Electrical_Methods Schlumberger, Wenner and Dipole Dipole

This power point explains electrical resistivity and their types

1. ELECTRICAL METHODS

2. Introduction There are three categories in electrical methods that are used in mineral exploration These are as follows: Electrical resistivity method Spontaneous (self) potential methods Induced Polarization (IP) methods

3. METHODS ELECTRICAL RESISTIVITY

4. Introduction Electrical resistivity were developed in the early 1900s but become widely used since 1970s. Due to availability of computers to process and analyse the data. Used extensively in the exploration of ground water sources and also to monitor types of ground water pollution, in engineering surveys to locate subsurface cavities, faults and fissures, permafrost, mine shafts, etc , and in achaeology for mapping out the aerial extent of remnants of buried foundations of ancient buildings. Electrical resistivity methods are also used extensively in downhole logging.

5. Application Exploration of bulk mineral deposit (sand, gravel) Exploration of underground water supplies Engineering/construction site investigation Waste sites and pollutant investigations Cavity, karst detection Glaciology, permafrost Geology Archaeological investigations

6. Measuring the conductivity of a rock involves measuring its resistance to the flow of electricity, or its “ resistivity ” .  Conductivity and resistivity are inversely related: high conductivity equates to low resistivity.  In practice, when measuring resistivity several different pairs of electrodes are set up at different spacings.  As the spacing between the electrode pairs increases, the detection depth increases.  In this manner, changes in resistivity with depth can be plotted. 

7. True resistivity Consider an electrically uniform cube of side length L through which a current (I) is passing (Figure below). The material within the cube resists the conduction of electricity through it, resulting in a potential drop (V) between opposite faces. The resistance (R) is proportional to the length (L) of the resistive material and inversely proportional to the cross-sectional area (A). the constant of proportionality is the 'true' resistivity (symbol: ρ ). According to Ohm's Law the ratio of the potential drop to the applied current (V/I) also defines the resistance (R) of the cube and these two expressions can be combined to form the product of a resistance Ω ) and distance (area/length; metres ); hence the units of resistivity are ohm- metres ( Ωm ).

8. (A)Basic definition of resistivity across a homogeneous block of side length L with an applied current I and potential drop between opposite faces of V. (B) The electrical circuit equivalent, where R is a resistor

9. True resistivity can now be calculated as: Resistance (R) is proportional to length (L) divided by area (A): where ρ is the true resistivity. for an electrical circuit, Ohm ’ s Law gives R=V/I where V and I are potential difference across a resistor and the current passing through it, respectively. Resistivity is then given by

10. Resistivities of common rocks/materials and selected ore minerals.

11. Current Conduction in Rocks There are three ways in which electric current can be conducted through rock: electrolytic, electronic (ohmic) and dielectric conduction. Electrolytic conduction Occurs by the relatively slow movement of ions within an electrolyte and depend upon the type of ion, ionic concentration and mobility. Electronic conduction is the process by which metals, for example, allow electrons to move rapidly, so carrying the charge. Dielectric conduction occurs in very weakly conducting materials (or insulators) when an external alternating current is applied, so causing atomic electrons to be shifted slightly with respect to their nuclie.

12. In most rocks, conduction is by way of pore fluids acting as electrolytes with the actual mineral grains contributing very little to the overall conductivity of the rock (except where those grains are themselves good electronic conductors). The resistivity of geological materials exhibits one of the largest ranges of all physical properties,from 1.6 x 10 -8 Ωm for native silver to 10 16 Ωm for pure sulphur. Igneous rocks tend to have the highest resistivities; sedimentary rocks tend to be most conductive, largely due to their high pore fluid content; and metamorphic rocks have intermediate but overlapping resistivities. The age of a rock also is an important consideration: a Quaternary volcanic rock may have a resistivity in the range 10-200 Ωm while that of an equivalent rock but Precambrian in age may be an order of magnitude greater.

13. Archie ’ s Law In sedimentary rocks, resistivity of pore fluid is probably single most important factor controlling resistivity of whole rock. Archie (1942) developed empirical formula for effective resistivity of rock: Where ρ and ρ w are effective rock resistivity, and resistivity of pore water respectively; ϕ is the porosity, s is the volume fraction of pores with water, a, m and n are constants where 0.5≤a≤2.5, 1.3≤m≤2.5 and n≈2

14. ρ w is controlled by dissolved salts and can vary between 0.05 ohm-m for saline groundwater to 1000 ohm-m for glacial melt water. Archie’ s Law ignores the effect of pore geometry, but is a reasonable approximation in many sedimentary rocks In granite, where porosity is due to fracturing law can break down

15. The objective of most modern electrical resistivity surveys is to obtain true resistivity models for the sub-surface because it is these that have geological meaning. The apparent resistivity is the value obtained as the product of a measured resistance (R) and a geometric factor (K) for a given electrode array The geometric factor takes into account the geometric spread of electrodes and contributes a term that has the unit of length (metres ). Apparent resistivity ( ρ a ) thus has units of ohm- metres .

