Direct current resistivity methods
The physical base of applying direct current (DC) resistivity
methods is that the subsurface distribution of a current
injected into the ground is influenced by the different
resistivity values of the formations through which the current
penetrates.
Voltage between different points of the ground surface is
generated by the flow of a subsurface current.
The voltage distribution on the surface bears the effects of
site lithology.
The main factors influence this voltage distribution are the
following:
the shapes of geological structures,
the sizes of geological structures,
the positions of geological structures,
and the resistivity values of geological structures.
Direct current resistivity methods
In the most simple case, the ground surface is a horizontal
plane, and there is no any inhomogeneity under the surface.
This theoretical model is called homogenous half-space.
In a homogenous half-space, the current radially spread out
from the location of electrode in all directions of the
subsurface space.
The current electrode, which is coupled to the ground,
functions as an entry point of the current.
By the effect of subsurface current flow, an electric potential
field is arisen.
The equipotential surfaces of this field are perpendicular to
the current flow lines at their each point and form half
spheres.
Direct current resistivity methods
Current flow lines and equipotential surfaces arising from a single
current electrode in the case of a homogenous half-space.
Direct current resistivity methods
In fact, a single current electrode is not able to transmit current to
the ground.
A pair of current electrodes is used to create a closed current
circuit through the subsurface media.
Accordingly, the current spreads out from one of the electrodes
(often represented by A), the current flow lines penetrate the
subsurface medium, then converge to the other electrode (often
denoted by B).
The current flow lines form curves between the entry and exit
points of the current, and the equipotential surfaces fit to this more
complex current flow.
In a common situation, the shapes of current flow lines and
equipotential surfaces are very complex, because the subsurface
interfaces separating rocks with different resistivity values break
their continuity causing sudden changes in their runs.
Direct current resistivity methods
Current flow lines and equipotential surfaces arising from a pair of
current electrodes in the case of a homogenous half-space.
Direct current resistivity methods
The effect of a layer boundary on the shape of a current flow line.
On the left side, the lower layer has a greater resistivity. The
current flow line is broken by the layer boundary. The angle of
incidence is greater than the angle of refraction.
On the right side, the reverse case can be seen.
Direct current resistivity methods
Current flow lines and equipotential surfaces arising from a pair of
current electrodes in the case of a two-layered half-space.
Direct current resistivity methods
The field equipment required for a direct current resistivity method
includes the main component parts below:
a pair of current electrodes,
a source of electrical energy,
a pair of potential electrodes,
a voltmeter,
and insulated cables.
Two different electrical circuit are created by using these parts:
a (supply) current circuit,
and a measurement circuit.
Direct current resistivity methods
The current circuit consists of a source of electric energy, a pair of
current electrodes denoted by A and B, as well as two cable
segments.
The current electrodes are usually made from copper or steal.
They are planted in the ground at a suitably chosen distance apart.
They provide an entry and an exit points for the subsurface branch
of the current circuit.
Generally a rechargeable battery or an accumulator is applied as a
source of electric energy, whose terminals (positive and negative)
are connected to the current electrodes by means of two insulated
cabel segments.
The positive terminal is linked to the current electrode A (the entry
point of the current to the ground), and the negative terminal is
linked to the current electrode B (the exit point of the current from
the ground).
Direct current resistivity methods
The main parts of the measurement circuit are a voltmeter
and a pair of potential electrodes.
The potential electrodes often denoted by M and N are made
from copper or steal similarly to the current electrodes.
The voltmeter is tied between the planted potential electrodes
by means of two insulated cable segments.
In such a way, the measurement of the potential difference on
the surface can be implemented.
In a real implementation of a DC resistivity instrument, the
measurement circuit usually contains a voltage divider for
adjusting the sensitivity of the voltmeter and an electric
compensator for eliminating the effect of self-potential from
the measured voltage.
Direct current resistivity methods
The main component parts of the current and measurement
circuits.
Direct current resistivity methods
The so-called electrode configuration, or electrode array, gives the
relative positions of the different electrodes.
There are several electrode arrays are used in practice.
Each of them has its own advantages and disadvantages.
