Pole-dipole arrays but poorly resolved by the Wenner array. The study has demonstrated the usefulness of numerical modelling for imaging of fractured zone necessary for hydrogeological purpose and through modelling, the user has unlimited power to image or simulate a real-world scenario seamlessly before carrying out the actual field survey. Keywords : Electrical resistivity array; fractured zones; finite element method; 2-D models; resolution, mean absolute error

Ambiguity in the interpretation of electrical resistivity dataset as well as other geophysical datasets can be reduced by numerical modelling. This allows one to exploit information of variable value from experience. For example, available well log information can be used to formulate a model, calculate the expected electrical resistivity responses, and subsequently design an efficient field survey to test the hypothesis. Alternatively, one could iteratively adjust a geologic model until the theoretical results fit the existing field measurements (Ojo and Olorunfemi, 2013). For example, the detectability of various two-dimensional earth models using multi-electrode systems in a noisy environment has been studied by (Sandor et al., 2011;Szalai et al., 2014). Such models are representative of fractured zones which are discontinuities in crystalline basement rocks generated by tectonic forces or intrusion of magmatic bodies (George et al., 2013). Hydrologically, they are regarded as structures favourable for the accumulation of groundwater in the subsurface. To image these structures, the Electrical Resistivity Tomography (ERT) method has been used successfully overtime and has proven to be a valuable geophysical tool for solving environmental, engineering and groundwater problems (Francese et al., 2009). Asides, mapping of fractured zone is also important for civil engineering developments Alagbe et al., 2013).
To obtain a reliable and high resolution geoelectric model of the subsurface, an appropriate electrode array must be adopted for the data acquisition to ensure maximum anomaly information, high signal to noise ratio and reasonable data coverage (Loke, 1999;Okpoli, 2013). The appropriate electrode array can be determined and an idea of the anomaly responses can be obtained at the planning stage of the survey using forward modelling rather than trial by error on the field. The usefulness of this was demonstrated by (Xianjin and Lagmanson, 1999) for mapping horizontal and vertical conductor using different electrode arrays. Recently, the use of nonconventional electrode array such as the quasi null arrays has been carried out by (Szalai et al., 2015). However, their practicality and limited knowledge of data interpretation restricted their use. This necessitated further investigation into the use of conventional electrode configuration such as Wenner, Dipole-Dipole and Pole Dipole arrays.
Therefore, in this study, we investigated the resolution capacity of these three conventional electrode arrays to delineate fractured zones at Apatara Farms, Iwo, Osun state using finite element Method (FEM) modelling approach.

MATERIALS AND METHODS
Study area: Apatara Farms (Fig.1) is located in Iwo town, Osun State which is in South-Western Nigeria. It lies between latitudes 6°50'N and 8° 10'N and longitudes 4°00'E and 5°l0'E. The prevailing climate is distinctly tropical with four climatic seasons (Iloeje, 1976). These include the: long dry or harmattan season (November -March); long wet season (March -July); short dry season (July-August) and short wet season (August -November). Geologically, Osun State is underlain by Precambrian rocks of the basement complex of Nigeria. Several varieties of these rocks possess appreciable degrees of economic mineralization. It has been reported that deep weathering profiles, erosion surfaces and alluvial deposits have accumulated important mineral deposits such as Laterites, Talc and Gold in stream sediments (Ajeigbe et al., 2014). Data Acquisition: In order to achieve the objectives of this study, the methodology was grouped into two: the synthetic modelling and real field collection.
Numerical modelling :The governing equation for boundary value related to the Direct Current (DC) resistivity forward problem can be expressed by the equation of continuity considering the mixed boundary condition given by Eq.(1) (Rücker, 2011) ….. (1) where is the conductivity distribution in the ground, J is the source current density and "u" is the electrical potential. Solving the forward problem requires the computation of the theoretical response for a given set of input model parameters, using the appropriate equations that relate the model to the data.
The fundamental FEM principle provides the approximated solution U h belonging to N discrete points (nodes) within the domain. This can be solved for a set of appropriate weighting functions w.
(2) to the weak formulation given by Eq.
(3), and determining the unknown weighting function using the Galekin's criterion (w j =N j ) (Zienkiewicz, 1977), the FEM approximation for the DC resistivity forward problem can be obtained as stated in Eq.(4).

