**Section 4a: Electrical Resistivity Surveying**

Electrical and
Electromagnetic Methods

Electric circuit has three
main properties:

- Resistance (R): resistance to movement of
charge

- Capacitance (C): ability to store charge

- Inductance (L): ability to generate current
from changing magnetic field arising from moving charges in circuit

Each electrical property is basis for a
geophysical method:

Resistivity: measures apparent resistance
of ground to direct current (DC) flow

Induced Polarisation: measures effect on current flow of
charge storage in ground

Spontaneous Potential: measures naturally occurring DC
currents

Electromagnetic Methods (EASC 307): measure apparent
resistance of ground to induced alternating current (AC) flow

Resistivity Applications

- Resistivity methods first developed in early
1900s

- Used extensively in borehole logging for oil
exploration from 1920s (Schlumberger)

- Surface resistivity in common use from 1970s in
mineral and groundwater exploration

- Surface resistivity now used to monitor
groundwater contamination, locate subsurface cavities and fissures

Resistance

Ohm’s Law

In an electrical circuit, the electrical resistance R of a
wire in which current I is flowing is given by Ohm’s
Law:

where V is potential difference across wire.

R is measured in ohms, V in volts, and I in amps.

Doubling length of wire or increasing its
diameter changes the resistance.

Resistance is **NOT** a fundamental
characteristic of the metal in the wire.

Resistivity

For a uniform wire or cube, resistance is proportional to
length and inversely proportional to cross-sectional area

Constant of proportionality is called __Resistivity ____r____:__

Resistivity r is the fundamental physical property of the metal in the wire

r
is measured in ohm-m (check above definition)

__Conductivity ____s__ is defined as 1/r, and is measured in Siemens per metre (S/m),
equivalent to ohm^{-1}m^{-1}.

Non-Uniform Bodies

Effect of Geometry

If two media are present in cube with resistivities r_{1}and r_{2}, then both their proportions
**and** their
geometry determine the resistance of cube.

__Apparent resistivity__ of above cubes is quite different
even though two resistivities are the same.

Anisotropy

In a uniform cube, electrical properties are same in each
direction and cube is said to be __isotropic__.

In a non-uniform cube, electrical properties can vary with
direction, and cube is said to be __anisotropic__.

- Anisotropy found in platey structures

- Ratio of maximum to minimum resistivity is
called coefficient of anisotropy, and is usually in range of 1-2.

Current Flow in Geological Materials

Electrical current can flow, i.e. electrical charges can
move, in rocks and soils, but process is usually different from current flowing
in a metal wire.

Three main mechanisms of current flow:

1) Electrolytic Conduction

- Occurs by relatively slow migration of ions in a
fluid electrolyte.

- Controlled by type of ion, ion concentration,
and ionic mobility.

2) Electronic Conduction (as in metal wire)

- Occurs in metals by rapid movement of electrons.

- Found in native metals and some metal oxides and
sulphide ores

3) Dielectric Conduction

- Occurs in weakly conducting materials, or
insulators, in presence of external alternating current

- Atomic electrons are shifted slightly relative
to nucleus

In most rocks, DC current flow is by
electrolytic conduction:

- controlled by pore fluid and pore geometry

- mineral grains of matrix contribute little,
except if metal ore

- geological materials show huge variation (10
^{24}) in resistivities: 1.6 x 10^{-8}for native silver to 1.6 x 10^{16}for pure sulphur

Archie’s Law

In sedimentary rocks, resistivity of pore fluid is probably
single most important factor controlling resistivity of whole rock.

Archie (1942) developed empirical formula for effective resistivity of
rock:

where f is porosity, s is the volume fraction
of pores with water, and r_{w} is resistivity of pore fluid.

a, m, and n are empirically determined constants:

0.5<a<2.5

1.3<m<2.5

n ~ 2

r_{w} is controlled by dissolved salts and can vary between 0.05 ohm-m for saline groundwater to 1000 ohm-m for glacial meltwater.

- Archie’s Law ignores the effect of pore
geometry, but is a reasonable approximation in many sedimentary rocks

- In granite, where porosity is due to fracturing
law can break down

Common Resistivity Values

Common Resistivity Values (cont)

Range of Resistivities
for Common Rock Types

Current Flow from One Electrode in a Uniform Earth

For single electrode planted in the Earth with circuit
completed by another very distant electrode, current flow is radially
symmetric.

