Electrical Methods

Lecture 5
 Introduction
• Electrical resistivity method is based on the difference in the electrical
conductivity or the electrical resistivity of subsurface materials.

• Useful because resistivity of earth materials varies by around 10

orders of magnitude.

• Resistivity, Electrochemical activity and dielectrical constant are some

of these properties that are generally studied through this methods.

• Developed by Conrad Schlumberger (France) and Frank Wenner

(United States) in early 20th century.
Theory of Electricity
 Electricity Basics
• Electric current
• Is the uniform flow of electrons (charges) in a circuit.
• can also be defined as the rate of change of charge
𝑑𝑞
𝑖= Coulomb/Sec =Ampere
𝑑𝑡
• Voltage
• The measure of energy given to the charge flowing in a circuit.
• Voltage (PD) is the electrical potential energy per coulomb of charge.
𝑃𝐸
𝑉= Volt (J/c)
𝑞
• Resistance
• The opposing force to the flow of electric current.
𝑉
𝑅= Ohm (Ω)
𝑖
 Electricity Basics (cont’d…)
• Resistivity (𝜌)
• Is the measure of how strong a conductor resists the flow of electric current.
𝐴 𝑉𝐴
𝜌= 𝑅 = Ω𝑚
𝑙 𝑖𝑙

Where A= cross section area of conductor (𝑚2)

R= resistance of the conductor (Ω)
𝑙= length (𝑚)
• Conductivity (𝜎)
• Is the measure of how well a conductor allows the flow of electric current.
• It’s the reciprocal of resistivity

𝜎 = 1Τ𝜌 Ω−1 𝑚−1

Resistivity
• This can be written alternatively in terms of field strength (E [V
/m]) and current density (j [A/m²]).

𝐸
𝜌=
𝑗
• Resistivity is one of the most variable physical properties.

1.6 × 10−8 < 𝜌 < 1016

Native silver Pure sulphur

Electrical Properties of Rocks
Earth as a Circuit
• In rocks, two basic types of conduction occur
• Electronic: Electrons are mobile in metallic ores and flow freely
– Metals (wires) and some ore bodies
• Electrolytic / Ionic: Salts disassociate into ions in solution and move
– Involves motion of cations (+) and anions (-) in opposite directions
 Schematic current flow in soil sample

An increase in the number of ions in soil water (groundwater contamination)

linearly decreases the soil resistivity.
 Resistivity of Earth Materials
The resistivity of the subsurface
depends upon
• The presence of certain metallic ores
• Especially metallic ores
• The temperature of the subsurface
• Geothermal energy!
• The presence of archeological
features
• Graves, fire pits, post holes, etc…
• Amount of groundwater present
• Amount of dissolved salts
• Presence of contaminants
• % Porosity and Permeability
 Archie’s Law
• Porous, water-bearing rocks / sediments may be ionic
conductors. Their “formation resistivity” is defined by Archie’s
Law:
𝜌 = 𝑎𝜌𝑤 ∅−𝑚 𝑆𝑤−𝑛
• ∅ = porosity
• 𝑆𝑤 = water saturation
• 𝜌𝑤 = resistivity of water
• 𝑎 ≈ 0.5 – 2.5
• 𝑛 ≈ 2 (if one-third of the pore space is filled with water)
• 𝑚 = cementation ≈ 1.3 – 2.5

• Archie’s law is an empirical model

• Note the exponents…what does this imply about the range of resistivity of
geologic materials?
General Rules of Thumb For Resistivity
• Igneous Rocks
Highest • Only a minor component of pore water

• Metamorphic Rocks
• Hydrous minerals and fabrics

• Sedimentary Rocks
• Abundant pore space and fluids
Lowest
• Clay: super low resistivity

Age of the rock is also important for the resistivity.

General Rules of Thumb For Resistivity
• Older Rocks
• More time to fill in fractures and pore
Highest space

• Younger Rocks
Lowest • Why? Abundant fractures and/or pore
space
Survey strategies and
interpretation
Equipment's for resistivity field work
• The necessary components for making resistivity
measurements include:
• Power source
• Meter for measuring current and voltage (which may be combined
in one meter to read resistance)
• Electrodes
• Current electrodes
• Potential electrodes
• Cables
• Reels.
Measurement Systems
Transmitter
• Power Supply
– DC
– AC (more common)