16. Current flow in a homogenous earth For a single current electrode implanted at the surface of a homogeneous medium of resistivity ρ , current flows away radially. The voltage drop between any two points on the surface can be described by the potential gradient (-δ V/δ x), which is negative because the potential decreases in the direction of current flow. Lines of equal voltage ('equipotentials') intersect the lines of equal current at right-angles.

17. The potential difference (δV ) across a hemispherical shell of incremental thickness δ r is given by: Where by the current density (J) is the current (I) divided by the area over which the current is distributed (a hemisphere; 2πr 2 ) Thus the voltage V r at a point r from the current point source is:

18. If, however, a current sink is added, a new potential distribution occurs (Figure below) and a modified expression is obtained to describe the voltage at any point. For a current source and sink, the potential V p at any point P in the ground is equal to the sum of the voltages from the two electrodes, such that: V p = V A + V B where V A , and V B are the potential contributions from the two electrodes, A( + I) and B( - I).

19. In reality, the sub-surface ground does not conform to a homogeneous medium and thus the resistivity obtained is no longer the 'true' resistivity but the apparent resistivity (ρ a ) which can even be negative. It is very important to remember that the apparent resistivity is not a physical property of the sub-surface. all field resistivity data are apparent resistivity while those obtained by interpretation techniques are 'true' resistivities.

20. Note: in order for at least 50 % of the current to flow through an interface at a depth of z metres into a second medium, the current electrode separation needs to be at least twice- and preferably more than three times-the depth.

21. Electrode configuration In resistivity surveying the electrical properties of the subsurface are determined by measuring the current passing through the ground via the current (transmitter) electrodes, and measuring the resultant potential difference produced between the potential (receiver) electrodes. The results depend on both the electrode configuration and the actual subsurface distribution of the electrical properties with respect to the electrode locations.

22. There are three main types of electrode configuration, namely; Wenner array Schlumberger array Dipole – dipole array Other array/configuration exists namely Pole – dipole Pole – pole gradient

23. Schlumberger Array

24. Schlumberger array consists of four collinear electrodes. The outer two electrodes are current (source) electrodes and the inner two electrodes are the potential (receiver) electrodes. the spacing between the current electrodes are not equal to the spacing between the potential electrodes. See the figure above for the arrangement of the electrodes.

25. For an arbitrary point on the line, P we find for a distance x from the centre: At the centre x = 0 , this give apparent resistivity;

26. If MN is sufficiently small, (-∂v/∂x) = V MN /2s Then apparent resistivity is given by: Where πL 2 /2s is the array constant.

27. Wenner Array Four electrodes are collinear and separations between adjacent electrodes is equal (a). Collecting electrodes in between current electrode.

28. Dipole - Dipole Current electrode and potential electrodes are placed equally as seen in the diagram below

29. Pole -Dipole In pole-dipole usually one current electrode is placed at infinity AM = na , AN = a(n+1), BM = infinity, and BN = infinity

30. Resistivity Survey Equipment required: Resistivity meter, cables (current and potential cables), Hand held GPS receivers, hammer, measuring tape, electrodes, etc. Resistivity meters consists of Voltmeter and Ammeter housed in one equipment. There are three modes of resistivity surveys: Resistivity profiling Resistivity sounding Combination of the two ( Imaging)

31. Cables

32. Field Arrangements

33. Vertical Electrical Sounding (VES) The objective of sounding is to determine the variation of electric conductivity with the depth. The essential idea behind VES, assuming conductivity variation with depth only, is the fact that as the distance between the current and potential electrodes is increased the current filament passing across the potential electrodes carries a current fraction that has returned to the surface after reaching increasingly deeper levels. i.e. the apparent resistivity is measured by expanding the electrode size while maintaining a common centre of measurement or station See figure below;

34. Principle of Equivalence It has been observed that the layer thickness and its resistivity cannot be determined uniquely. Provided the product of resistivity and thickness is kept constant, the thickness may vary while keeping the product constant without affecting the fitting of the curve. This phenomenon is called equivalence.