The electrical resistivity method is utilized to map subsurface structures and materials by measuring their resistivity, influenced by factors like porosity and dissolved solids. While offering advantages such as quantitative modeling and stratigraphic estimation, it faces limitations in industrial areas due to electrical noise and requires specific site conditions for effectiveness. Survey designs vary according to objectives, with common arrays like Schlumberger and Wenner facilitating both sounding and profiling modes to investigate subsurface resistivity distributions.

1. Amit K. Mishra
Assistant Professor
School of Earth Science (Geology)
Banasthali Vidyapith

2. Fundamentals
• The electrical resistivity method is used to map the subsurface electrical resistivity
structure, which is interpreted by the geophysicist to determine geologic structure
and/or physical properties of the geologic materials.
• The electrical resistivity of a geologic unit or target is measured in ohm-meters,
and is a function of porosity, permeability, water saturation and the concentration
of dissolved solids in pore fluids within the subsurface.
• Electrical resistivity methods measure the bulk resistivity of the subsurface as do
electromagnetic methods.
• The difference between the two methods is in the way that electrical currents are
forced to flow in the earth.
• In the electrical resistivity method, current is injected into ground through surface
electrodes, whereas in electromagnetic methods, currents are induced by the
application of time-varying magnetic fields

3. Advantages
• A principal advantage of the electrical resistivity method is that quantitative
modeling is possible using either computer software or published master curves.
• The resulting models can provide accurate estimates of depth, thickness and
electrical resistivity of subsurface layers.
• The layered electrical resistivities can then be used to estimate the electrical
resistivity of the saturating fluid,
which is related to the total concentration of dissolved solids in the fluid.

4. Limitations
• Limitations of using the electrical resistivity method in ground water pollution
investigations are largely due to site characteristics, rather than in any inherent
limitations of the method.
• Typically, sites are located in industrial areas that contain an abundance of
broad-spectrum electrical noise.
• In conducting an electrical resistivity survey, the voltages are relayed to the
receiver over long wires that are grounded at each end.
• These wires act as an antenna receiving the radiated electrical noise that in turn
degrades the quality of the measured voltages

5. • Electrical resistivity surveys require a fairly large area, far removed from power
lines and grounded metallic structures such as metal fences, pipelines and
railroad tracks.
• This requirement precludes using this technique at many ground water pollution
sites.
• However, the electrical resistivity method can often be used successfully off-site
to map the stratigraphy of the area surrounding the site.
• A general “rule of thumb” for electrical resistivity surveying is that grounded
structures be at least half of the maximum electrode spacing away from the axis
of the electrode array.
• Electrode spacing and geometry or arrays (Schlumberger, Wenner, and Dipole-
dipole) are discussed in detail in the section below entitled, Survey Design,
Procedure, and Quality Assurance.
• Another consideration in the electrical resistivity method is that the fieldwork
tends to be more labor intensive than some other geophysical techniques.
• A minimum of three crewmembers is required for the fieldwork.

6. Instrumentation
• Electrical resistivity instrumentation systems basically consist of a transmitter and
receiver.
• The transmitter supplies a low frequency (typically 0.125 to 1 cycles/second or
“Hertz”) current waveform that is applied across the current electrodes.
• Either batteries or an external generator, depending on power requirements can
supply power for the transmitter. In most cases, the power requirements for most
commonly used electrode arrays, such as Schlumberger (pronounced “schlum-bur-
zhay”) and Wenner arrays are minimal and power supplied by a battery pack is
sufficient.
• Other electrode configurations, such as Dipole-dipole arrays, generally require
more power, often necessitating the use of a power generator.
• The sophistication of receivers range from simple analog voltmeters to
microcomputer-controlled systems that provide signal enhancement, stacking, and
digital data storage capabilities. Most systems have digital storage of data.
• Some systems may require the field parameters to be input via PC (personal
computer) prior to collection of the data.
• The trend in manufacturers of resistivity equipment is to have the entire system
controlled form a PC or preprogrammed software built into the instrument.

