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1.3.3a DC Electrical methods All the EM methods are described conceptually by the two cartoons in the sketch of Figure 1.3.3. Figure 1.3.3 -1- Only two means are available for causing current to flow in the ground: in the first current is injected by means of a current source, a wire and two electrodes (Figure 1.3.3a) the sum of which is called an electric bipole. Since current is conserved the current in the ground is the same as the current in the wire (I) and the latter is easily measured. The current in the ground produces two fields, an electric field, E, given by Ohm's Law as the product of the current density, J, and the resistivity, , of the ground and a magnetic field given by Ampere's Law or the law of Biot and Savart. The electric field is intuitively readily understood as the voltage drop per unit separation measured between two electrodes by an ideal voltmeter in the medium (an ideal voltmeter drains no current and has itself no impact on the current distributions). For surface electrical surveys the necessary voltage electrodes are on the surface as shown, but they can be in bore holes. If the ground is of uniform resistivity, the current injected is known and the spacing of the electrodes is known then the measured voltage is linearly related to the ground resistivity through simple formulae. If the ground is not uniform, the currents will be distorted by the inhomogeneities and voltage measurements along the surface become indirect measures of the conductivity distribution. An example of this phenomenon is the response of the cave of Figure 1.3.3a. The presence of the cave, a perfect resistor, distorts the current flow near the surface above it. This increases the voltage drop across the measuring electrodes above it which in turn produces an apparent increase in the resistivity of the ground if the uniform half space relationship described above is used as a reference. Physically and mathematically the inhomogeneity appears like a secondary source which, in the case of the cave, creates a current pattern which opposes the incident current and reduces it to zero inside the body. For the spherical shape used in the example the opposing current field is that of an electric bipole. This secondary -2- source is, in fact, caused by the accumulation of charge that occurs when a current flows normal to the interface between two media of different conductivity. This charge accumulation is shown schematically in the cartoon of Figure 1.3.3a. The resulting fields can be calculated using the same techniques as used in electrostatics. DC fields are also conservative in that they are curl free and so formally they should also be included with magnetics and gravity as potential fields. However the actual field measurements are usually made with alternating current so there is a time rate of change of magnetic field associated with them with a consequent component of current induced by Faraday's Law. These fields are not curl free and so it is best to approach the electrical methods as a particular subset of the more general electromagnetic problem. The magnetic field associated with the current flow is not so easily understood intuitively. There is, first of all, an easily calculable field caused by the current in the wire connecting the electrodes and there is another component caused by the currents in the ground. For a uniform or layered half space, the fields of point current sources at each electrode are equal to these of simple vertical wires. If the ground is uniform the resulting magnetic fields measured on the surface are independent of the ground conductivity and so depend only on the magnitude of the current and the geometry of the source current line and the location of the magnetic field detector. If the ground is inhomogeneous the current departs from the uniform half space distribution and the magnetic field measured on the surface, or in boreholes, depends on the conductivity distribution. Surveys conducted in this manner are called magnetometric resistivity surveys and they can play an important role for certain types of target detection. -3- An important method which is included with DC resistivity is the Induced Polarization (IP) method. In some soils and rocks it is observed that the measured resistivity decreases with increasing frequency of the alternating current injected into the ground. The effect is observed at frequencies lower than those that could cause secondary fields through Faraday's Law. The cause is a capacitive-like energy storage that can occur whenever ionic charge carriers in the pore solution encounter zones of differing ion mobility or interfaces between pore solution and metals or metallic minerals. Charges accumulate in such zones much as charge accumulates on the plates of a capacitor and the effect on voltage measurements is likewise similar to the effect observed when a capacitor is introduced in parallel with resistors in an electric circuit. The effect is used to determine the presence of metallic minerals, metals, and clay content. -4-