Download 1.3.3a DC Electrical methods All the EM methods are described

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Transcript
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
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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.
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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.
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