CRONOGRAMA 2 3 4 RECURSO S 4.1 Reunión con

All the arrays of electrodes used to obtain the apparent resistivity are variants of the four-electrode scheme. All the arrays are basically superposition of the fundamental equation for the potential from a current source with appropriate sign for the current. The formulas for apparent resistivity are a product of the impedance ^𝑉

𝐼 (Ohms) and a geometric factor with the units of length (meters).

To investigate the resistivity distribution with depth, called a sounding, the arrays are expanded about a center point. In the more general case the apparent resistivities are plotted as a function of array spacing and lateral position using plotting conventions that have become accepted for each

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type of array. The choice of array to be used depends on the objective of the research. Example of some arrays is as follows:

● Dipole-dipole

●Wenner

● Schlumberger

● Pole-pole

● Pole-dipole

For the purpose of this project, the Dipole-dipole array would be employed. The last four arrays will only be mentioned for the sake of completeness.

2.6.1 Dipole-Dipole Array

The dipole-dipole array is very sensitive to horizontal changes in resistivity, but relatively insensitive to the vertical changes in the resistivity and it is useful in mapping vertical structures such as dykes and cavities but relatively poor in mapping horizontal structures such as sills or sedimentary layers (Ewusi, 2006). The dipole-dipole array is logistically the most convenient in the field, especially for large spacing. In the dipole-dipole array, the potential electrodes are situated outside the current electrodes. Each pair has a constant separation and it is such that if the separation between individual pairs is ‘a’, the separation between the separate pairs becomes ‘na’.

The convention for the dipole-dipole array in Fig. 2.7 is that current and voltage electrode spacing is the same, a, and the spacing between them is an integer multiple of a. Therefore 𝜌_𝑎 = 𝜋𝑛(𝑛 + 1)(𝑛 + 2)𝑎^∆𝑣

𝐼

Fig. 2.7 The Dipole-dipole electrode configuration

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This array is relatively sensitive to vertical changes in the subsurface resistivity below the center of the array and less sensitive to horizontal changes in the surface resistivity (Loke, 2000). The Wenner array is now seen to be a simple variant of the pole-dipole in which the distant pole at infinity is brought in and all the electrodes are given the same spacing, a, as seen in the following configuration (Fig. 2.8). In Wenner array, vertical resolution of the various resistivities of the subsurface layers is achieved by increasing the common distance between the electrodes while maintaining the location of the center point of the array. Wenner current and potential electrodes are placed at equal distance from each other. For Wenner array, 𝜌_𝑎 = 2𝜋𝑎 ^∆𝑣

𝐼

Fig. 2.8 The electrode array for Wenner configuration 2.6.3 Schlumberger Array

One of the first arrays used in the 1920’s and still popular today is the Schlumberger array (Fig.

2.9). It is another variant of the pole-dipole, again with the second current electrode placed symmetrically opposite the first. The voltage difference is consequently doubled and so the apparent resistivity is the same as that for the general pole-dipole with a factor of 1/2 in the geometric factor. In a Schlumberger sounding the potential electrodes are usually kept small and fixed while only the s spacing is changed (Loke, 2001). Further, it is conventional to consider the spacing to be the distance from the center of the array to the outermost electrodes, i.e. AB/2. In the Schlumberger array, the current electrodes, separated by AB are symmetrical about the potential

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electrodes, MN. The current electrodes are then expanded and the geometric factor assumes the form. 𝜌_𝑎 =^π(

s2− a2 4 ) a

∆v I

Fig. 2.9 The Schlumberger electrode configuration

2.6.4 Pole-Pole Array

The simplest array is one in which one of the current electrodes and one of the potential electrodes are placed so far away that they can be considered at infinity. This array can actually be achieved for surveys of small overall dimension when it is possible to put the distant electrodes some practical distance away. For a survey in an area of a few square meters “infinity” can be on the order of a hundred meters. The Fig. 2.10 represents a pole-pole array.

𝜌_𝑎 = 2𝜋𝑛^∆𝑣

𝐼

Fig. 2.10 The Pole-pole electrode configuration

2.6.5 Pole-Dipole Array

If only one of the current electrodes is placed at “infinity” the configuration and the apparent resistivity are as shown in Fig. 2.11. This array is used frequently in resistivity surveying and the spacing are usually described, and taken, in integer multiples of the voltage electrode spacing. The standard nomenclature is to call the potential electrode spacing a, pole-dipole sounding data is

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plotted as apparent resistivity versus, a. The pole-pole, pole-dipole and dipole-dipole arrays are normally used in profiling mode to map lateral as well as depth variations in resistivity. The resulting “maps” of apparent resistivity are contoured at constant (usually logarithmic) intervals.

The contoured sections are called “pseudo sections” because they look somewhat like resistivity cross-sections of the ground but they are not, they are simply a graphical representation of the data.

The vertical scale is not depth but some function of the array spacing.

𝜌_𝑎 = 2𝜋𝑟(𝑛 + 1)𝑎^∆𝑣

𝐼

Fig. 2.11 The Pole-dipole electrode configuration

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CHAPTER THREE MATERIALS AND METHOD 3.1 Field Measurement

Preliminary work in the area took the form of reconnaissance survey using global positioning system (GPS) device and VLF-EM method. The three study sites investigated were used previously for road fill, the sites were excavated to depths of about 10m. Two methods of geophysical investigation were used for this research: Very Low Frequency-Electromagnetic method (VLF - EM) and electrical resistivity tomography method. For the design of the geophysical survey, several factors were taken into account, such as the area under investigation and the existing geological and hydrogeological information. The rough terrain and the requirements of increased investigation depths mainly in the region also played an important role in designing this survey. The geophysical survey was conducted in two phases. An initial reconnaissance survey delineated the regions of geological and hydrogeological interest. Based on the reconnaissance survey results, we conducted a high resolution survey using electrical resistivity tomography method, in order to image the subsurface features in the investigated area.