7. Survey Design, Procedure and Quality
Assurance
• Survey design depends on the specific characteristics of the site and the
objective of the survey.
• The three most common modes of electrical resistivity surveying are profiling,
sounding, and profiling-sounding, each having its own specific purpose.
• If the purpose of the survey is to map the depths and thickness of stratigraphic
units, then the electrical resistivity data should be collected in the sounding
mode.
• Lateral electrical resistivity contrasts, such as lithologic contacts, can best be
mapped in the profiling mode.
• In cases where the electrical resistivity is expected to vary both vertically and
horizontally, such as in contaminant plume mapping, the preferred mode is
profile sounding.

8. Sounding Mode
• The two most common arrays for electrical resistivity surveying in the sounding
mode are the Schlumberger and Wenner arrays.
• Increasing the separation of the outer current electrodes, thereby driving the
currents deeper into the subsurface increases the depth of exploration.
Profiling Mode
• The two most common arrays for electrical resistivity surveying in the profiling
mode are the Wenner and dipole-dipole arrays.
• The electrode geometry for the Wenner array is the same as the sounding mode
— the difference is that in profiling mode the entire array is moved laterally
along the profile while maintaining the potential and current electrode separation
distances.

9. The general four-electrode method
• Consider an arrangement consisting of a pair of current electrodes and a pair of
potential electrodes (Fig.)
• The current electrodes A and B act as source and sink, respectively.
• At the detection electrode C the potential due to the source A is ρI/(2 rAC),
while the potential due to the sink B is -ρI/(2 rCB).
• The combined (UC)potential at C is

10. Similarly, the resultant potential at D is
The potential difference measured by a
voltmeter connected between C and D is
All quantities in this equation can be measured at the ground surface except the
resistivity, which is given by

11. Special electrode configurations
• The general formula for the
resistivity measured by a four
electrode method is simpler for
some special geometries of the
current and potential electrodes.
• The most commonly used
configurations are the Wenner,
Schlumberger and double-dipole
arrangements.
• In each configuration the four
electrodes are collinear but their
geometries and spacing are
different.

12. Wenner configuration
• In the Wenner configuration (Fig. 4.49a) the current and potential electrode pairs
have a common mid-point and the distances between adjacent electrodes are
equal, so that r A C = rDB=a, and rCB=rAD=2a.
• Value of resistivity in this configuration is

13. Schlumberger configuration
• In the Schlumberger configuration (Fig. b) the current and potential pairs of
electrodes often also have a common mid-point, but the distances between
adjacent electrodes differ.
• Let the separations of the current and potential electrodes be L and a,
respectively. Then rAC = rDB=(L – a)/2 and rAD=rCB=(L+a)/2. Substituting in the
general formula, we get
• In this configuration the separation of the current electrodes is kept much
larger than that of the potential electrodes (L>>a). Under these conditions..

14. Double-dipole configuration
• In the double-dipole configuration (Fig. C) the spacing of the electrodes in each
pair is a, while the distance between their mid-points is L, which is generally
much larger than a. Note that detection electrode D is defined as the potential
electrode closer to current sink B.
• In this case rAD = rBC=L, rAC= L+a, and rBD=L – a.
• The measured resistivity is

15. Apparent Resistivity
• In the idealized case of a perfectly uniform
conducting half-space the current flow lines
resemble a dipole pattern and the resistivity
determined with a four-electrode
configuration is the true resistivity of the
half-space.
• But in real situations the resistivity is
determined by different lithologies and
geological structures and so maybe very
inhomogeneous. This complexity is not taken
into account when measuring resistivity with
a four-electrode method, which assumes that
the ground is uniform. The result of such a
measurement is the apparent resistivity of an
equivalent uniform half-space and generally
does not represent the true resistivity of any
part of the ground.

16. • Consider a horizontally layered structure in which a layer of thickness d and
resistivity ρ1 overlies a conducting half-space with a lower resistivity ρ2 (Fig.
4.52). If the current electrodes are close together, so that L<<d, all or most of the
current flows in the more resistive upper layer, so that the measured resistivity is
close to the true value of the upper layer, ρ1. With increasing separation of the
current electrodes the depth reached by the current lines increases. Proportionally
more current flows in the less resistive layer, so the measured resistivity
decreases.
• Conversely, if the upper layer is a better conductort han the lower layer, the
apparent resistivity increases with increasing electrode spacing. When the
electrode separation is much larger than the thickness of the upper layer (L >>d)
the measured resistivity is close to the value ρ2 of the bottom layer. Between the
extreme situations the apparent resistivity determined from the measured current
and voltage is not related simply to the true resistivity of either layer.