In order to select a suitable electrode array for a particular survey,
we must balance the expectable advantages and disadvantages of
using one and another.
In field practice, the symmetrical electrode arrays are usually
favoured.
The most frequently used ones are:
the Schlumberger array,
the Wenner array,
and the dipole-dipole array.
Direct current resistivity methods
The Schlumberger array is characterized by the following
properties:
the midpoint of the space between potential electrodes is
identical with the midpoint of the space between current
electrodes (this is the symmetry point of the array).
The line segment MN less than the one third of the line
segment AB (MN < AB/3),
Direct current resistivity methods
The Wenner array can be considered as a special case of the
Schlumberger array.
The single difference between them is that the line segment MN
just equals to the one third of the line segment AB (MN = AB/3).
Direct current resistivity methods
Dipole-dipole array is characterized by the properties below:
the pair of potential electrodes is not sited between the current
electrodes, so there is no common midpoint,
but all the electrodes are fitted to a straight line,
the space between M and N is equal to the space between A
and B (MN= AB),
and the space between the current or potential electrodes is
less than the distance between the two different midpoints
MN = AB < L.
Direct current resistivity methods
It is generally true for all the electrode configurations that the
resistivity of a homogenous half-space can be obtained by means
of the following formula:
where U is the measured voltage, I is the intensity of transmitted
current, an K is known as the geometrical factor.
The value of geometrical factor depends only on the geometrical
parameters of the actual electrode configuration.
For different electrode configurations, different formulae are used
to calculate the value of K.
Of course, the resistivity formula above does not give a true
resistivity value for inhomogeneous half-spaces, such as a
horizontally layered half-space.
Therefore, the resistivity value obtained by a voltage measurement
above an inhomogeneous half-space (which is always the case in
reality) is called apparent resistivity denoted by a.
Direct current resistivity methods
So, the correct version of the resistivity formula contains the
apparent resistivity instead of the true resistivity of a homogenous
half-space:
An apparent resistivity value includes the effects of all the rock
formations through which the current has penetrated.
The relationship between the apparent resistivity value and the
parameters of the geological structures (e. g. true resistivity values
of layers, thicknesses of layers, depth values of layer boundaries)
depends on the site geology and the field parameters (parameters
of the electrode array, the intensity of applied current) in a complex
way.
Direct current resistivity methods
Extracting the information about the geological structures from the
raw (measured) data is performed by different types of data
processing and evaluation methods.
Of course, the algorithms of these methods is implemented in the
form of various software which makes it easier for us to obtain the
useful information.
The objective of direct current resistivity surveys is to reveal the
resistivity variations of inhomogeneous subsurface both
horizontally and vertically.
By the direction along which the resistivity variations are aimed at
investigating, two direct current resistivity methods were
developed:
vertical electrical sounding (VES),
(horizontal) electric profiling (EP).
While vertical electrical sounding is used for the purpose of
determining the vertical variation of resistivity, electrical profiling is
aimed at determining the horizontal or lateral variation of resistivity.
Vertical electrical sounding (VES)
In order that a VES survey can be implemented in field practice, a
controlled form of modifying the investigation depth is required.
In resistivity surveys, investigation depth, or penetration depth, is
not a depth level but a depth range.
It gives the depth range in which the current density is high enough
to provide information about the subsurface structure by measuring
the voltage on the surface between two electrodes.
Above and below the investigation depth, the current intensity is so
low that the effects of these domains on the measured voltage can
be negligible.
In the case of symmetrical electrode configurations, the increase of
investigation depth can be achieved by the increase of the space
between the current electrodes (AB).
Vertical electrical sounding (VES)
Typically used electrode configuration for VES surveys is the
Schlumberger array.
The common midpoint of the current and potential electrodes is
fixed during the whole measurement.
The space between the current electrodes is increased after the
measurement of each apparent resistivity.
By this stepwise movement of current electrodes, the current is
able to penetrate deeper and deeper parts of the subsurface
space.
The space between the current electrodes is generally
logarithmically increased with at least 10 steps per decade.
If the space between the current electrodes is quite long, the space
between the potential electrodes is to be increased.
By this change, keeping the measured voltage above the noise
level and the detection level of the instrument is ensured.
