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 2D  and  3D  resistivity  imaging  methods  are  simple,  fast,  inexpensive,  and  relatively  accurate  techniques  used  in geophysical  exploration.  In  this  study,  2D  and  3D  resistivity  imaging  methods  were  used  to  produce  images  of  the subsurface structure of the capitol gate area of the University of Benin, Edo state Nigeria where orthogonal set of 2D geoelectrical resistivity field data were collected using the conventional Wenner array configuration. The observed 2D apparent resistivity data were processed and then collated into 3D data set which was processed using a 3D inversion code. The 3D model resistivity images obtained from the inversion are presented in horizontal and vertical depth slices in contour and block images. This study was carried out to show the effectiveness of 3D geoelectrical resistivity imaging using parallel 2D profiles.



Figure 1.1:  A picture of the study area. (Source: Google – Earth) —————- 4


Figure 2.1:  The arrangement of electrodes for a 2-D electrical survey ———- 13


Figure 3.1:  The flow of current from a point current source ———————- 22


Figure 3.2:  The conventional four electrode array ———————————- 24


Figure 3.3:  Wenner array —————————————————————- 28


Figure 3.4:  Different Wenner arrays ————————————————— 29


Figure 3.5:  Dipole-dipole array——————————————————— 30


Figure 3.6:  Wenner – Schlumberger array ——————————————- 31


Figure 3.7:  Pole-dipole array ———————————————————– 33


Figure 3.8:  The models used in 3-D inversion ————————————– 39


Figure 3.9:  3-D data grid formats —————————————————— 42


Figure 4.1:  The 2-D Imaging for Wenner array obtained

from the survey area (Transverse 1)———————————— 49


Figure 4.2:  The 2-D Imaging for Wenner array obtained

from the survey area (Transverse 2) ———————————– 50


Figure 4.3:  The 2-D Imaging for Wenner array obtained


from the survey area (Transverse 3) ———————————– 51


Figure 4.4:  The 3-D Imaging Horizontal view obtained from


the survey area ————————————————————– 52


Figure 4.5: The 3-D Imaging Vertical view obtained from


the survey area ————————————————————- 52


Figure 4.6:  The 3-D Imaging Linear sensitivity ————————————- 53


Figure 4.7:  The 3-D Model sensitivity ———————————————— 53


Figure 4.8:  The 3-D Horizontal model sensitivity

value obtained from the survey area ———————————– 54


Figure 4.9:  The 3-D Vertical model sensitivity value

obtained from the survey area ——————————————– 54


Figure 4.10: 3-D Horizontal block model obtained from the survey area ——– 55


Figure 4.11: 3-D Vertical block model obtained from the survey area ———- 55



Table 1:        Resistivity‟s of some common rocks, minerals and chemicals ——- 9


Table 2:        2-D Wenner Array Electrical Resistivity Field Record ————— 42



The purpose of electrical surveys is to determine the subsurface resistivity distribution by making measurements on the ground surface. From these measurements, the true resistivity of the subsurface can be estimated. The ground resistivity is related to various geological parameters such as the mineral and fluid content, porosity and degree of water saturation in the rock. Electrical resistivity surveys have been used for many decades in hydrogeological, mining and geotechnical investigations. More recently, it has been used for environmental surveys.


The goal of geoelectrical resistivity surveys is to determine the distribution of subsurface resistivity by taking measurements of the potential difference on the ground surface. For a typical inhomogeneous subsurface, the true resistivity distribution is estimated by carrying out inversion on the observed apparent resistivity values. In environmental and engineering investigations, the subsurface geology is usually complex, subtle and multi-scale such that both lateral and vertical variations in the petrophysical properties can be very rapid. Two dimensional (2D) geoelectrical resistivity imaging has been widely used to map areas with moderately complex geology (Griffiths and Barker 1993; Griffiths et


al.1990; Dahlin and Loke 1998; Olayinka 1999; Olayinka and Yaramanci 1999; Amidu and Olayinka 2006). In the 2D model of interpretation, the subsurface resistivity is considered to vary both laterally and vertically along the survey line but constant in the perpendicular direction. The major limitation of the 2D geoelectrical resistivity imaging is that measurements made with large electrode spacing are often affected by the deeper sections of the subsurface as well as structures at a larger horizontal distance from the survey line. This is most pronounced when the survey line is placed near a steep contact with the line parallel to the contact (Loke 2001).


Geological structures and spatial distributions of sub-surface petrophysical properties and/or contaminants commonly encountered in environmental, hydrogeological and engineering investigations are inherently three dimensional (3D). Thus, the assumption of the 2D model of interpretation is commonly violated. Images resulting from 2D geoelectrical resistivity surveys can contain spurious features due to 3D effects. This usually leads to misinterpretation and/or misrepresentation of the observed anomalies in terms of magnitude and location; and the 2D images produced are only along the survey lines and not the entire investigation site. Thus, geometrically complex heterogeneities cannot be adequately characterized with vertical electrical sounding or 2D electrical

resistivity imaging alone. Hence, a 3D geoelectrical resistivity survey with a 3D model of interpretation, where the resistivity values are allowed to vary in all the three directions, namely vertical, lateral and perpendicular directions, should in theory give a more accurate and reliable results.


In this research, measurements of the orthogonal 2D profiles were made using the conventional Wenner electrode configuration with the aid of an automatic electric imaging device, terrameter SAS 1000.


