Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 239

water is to flow there must be some form of driving force
(the in uence of gravity on the pressure and low of the
water will be ignored here). In this case it is the difference
in water pressure created by the pump. The water ows
away from the area of higher pressure and towards areas of
lower pressure. As long as the pump maintains the pres-
sure difference, the flow of water continues. The ow may
also be stopped by the valve, which if shut breaks the
continuity of fluid flow through the system. Continuity of
the system is a second requirement for flow to occur.
Let us now modify the system so that the water is forced
to flow through a cylinder of homogeneous rock encased in
a water-tight seal (so that the water does not flow out of the
sides of the rock specimen) ( Fig. 5.3b ) . The flow of water
through the pipes can be thought of as occurring without
hindrance, but the ease with which the water

measured in volts (V), which is often referred to as simply
the voltage. This is what causes movement ( (flow) of
charges through the wires connected to the battery. Recall
that it is the movement of charges that constitutes an
electric current. Current (I) is measured in amperes (A)
and is quanti ed in terms of the amount of electric charge
that flows in one second, i.e. the rate of ow.
The movement direction of the charges depends on their
polarity. Negatively charged electrons move from the
lowest to the highest potential in a circuit, i.e. electrons
move from the negative terminal through the external
circuit to the positive terminal of a battery. However, by
convention, the direction of current flow is taken as the
flow of positive charges from the more positive to the more
negative potential. The electric current flows as long as the

electrical pressure or force (voltage) is maintained and is
suf cient to overcome any hindrance to the flow. This
requires that the switch, equivalent to the hydraulic valve,
is closed to complete the circuit.
Consider now the amount of charge passing through the
cross-sectional area of the wires. It is quanti ed as the
current density and, assuming that the current is distrib-
uted uniformly across the area, is a measure of the amount
of current passing through a unit area and speci ed in
units of A/m 2 . Increasing the current increases the number
of charges flowing and increases the current density, and
similarly, decreasing the cross-sectional area of the wires
(thinner wires) increases the current density.
Just as the cylinder of rock resisted the flow of water, a
substance will also resist the flow of charges. A resistor has
been included in the circuit in Fig. 5.3d and its associated
resistance (R) to the flow of current is a form of electrical
impedance. If it is increased whilst maintaining the same
electrical potential, then the current flow is reduced. As
with the water analogy, the actual resistance to the

ows through
the cylindrical rock specimen depends on two factors:

The porosity and permeability of the rock. If the speci-
men is a highly porous and permeable sandstone, the
low of the water is hindered less than if it has low
porosity and permeability as might occur in, say, a
gneiss. In other words, the ease of flow is a function of
some inherent characteristics of the rock. Even when
highly porous, the tortuosity of the pore system will
affect the ease with which flow can occur, with ow
paths that are complex and convoluted causing more
energy to be lost through processes such as friction.

•

The dimensions of the rock specimen. Increasing the
length of the cylinder will make it harder to drive the
water through the longer specimen. On the other hand,
increasing the diameter of the cylinder presents a larger
cross-sectional area of pores for the water to

•

ow

through, so its passage will be easier.

Electrical storage batteries and generators create electrical
potential energy. In a battery this is done through a
chemical reaction, in a generator it is done mechanically
through electromagnetic induction (see Section 5.2.2.2 ).
The resulting electrical potential energy is available to drive
charges through an electrical circuit external to the poten-
tial energy source, i.e. to produce a flow of electric current.
Consider now the analogous electrical circuits of our
plumbing systems ( Figs. 5.3c and d ). The battery (or it
could be a generator) can be thought of as an electrical
pump. Just as the water pump creates a difference in water
pressure, the battery creates a difference in electrical pres-
sure (electrical potential energy) known as the electromo-
tive force (emf).

flow of
electric current is partly a function of the geometry of the
substance and partly due to its inherent properties. Recall
that the pressure difference created by the pump was
constant, with the flow of water through the specimen
dependent on its porosity and permeability and its dimen-
sions. As with the flow of water, increasing the cross-
sectional area reduces the electrical resistance, whereas
increasing the length increases the resistance. To make a
meaningful statement about how much a substance
opposes the passage of electric current, it is necessary to
remove the geometrical effects of the specimen from elec-
trical measurements made on it to obtain the equivalent
that would result from a unit cube of the material. This is

It produces a potential difference