17. There are four basic type of sounding curve depending on the resistivity
distribution with depth.
If ρ1 , ρ2 and ρ3 are the resistivity of the subsurface layers with ρ1 at the top
followed by ρ2 and ρ3
i. ρ1 < ρ2 < ρ3 is defined as A-type ii.
ρ1 ρ3 is defined as K-type
iii. ρ1 > ρ2 < ρ3 is defined as H-type iv.
ρ1 > ρ2 > ρ3 is defined as Q-type
Vertical electrical sounding (VES)

18. The four common shapes of apparent resistivity curves for a layered structure consisting of three
horizontal layers.

19. The apparent resistivity curve for a three-layer structure generally has one of four
typical shapes, determined by the vertical sequence of resistivities in the layers
(Fig).
The type K curve rises to a maximum then decreases, indicating that the
intermediate layer has higher resistivity than the top and bottom layers.
The type H curve shows the opposite effect; it falls to a minimum then increases
again due to an intermediate layer that is a better conductor than the top and bottom
layers.
The type A curve may show some changes in gradient but the apparent resistivity
generally increases continuously with increasing electrode separation, indicating that
the true resistivities increase with depth from layer to layer.
The type Q curve exhibits the opposite effect; it decreases continuously along with a
progressive decrease of resistivity with depth.

20. Resistivity profiling
• In contrast to the sounding examining a resistivity-depth distribution, the
resistivity profiling maps lateral distribution of resistivities.
• The method is very versatile and hence used for various tasks,
scales and depths.
• The depth of investigation is selected by the distance of current electrodes and
character of measured anomalies (complexity, precision of anomaly indicators,
etc.) depends on the electrode configuration.
• The small inter-electrode distances could provide a very detailed image of near-
surface inhomogeneities for archaeological prospection. In contrast, large inter-
electrode distances easily maps depths of tens of meters.

21. Principles
 When using a standard four-electrode resistivity spread in a DC mode, if the current is
abruptly switched off, the voltage between the potential electrodes does not drop to zero
immediately.
 After a large initial decrease the voltage suffers a gradual decay and can take many seconds
to reach a zero value.
 A similar phenomenon is observed as the current is switched on. After an initial sudden
voltage increase, the voltage increases gradually over a discrete time interval to a steady-state
value.
 The ground thus acts as a capacitor and stores electrical charge, that is, becomes electrically
polarized.
 If, instead of using a DC source for the measurement of resistivity, a variable low- frequency
AC source is used, it is found that the measured apparent resistivity of the subsurface
decreases as the frequency is increased.
 This is because the capacitance of the ground inhibits the passage of direct currents but
transmits alternating currents with increasing efficiency as the frequency rises.
Induced polarization (IP) method

22. The phenomenon of induced polarization. At time t0 the current is switched off and the
measured potential difference, after an initial large drop from the steady- state value ΔVc,
decays gradually to zero. A similar sequence occurs when the current is switched on at time t3.
A represents the area under the decay curve for the time increment t1-t2.

23. The measurement of a decaying voltage over a certain time interval is known as time-domain IP
surveying.
Measurement of apparent resistivity at two or more low AC frequencies is known
as frequency-domain IP surveying.
Time-domain IP measurements involve the monitoring of the decaying voltage after the current
is switched off. The most commonly measured parameter is the chargeability.
IP equipment is similar to resistivity apparatus but uses a current about 10 times that of a
resistivity spread; it is also rather more bulky and elaborate.
Theoretically, any standard electrode spread may be employed but in practice the double-
dipole, pole–dipole and Schlumberger configurations are the most effective.
Electrode spacings may vary from 3 to 300m with the larger spacings used in reconnaissance
surveys.
USE
The IP method is extensively used in base metal exploration as it has a high success rate in
locating low-grade ore deposits such as disseminated sulphides.