Vertical electrical sounding (VES)
The measured results are represented on log-log plots.
The horizontal axis of an apparent resistivity plot is logarithmically
scaled by the half of the current electrode spacing (AB/2), while the
vertical axis is logarithmically scaled by the apparent resistivity.
In the case of Schlumberger array, the half of the current electrode
spacing can be considered as an estimation of the investigation
depth belonging to the actual current electrode space.
So, the apparent resistivity values belonging to greater current
electrode spacing mostly reflect the effects of deeper formations
rather than shallower ones.
By the visual analysis of an apparent resistivity curve, we can often
determine the main properties of a subsurface structure (the
number of layers and the resistivity relations among the layers).
An increasing or decreasing trend along an apparent resistivity
curve indicates the effect of another layer with higher or lower
resistivity than the previous one.
Vertical electrical sounding (VES)
Apparent resistivity curve computed for a two-layered half-space.
The lithology bar, on the right side, shows the parameters of the
geophysical model.
Vertical electrical sounding (VES)
Apparent resistivity curve computed for a two-layered half-space.
The lithology bar, on the right side, shows the parameters of the
geophysical model.
Vertical electrical sounding (VES)
Apparent resistivity curve computed for a two-layered half-space.
The lithology bar, on the right side, shows the parameters of the
geophysical model.
Vertical electrical sounding (VES)
The quantitative interpretation of an apparent resistivity curve is
executed by means of computer programs.
These programs provide the numerical solution of inverse problem
for a horizontally layered half-space.
(The so-called geophysical inversion methods are used for
estimating the values of parameters describing the geophysical
models.)
Since the horizontally layered half-space is a one dimensional (1D)
model for the approximation of a subsurface structure, the VES
method can only be applied to areas where the subsurface
structure is assumed to be horizontally layered with very little
lateral variation.
Electric profiling (EP)
When the aim of the electrical measurement is discovering
the lateral (or horizontal) variations of the subsurface
structure, the electric profiling method is applied.
Such frequently arising problems are the following:
tracking the change in the relief of a subsurface
basement with high resistivity,
detecting the site of faults and significant changes in
rock facies.
An electric profiling survey is executed along a line on the
ground surface.
Electric profiling (EP)
One of the most frequently used electrode configuration for EP is
the Wenner array.
In the Wenner procedure of EP, the spaces between the
electrodes are not change during the whole measurement, but the
electrode array is moved to the next station after each
measurement of apparent resistivity.
Because the space between the current electrodes is constant,
there is no controlled change in the investigation depth.
Any change in investigation depth is caused by lateral changes in
resistivity, because the investigation depth is shallower for rock
formations with lower resistivity (e.g. clays, shales).
By this stepwise movement of the electrode configuration along a
survey line, the lateral variations of the resistivity can be revealed.
Electric profiling (EP)
The Wenner procedure of electric profiling
Electric profiling (EP)
Another frequently used electrode configuration for EP is the
gradient array.
The gradient array is not a symmetrical array.
The locations of the current electrodes are not changed during the
whole measurement.
There is a long space between them (it can reach as long as a few
hundred meters), and the potential electrodes with a short constant
space are moved between the current electrodes. After the
measurement of an apparent resistivity value, the potential
electrodes are relocated to the next station.
Electric profiling (EP)
The gradient procedure of electric profiling
Electric profiling (EP)
The measured results of an EP survey is represented on a semilog plots.
The horizontal axis of an apparent resistivity profile is linearly
scaled by the distance along the survey line, and the vertical axis is
logarithmically scaled by the apparent resistivity.
An increasing or decreasing trend along an apparent resistivity
profile indicates the effect of a lateral inhomogeneity with higher or
lower resistivity than the previous segment of the profile .
Electric profiling (EP)
The figure illustrates the principle of the electric profiling method.
The changes in the relief of the igneous rock with high resistivity modify
the current density under the surface. The current flow lines are less
capable of penetrating a rock with higher resistivity. They converge to the
rocks with lower resistivity. This lateral variation of the current density
results in the variation of measured voltage. Because the apparent
resistivity depends on the measured voltage, it also varies with the
distance along the survey line.