• Ammeter
• Metal electrodes

Receiver
• Voltmeter
• Metal Electrodes
Potential in a homogeneous medium Battery

a) Current Source on Surface current

• Let a current of a strength (I) enter at point C on

the ground surface.
• Ohms law p
𝜕𝑉 𝜌𝐼 𝜌𝐼
=− =−
𝜕𝑟 𝐴 2𝜋𝑟 2 current

equipotential

• Thus, the potential Vr at distance r is obtained by

integration.
𝜌𝐼 𝜌𝐼
𝑉𝑟 = න 𝜕𝑉 = − න 2
𝜕𝑟 =
2𝜋𝑟 2𝜋𝑅

• At point (P), a distance (R) away from the source

the potential is given by:
𝜌𝐼
𝑉=
2𝜋𝑅
b) Two Current Electrodes: Source and Sink
• What if we move the other current electrode in from far away?

𝜌𝐼 𝜌𝐼
• 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 = and 𝑉𝑠𝑖𝑛𝑘 =
2𝜋𝑟𝑠𝑜𝑢𝑟𝑐𝑒 2𝜋𝑟𝑠𝑖𝑛𝑘

• Total voltage at P:
𝜌𝐼 1 1
𝑉𝑃 = 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 − 𝑉𝑠𝑖𝑛𝑘 = −
2𝜋 𝑟𝑠𝑜𝑢𝑟𝑐𝑒 𝑟𝑠𝑖𝑛𝑘
 Measurement Practicalities
• It is inconvenient to measure potential at single point unless the
other end of our volt meter is at infinity.
• It is easier to measure potential difference (∆𝑉).
• This lead to use of four electrode array for each measurement

• Resulting measurement
given as:
𝜌𝐼 1 1 1 1
∆𝑉 = 𝑉𝑃1 − 𝑉𝑃2 = − − +
2𝜋 𝑟1 𝑟2 𝑟3 𝑟4

• Can be rewritten as:

𝜌𝐼𝐺 𝐺
∆𝑉 = Where is Geometrical Factor of array
2𝜋 2𝜋
Apparent Resistivity
• If the medium is in-homogenous and or anisotropic, the
resistivity is called apparent resistivity (𝜌𝑎 ).
• resistivity we would get assuming that no boundary or change in
resistivity is present.

2V
a =
IG

They are interpreted to obtain the true resistivities of the

layers in the ground.
 Supplement Notes
• True resistivity of the subsurface if it is homogeneous.

• Where the ground is uniform, the resistivity should be constant and i

ndependent of both electrode spacing and surface location.

• When subsurface inhomogeneities exist, the resistivity will vary with

the relative positions of electrodes.

• In general, all field data are apparent resistivity. They are interpret
ed to obtain the true resistivities of the layers in the ground.
 Electrode configurations
There are three main types
of electrode configuration in
common use

• Wenner arrays

• Schlumberger array

• Dipole-dipole arrays
Geometrical factors
Array advantages and disadvantages
Geologic variations on the
resistivity measurements

Uniform half-space

two-layer ground with lower

resistivity in upper layer

two-layer ground with higher

resistivity in upper layer
Geo-electric Layering
• Often the earth can be
simplified within the region of
our measurement as consisting
of a series of horizontal beds
that are infinite in extent.

• Goal of the resistivity survey is

then to determine thickness and
resistivity of the layers.
Geo-electric Layering (Cont’d…)
 Survey design and procedure
• Survey design depends on the specific characteristics of the site
and the objective of the survey.
• There are only two basic procedures in resistivity work.
• Geoelectric Sounding/Vertical electrical Sounding (VES)
• Determination of the vertical variation of the resistivity.
• The current and potential electrodes are maintained at the same relative
spacing and the whole spread is progressively expanded about a fixed centra
point.
• As the distance between the current electrodes is increased, so the depth to
which the current penetrates is increased.
• Profiling (Geoelectric Mapping)
• Determination of lateral variation of resistivity in defined horizons.
• The current and potential electrodes are maintained at a fixed separation and
progressively moved along a profile
 Vertical Electrical Sounding (VES)
• Electrical sounding is the process by which the variation of resistivity with
depth below a given point on the ground surface is deduced.
• The procedure is based on the fact that the current penetrates continuously
deeper with the increasing separation of the current electrodes.
• The two most common arrays for electrical resistivity surveying in the
sounding mode are the Schlumberger and Wenner arrays.
Wenner Sounding Schlumberger Sounding
VES-1 VES-1
a=1m AB/2=1.5, MN/2=0.5

