Fabrication of resistivity meter and its evaluation within shallow depth of investigation

The high cost of imported and popular resistivity meters has led many geoscientists, geophysical companies and tertiary institutions to go for locally fabricated resistivity meters. These demands and interests in the locally made resistivity meters inspired the authors for solution by designing and fabricating a resistivity meter with voltage and current output. For its evaluation and comparison, the fabricated resistivity meter and ABEM SAS 300 terrameter were used to carry out the same investigations at the same locations in different parts of Nigeria. The investigations carried out involved horizontal profiling (HP), using Wenner configuration and vertical electrical sounding (VES), using Schlumberger configuration. The results obtained are presented as tables, graphs and sounding curves. The RMS errors of the sounding curves generated from VES, range from 2.5 to 4.1. The comparison of the field data obtained from both meters showed good correlation.


Introduction
Procurement of imported resistivity meters by geoscientists, geophysical companies and institutions of higher learning is becoming unaffordable or impossible in Nigeria. This is consequent upon the cost implications, resulting from very high exchange rate, of purchase of the imported resistivity meters, importation duties and logistic of shipment from the manufacturer to the country. This has resulted in many geoscientists, geophysical companies and tertiary institutions developing more interest and demand for locally fabricated resistivity meter. As a result of unavailability of the resistivity meter in many universities in Nigeria, students and researchers usually hire from private companies or agencies [1]. Many times, when these imported meters get damaged, they have to be sent back to the source for repair and this always resulted in waste of financial resources on shipment cost (to and from the manufacturer) and delay in on-going research.
Resistivity meter is used to carry out investigations in electrical resistivity method. Electrical resistivity method has been widely and routinely used for hydrogeological, engineering and environmental investigations [2,3,4,5,6,7,8,9,10]. This method utilizes direct currents or low frequency alternating currents. In the resistivity method, artificiallygenerated electric currents are introduced into the ground through a pair of current electrodes and the resulting potential differences are measured through a pair of potential electrodes at the surface [11] in order to obtain subsurface layers resistivities. Soil resistivity is the key factor that determines what the resistance of a grounding electrode will be [12].
Inspired by the great demand for locally made resistivity meter, the authors have provided solution on how to design, construct and fabricate resistivity meter with voltage and current output for shallow investigation.

Theory of electrical resistivity method
In electrical resistivity survey, electric current (I) is passed into the ground through current electrodes (A and B) and the resulting potential difference (ΔV) is measured between the potential electrodes M and N. The resistivity of the subsurface medium is derived by the division of the values ΔV by I multiplied by the geometric factors of the electrode configuration used.
By considering a cylindrical conductor of length L and a cross sectional area A ( Figure 1) with current (I) being passed through it, the resistance (R) can be derived as: where ρ which is the proportionality constant is referred to as the resistivity in ohm-meter (Ω-m). The relationship of the current (I), potential difference (ΔV) and resistance (R) is established by Ohm's law as: The combination of equation (2) and (5) gives:  The potential at electrode M due to current at electrode A is given as The potential at electrode M due to current at electrode B is given as The potential (VMA,MB) at an interval electrode M is the sum of the potential contribution VMA and VMB from the current source A and the sink B respectively: The potential at electrode N due to current at electrode A is given as The potential at electrode N due to current at electrode B is given as  The potential (VNA,NB) at an interval electrode N is also the sum of the potential contribution VNA and VNB from the current source A and the sink B respectively: Since absolute potentials are difficult to monitor, hence the potential difference (ΔV) between electrodes A and B is measured by [11]: This is the generalized resistivity equation for any electrode array system. Equation (18) could also be written as ρ = GR Where G is the geometric factor of the array. Many electrode arrays (configurations) are employed in resistivity method. Electrode array is the pattern of arrangement of the current and potential electrodes. The most common electrode configurations are Wenner and Schlumberger configurations.