The observed orthogonal set of 2D apparent resistivity data were collated into 3D data set and then inverted using a 3D inversion code, RES3DINV (Loke and Barker 1996b ). The resistivity sounding was conducted to obtain 2D layering information which aids the interpretation of the 3D geoelectrical resistivity imaging. The survey was conducted, as part of experimental studies to determine the effectiveness of using parallel or orthogonal sets of 2D profiles to generate 3D data set in geoelectrical resistivity imaging, with the aim of determining the subsurface structures of the location of study.



Figure 1.1: A picture of the study area. (Source: Google – Earth)


This work was carried out at the capitol gate region of the University of Benin, Benin City, Edo State Nigeria. This area of study is overlain by different materials which range between loose sandy to very coarse sand. The color of the sediment in this area is brownish or blackish which is of the Benin formation that overlies the entire Niger delta basin.


The Agbada formation underlies the Benin formation and consists primarily of sand and shale. It is of fluviomarine origin. It is the main hydrocarbon-bearing


window. A nearby formation, the Akata formation, is composed of shale, clays and silt at the base of the known sequence. They contain a few streaks of sand. The thickness of this sequence is not known for certain, but may reach 700m in the central part of the Delta.



Most surveys on modern electrical resistivity aim to obtain the true resistivity values of subsurface structures because true resistivity is geologically significant.


Resistivity imaging technique depends on Ohm‟s law, which states that the electric current (I) in a material is proportional to the potential difference across it. The linear relationship between these two variables is expressed by the following equation:


V=IR (1.1)



Where (I) is the current, (V) is the potential difference, and (R) is the resistance. The above equation is the linear relationship between (V) and (I). For a given material, resistance is proportional to length (L) and inversely proportional to the cross-sectional area (A) of the conductor. These relationships are expressed in the following equation:


R = ρ L / A (1.2)

The proportionality constant (ρ) is the resistivity of the conductor. Resistivity, a physical property of materials, is the ability to resist flow of charges. It is the measurement of how strongly a material resists the flow of electric current (Denchik and Chapellier, 2005). Ohm‟s Law states that, “For many materials


(including most metals), the ratio of the current density to the electric field is a constant, σ, that is independent of the electric field producing the current” (Serway and Jewett, 2007)


J = σ E (Ohm‟s Law) (1.3)



The constant of proportionality (σ) is the conductivity of the material, (J) is the current density, and (E) is the electric field. The inverse of conductivity is resistivity (ρ)


E = ρ J (1.4)



For  a  homogeneous  area  with one  electrode, the  potential  separates  radially
away from the  current  source, where the area (A) is a half sphere (2πr²) with
radius (r). Equation (1.2) is rewritten as
ρ = R K (1.5)

Where K = 2πr for a half sphere. Equation 5 consists of two parts. The first part is resistance (R) and the second part is geometric factor (K), which describes the geometry of the electrode configuration.


The geological structures of the ground are inhomogeneous, and the obtained values of resistivity represent apparent resistivity instead of true resistivity (Lowrie, 2007; Reynolds, 1997). Therefore, the resistivity (ρ) in Equation (1.5) changes to apparent resistivity (ρa) in an inhomogeneous area:


ρa= R K (1.6)
Equation  (1.6)  is  used  to  calculate apparent  resistivity, which  depends  on  the
type  of  subsurface  structure  and the arrangement of current electrodes and


voltage poles. True resistivity can be calculated from apparent resistivity with the use of RES2DINV, a commercial software that uses numerical methods to estimate true resistivity and plot a 2D or 3D image (Loke, 2011).





Electric current flows in earth materials at shallow depths through two main methods. They are electronic conduction and electrolytic conduction. In electronic conduction, the current flow is via free electrons, such as in metals. In electrolytic conduction, the current flow is via the movement of ions in groundwater. In





environmental and engineering surveys, electrolytic conduction is probably the more common mechanism. Electronic conduction is important when conductive minerals are present, such metal sulfides and graphite in mineral surveys. (Loke, 2013)


Resistivity surveys give a picture of the subsurface resistivity distribution. To convert the resistivity picture into a geological picture, some knowledge of typical resistivity values for different types of subsurface materials and the geology of the area surveyed, is important.


Table 1 shows the resistivity values of common rocks, soil materials and chemicals (Keller and Frischknecht 1966; Daniels and Alberty 1966).


Resistivity values have a much larger range compared to other physical quantities mapped by other geophysical methods. The resistivity of rocks and soils in a survey area can vary by several orders of magnitude. In comparison, density values used by gravity surveys usually change by less than a factor of 2, and seismic velocities usually do not change by more than a factor of 10. This makes the resistivity and other electrical or electromagnetic based methods very versatile geophysical techniques.

Table 1: Resistivity‟s of some common rocks, minerals and chemicals.




Sandstone 8 –   2.5 – 0.125  
Shale 20 – 2 5 – 0.05  
Limestone 50 – 4 2.5 – 0.02  
Clay 1 – 100 0.01 – 1
Alluvium 10 – 800 1.25 – 0.1  
Groundwater 10 – 100 0.01 -0.1  
Sea water 0.2   5    
Iron 9.074 1.102    
0.01M Potassium 0.708 1.413    
0.01 M Sodium 0.843 1.185    
0.01 M acetic acid 6.13 0.163    
Xylene 6.998 1.429  



This study is aimed at using electrical resistivity data obtained from the capitol gate region of the University of Benin, Benin City in Edo state Nigeria to locate the subsurface geologic features underneath the ground. The specific objective of this study is to show the 3D geoelectrical resistivity imaging of the subsurface of the area under study.


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