a=2m AB/2=2, MN/2=0.5

a=3m AB/2=3, MN/2=0.5

a=4m AB/2=4, MN/2=0.5

a=5m AB/2=5, MN/2=0.5

AB/2=5, MN/2=1
Data Table
Data Table
a,m R ρa
AB/2 R ρa
1
1.5
2
2
3
3
4
4
ρa Field Curve ρa Field Curve

a,m AB/2
Electrical horizontal profiling (mapping or trenching)
• Lateral changes in resistivity can be effectively mapped using
electrical profiling.
• Can use similar arrays to VES
• Patterns vary depending on what array is used
• Patterns are complicated because electrodes may be in zones of
different properties.
• Usually involves moving an electrode array of constant
separation horizontally along surface.
• The two most common arrays for electrical resistivity surveying
in the profiling mode are the Wenner and dipole-dipole arrays.
 Multielectrode Systems
• Soundings and mappings are very time consuming.
• Therefore multielectrode systems are developed. Typically 50
electrodes are laid out in two strings of 25 electrodes, with
electrodes connected by a multi core cable to a switching box and
resistance meter. The whole data acquisition procedure is software
controlled from a laptop computer.
• Increase electrode separation as well as make measurements at multiple
locations along the horizontal axis.
• Provides data for two dimensional interpretation of subsurface.
Field Considerations for DC Resistivity
• Good electrode contact with the earth
• Wet electrode location
• Add NaCl solution or bentonite.

• Surveys should be conducted

along a straight line whenever
possible
• Try to stay away from cultural
features whenever possible
(power lines, pipes, grounded
metal fences, pumps, etc)
Sources of noise in data
1. Electrode Polarization

2. Telluric Currents

3. Presence of Nearby Conductors

4. Low Resistivity at the Near Surface

5. Near-Electrode Geology and Topography

6. Current Induction in Measurement Cables

 Interpretation methods
Qualitative
methods
• Looking for
changes in
apparent
resistivity that
will enhance your
understanding of
what you
already know
about the
geology
Interpretation of Geoelectric Data
• Aim of the interpretation: Determination of the resistivity and
thickness of each layer from the observed resistivities.
 Interpretation methods
Qualitative methods
• Sometimes
pseudo-sections
can be interpreted
qualitatively
directly if
• Good data
quality
• Simplified
geology
• This is the
exception rather
than the norm
 Interpretation methods
Quantitative methods (Master
Curves)
• Simple for two layer case.
• Plot data at same scales as
master curves.
• Overlie shallow-layer
resistivity asymptote with ‘1’
on master curves.
• Determine depth to layer,
and resistivity of lower
layer by comparing scaled
master-curve values to data
values
• Gets rapidly more difficult
as more layers added.
 Interpretation methods
Quantitative methods
(Forward Modeling)
• Using mathematical
expressions that describe
the physics to calculate the
data that would result
from a given combination
of geoelectric model and
electrode configuration.
• Generally a linear
process.
• Forward modeling
produces unique results.
 Interpretation methods
Quantitative methods (Inverse Modeling)
• Going the opposite direction. We measure data and know the array
configuration, and through inversion wish to determine a geoelectric
model that would produce data similar to those measured.
• Generally problem is non-linear.
• Problem is non-unique. Thus must add constraints of some sort to provide a
reasonable answer.
• Danger in over-interpreting the results.
• Benefits:
• Automatic, it helps to remove user bias. However sometimes the user’s bias is
needed to produce a decent model
• Automatically removes differences associated with different electrode
collection schemes.
Inverse Modeling
Inversion scheme in geoelectric sounding
Advantages and disadvantages of electrical method
Advantages Disadvantages
• It is a very rapid and • It can only detect absolutely
economical method. different strata like rock and water.
• It provides no information about the
sample.
• It is good up to 30m depth.
• Cultural problems cause interference,
e.g., power lines, pipelines, buried
• The instrumentation of this casings, fences.
method is very simple. • Data acquisition can be slow
compared to other geophysical
• It is a non-destructive methods, although that difference is
method. disappearing with the very latest
techniques.
 Applications
• Engineering site investigations
• Burial of trunk sewer
• Location of buried foundations
• Landslides
• Groundwater and landfill surveys
• Detection of saline groundwater
• Groundwater potential
• Mineral exploration
• Glaciological applications
Groundwater exploration
Mineral exploration, detection of cavities
Waste site exploration
Oil exploration
Questions