Current Density

If current I flowing into ground at electrode, that current
is distributed over hemispherical shell. Current density J given by:

J decreases with increasing distance as current dissipates.

Voltage at Distance r

From Ohm’s Law applied to a hemispherical shell of radius r
and thickness dr, voltage change across shell is
given by:

So voltage (or potential) at distance r given by
summing shells:

(V_{r}=0, inf)

Potential Difference with Two Electrodes

If second electrode is placed at B close to first electrode
located at A, it affects current distribution and ground potential:

Potential at any point P in ground is equal to
sum of potential from each electrode (c.f. work done going uphill by different paths):

For electrodes at M and N, can use single electrode
expression:

Actually measure differences in potential,. Between M and N is:

So resistivity of ground is:

Resistivity given by measured voltage and
electrode geometry

Current Flow in Uniform Earth with Two Electrodes

Current injected by electrode at S_{1}
and exits by electrode at S_{2}:

Lines of constant potential (equipotential) are
no longer spherical shells, but can be calculated from expression derived
previously.

Current flow is always
perpendicular to equipotential lines.

- Where ground is uniform, measured resistivity
should not change with electrode configuration and surface location

- Where inhomogeneity present, resistivity varies
with electrode position. Computed value is called
__apparent resistivity____r__._{A}

Depth of Current Penetration

Current flow tends to occur close to the surface. Current penetration
can be increased by increasing separation of current electrodes.

Proportion of current flowing beneath depth z as
a function of current electrode separation AB:

Example

If target depth equals electrode separation,
only 30% of current flows beneath that level.

- To energise a target, electrode separation
typically needs to be 2-3 times its depth.

- High electrode separations limited by
practicality of working with long cable lengths. Separations usually less
than 1 km.

Electrode Configurations and Geometric Factors

The general expression for resistivity derived previously,
which in practice is the apparent resistivity, can be written as:

where R is a resistance term given by *R=**d**V/ I *and K is given by:

K is called the __geometric
factor__ for the electrode array.

Electrode Arrays

- An electrode array consists of two electrodes at
which DC current flows into and out of the ground plus two electrodes between
which the potential difference at the surface is measured .

- The
__apparent__resistivity measured by different arrays is not the same, because the geometric factor K is different.

Example

Suppose current and potential electrodes are equally spaced.
Then K simplifies to:

This type of array is called a Wenner
Array invented in 1912

Common Electrode Arrays

- Below are electrode arrays most commonly used in
resistivity

- C are current electrodes and P are potential
measurement electrodes. X is location assigned to measurement.

Geometric Factors and Apparent Resistivities

Wenner Array

Schlumberger Array

Dipole-Dipole

Square

Properties of Different Electrode Arrays

Different subsurface current flow from different electrode
arrays.

Relative contributions from
subsurface to measured potential for different electrode arrays (dashed lines
negative):

A. Wenner: Alternating +ve and –ve near-surface
regions cancel, and main response is from depth, which is fairly uniform
laterally. Good for determining depth variations in
1-D Earth.

B. Schlumberger: Equivalent vertical resolution to
Wenner (distance between contours), but deep response is concave upwards. More sensitive to lateral variation in Earth.

C.Dipole-Dipole: Poor vertical resolution as contours spaced widely. Lobes
from each dipole penetrate deeply indicating good
sensitivity to lateral variation at depth.

Offset Wenner Array

Wenner array often offset to repeat reading.
Average value used.

Example

Consider buried sphere with resitivity of 100 ohm-m.

- When sphere in area of positive signal
contribution, measured apparent resistivity is 91.86 ohm-m.

- When sphere in area of negative signal
contribution, measured apparent resistivity is 107.81 ohm-m.

- Average of two readings is
99.88 ohm-m.

- Example of reduced error: Offset Wenner curve is
smoother.

Current Flow in Layered Media

More realistic to consider vertical layers, for example
water saturated horizontal aquifer.