Instrumentation
The designed meter is divided into different operation units. These units are power source, inverter, rectification, smoothing and metering. The block and circuit diagrams for the designed meter are shown in Figs. 4 and 5 respectively. A 12V battery was used as the power supply source. The inverter unit was used to convert the low voltage from the direct current (DC) from battery to high voltage alternating current (AC). In the rectification unit, a bridge rectifier was used to produce a full wave rectification. A bridge rectifier can be obtained either by using four separate individual diodes or a specially made one containing four diodes already joined together. Smoothing was carried out by connecting a large value electrolytic capacitor connected across the DC output of rectification unit. This capacitor acts as a reservoir to smoothing the effect of rectification. The metering unit which consists of two multimeter were used in taking the current and the voltage readings separately.

Field procedure and techniques
For the field procedure, both the current and potential electrodes were connected to this meter through four reels of wire. The direct current generated from the fabricated resistivity meter was introduced into the ground via currents electrodes by pressing the 'Send' button ( Figure 6) on the meter. The resulting potential differences were measured through a pair of potential electrodes. Both the current (I) and voltage (V) readings were read from the two multimeter, set to direct current and direct voltage modes separately. The resistance (R) was then calculated using Ohm's law, which states that V = IR.
Two field techniques were adopted in order to evaluate the fabricated resistivity meter. These were horizontal profiling (HP) and vertical electrical sounding (VES). Horizontal profiling was used to investigate lateral variations in ground resistivity with respect to a particular datum. The VES was used to investigate vertical variations of ground resistivity. Wenner electrode configuration was adopted for HP while Schlumberger configuration was adopted for VES. Inter electrode spacing of a = 10 m was used for the Wenner configuration. A maximum spread of AB/2 = 100 m was used for the Schlumberger configuration.

Figure 6
The fabricated resistivity meter.

Results and discussion
Both the fabricated resistivity meter and the imported ABEM SAS 300 terrameter were used to carry out the same investigations at the same locations in different parts of Nigeria. The different parts of the country investigated span from basement complex to sedimentary rocks environment. The area covered were Ibadan, Ogbomosho, Oyo town, Iseyin, Abeokuta, Ile-Ife, Ado-Ekiti, Akure, Ondo town, Owo, Akungba, Ikare, Ore, Ode-Aye, Okitipupa, Igbotako, Igbokoda, Auchi, Benin, Ikeja and Igarra (Figure 7). A total of fifty-two (52) horizontal profiling and, one hundred and eight (108) vertical electrical soundings were conducted across the study area. The results obtained from the fabricated meter were compared with that of the ABEM SAS 300 terrameter which served as a well-known imported meter. Tables  1 and 2 show the results of the typical field data for the horizontal profiling (HP) from site 3 in Akure. Figures 8 and 9 show the respective graphs of the obtained HP. The typical field data for some of the obtained VES are presented as tables (Tables 3, 4 The relationship between the apparent resistivity data obtained from both meters was established and presented in graph form (Figure 14). The apparent resistivity data for both horizontal profiling and vertical electrical sounding for the fabricated meter were plotted on x-axis against its corresponding apparent resistivity data for the ABEM terrameter on the y-axis. A linear relationship was obtained and a straight line was fitted by regression to obtain coefficient of correlation. About one thousand, eight hundred and ten (1,810) data points were used to generate this graph. The coefficient of correlation (R 2 ) had a value of 0.993. The high coefficient of correlation established the reliability of the fabricated resistivity meter.

Figure 10
Sounding curve for the fabricated resistivity meter from site 1 (Akure).

Figure 12
Sounding curve for the fabricated resistivity meter from site 2 (Owo).

Figure 14
Graph showing relationship between the resistivity data obtained from fabricated resistivity meter and ABEM terrameter.

Conclusion
In conclusion, comparison of the results obtained from the fabricated resistivity meter with the imported ABEM SAS 300 terrameter showed good correlation. This has erased the negative thinking that locally made resistivity meters are not accurate and reliable. It should be noted that depth of investigation for this locally made meter here is only for shallow depth investigation (a depth of less than 40m). More researches are going on for fabrication of improved and advanced locally made meter for deeper depth investigation.