….. (4)
With j = 1,……… N The FEM solution presented by Eq. (4) was implemented in the EM2DMODEL software developed at the Korea Institute of Mining and Geology (KIGAM) (Yi et al., 2003) and used for the numerical modelling in this paper. Using the EM2DMODEL software, the theoretical responses for the Wenner (Wen), Dipole-Dipole (Dpdp) and Pole-Dipole (Pdp) electrode arrays over the various 2-D earth models were computed. For the synthetic case, forty-eight generic 2-D earth models of geological relevance were simulated based on the known stratigraphy in basement complex terrain. These include: the top soil, weathered layer, fractured basement and fresh basement. However, only five of these models were reported in this paper. Example of reasonable estimates of the thickness and resistivity values for different lithology in the basement complex is summarized by (Olorunfemi, 2008) and presented in Table 1 where the 2-D resistivity models representative of different lithology in the subsurface were assigned different resistivity values with varying thicknesses and depths of burial. As a further concession to real field conditions, the theoretical apparent resistivity data computed for each model was contaminated with 5% Gaussian noise (Press et al., 1996).  Real field data: To further investigate and verify the results of the numerical simulation, a resistivity field survey was carried out over an established fault zone at Apatara Farms, in Iwo, Southwestern part of Nigeria with the same model parameters used in numerical modelling. The two-dimensional (2D) electrical resistivity imaging was carried out along four traverses with each of length 200 m (Fig. 1). The PASI resistivity meter was used for the data collection. Like in the synthetic cases, the three conventional electrode arrays used were the Wenner, Dipole-Dipole, and Pole-Dipole with electrode spacing in the range of 10 to 60 m.
Data Processing: Both the apparent resistivity measurements for the synthetic and field data were processed in order to obtain the true resistivity distribution using the DIPRO inversion software. It is a 2.5D inversion code that solves the forward problem of electrical resistivity using either the finite difference method (FDM) or the finite element method (FEM). In this study, however, the 2.5D FEM was used. We  It is also observed that inverted resistivity of fractured zone for dipole-dipole is extremely high at the contact with fresh basement signifying the reflection of basement resistivity. This is tagged as "edge effect". Wenner array is less susceptible to this effect.   To understand the depth resolution capacity of the three electrode arrays, plots of model misfit against depth are presented in Figs. 3(a -c). Graph of MAPE against depth is represented by solid lines while RMS against depth is represented by broken lines. Also, the model misfits estimated for the fractured zone are presented in Table 2 give RMS in the range of 1.2-7.2%, MAE (0.7-1.6%), MAPE (0.2-1.6%) for Wenner array. Pole-Dipole gives misfit ranging from 1.2-37.9% for RMS, MAE between 0.6 -6.6% and MAPE from 0.2-6.6% when the fractured zone is located at the surface. This implies that the Wenner gives the least model misfit when the fractured zone is placed at the surface followed by Pole-Dipole while Dipole-Dipole gives the highest misfit. This suggests that the Wenner array is preferable and efficient for delineating near surface fractures. With increasing depth of the fractured zone, the model misfit estimated for each array increases but gives approximately the same value at 5m depth. Generally, this indicates a decrease in the resolving power of each electrode array with increasing depth of burial of the fractured zone. However, the misfit error values using the Dipole-Dipole array is smaller than other arrays with increasing depth beyond 5 m as shown in the Figs. 3(a -c). Thus, the Dipole-Dipole array is preferable and more reliable for imaging fractures at deeper depth. This verifies the conclusions of (Sandor et al., 2011;Szalai et al., 2014)     The field inversion results (Fig.4) (Perren, 2005) where the Wenner array has been said to be insensitive to vertical structure unlike Dipole-Dipole which has geoelectric contour patterns that are almost vertical. Based on the results of this study, Wenner array can only be used to delineate shallow vertical structure and an improved resolution is expected if the fractured zone has appreciable width of not less than two times the electrode spacing used. Likewise, the actual geometry of the fractured zone might be difficult to delineate when the pole dipole electrode array is employed. Conclusions: This paper investigated the resolution capacity of three electrode configurations -the Wenner, dipole-dipole and pole-dipole at imaging fractured zone of different resistivity, thicknesses and depth of burial. The resolution capacity of the electrode arrays was determined in terms of the model misfit errors. Generally, the true resistivity values of the models were fairly reconstructed and underestimated. The importance of numerical simulation for survey design and planning prior to field data acquisition has been underscored in this study as time and cost will be minimized.

Acknowledgments:
The authors wish to express their sincere appreciation to Tertiary Educational Fund (Tetfund) for funding this research and the University of Lagos, Nigeria for creating an enabling environment to conduct the research. Also, we are grateful to the anonymous reviewers for their useful criticism which has improved this manuscript.