Current flowing vertically through layers will traverse each
in series, like resistors connected in series in an electrical circuit.
Transverse resistance given by:

Current flowing laterally will tend to take path of least resistance,
and layers will behave as resistors connected in parallel. Longitudinal
conductance given by:

Problem is that measured resistivity is a
function of both layer resistivity and layer thickness, and both cannot be
easily resolved.

Example

5-m thick layer with resistivity of 100 ohm-m, has same
lateral resistivity as 10-m thick layer with 200 ohm-m resistivity.

Refraction of Electrical Current

In a uniform Earth with no boundaries, with two widely
separated electrodes (one at infinity), current flow is radially symmetric.

If nearby boundary, current flow is deviated: away from more
resistive medium, towards more conductive one.

Current flow refracts at boundary in proportion to change in
resistivity:

Example of Current Flow in Two Layer Medium

Have already found direction of current flow between two
electrodes in uniform medium:

In two layer medium, current travels
preferentially in low resistivity medium.

Method of Images

Potential at point close to a boundary can be found using
"Method of Images" from optics.

In optics:

Two media separated by semitransparent mirror of reflection
and transmission coefficients k and 1-k, with light source in medium 1.

- Intensity at a point in medium 1 is due to source and its
reflection, considered as image source in second
medium, i.e source scaled by reflection coefficient k.

- Intensity at point in medium 2 is due only to source scaled
by transmission coefficient 1-k as light passed through boundary.

Electrical Reflection Coefficient

In electrical current flow:

Consider point current source and find expression for
current potentials in medium 1 and medium 2:

Use potential from point source, but 4p as shell is spherical:

Potential at point P in medium 1:

Potential at point Q in medium2:

At point on boundary mid-way between source and its image:

r_{1}=r_{2}=r_{3}=r say. Setting V_{p}
= V_{q}, and cancelling we get:

Solving for k:

k is electrical reflection coefficient and used in
interpretation

Practical Resistivity Surveys

By Ohm’s Law we need to measure the current that flows into
the ground and the potential difference at various surface locations.

Need high resistance in potential measuring
circuit to avoid short circuiting ground: most commercial systems have
>1Mohm.

Problems:

- With DC currents, anions build up around anode
(+ve electrode), and cations around cathode (-ve electrode).

- Telluric currents, naturally occurring currents,
flow in Earth and create regional potential gradients that confuse
readings.

- Cable lengths also restrict surveys, particular
for deep objectives where electrode separations must be large

Solutions:

- Use very low frequency AC alternating current to
reduce ion buld up: anode and cathode are switched repeatedly.

- Average measurement over several cycles, so
effects of telluric currents and anion buildup tend to cancel.

Complication:

Depth of penetration changes with AC frequency, so need to
select appropriate value for survey:

·
10 m deep target requires ~100 Hz

- 100 m deep target requires ~10
Hz

Two Main Survey Methods:

Vertical Electrical Sounding: Depth variation in resistivity

Constant Separation Traversing: Lateral variations in resistivity

Vertical Electrical Souding (VES)

Increasing distance between current electrodes increases
depth of current penetration into Earth.

Vertical Electrical Sounding (r_{a} vs. depth)

Measurements are repeated as array is expanded about
a fixed point, maintainng the relative spacing of the electrodes.

Used to find overburden thickness, aquifers and
other horizontal structures

Wenner:

- All four electrodes have to be moved for each
measurement

Schlumberger:

- Potential electrodes are kept fixed until
measured voltage decreases to low values as potential gradient in ground
falls with increasing current electrode separation.

- Then moved and process repeated.

Dipole-Dipole and Square:

- Rarely used for VES surveys

Constant Separation Traversing (CST)

Constant Separation Traversing (r_{a} vs. lateral distance)

Measurements are repeated as array is moved
along a profile with electrodes maintained at fixed distances.

Used to detect shear zones, faults and other
vertical boundaries

- In practice, acquisition can be simplified by
laying out more than four electrodes, and using a subset for the reading.

- While reading made, electrodes can be moved from
back to front of line to speed up acquisition.

Example

With 12 electrodes at 5 m intervals:

- Record Wenner array of 10 m spacing (distance
between adjacent electrodes) using alternating electrodes.
- 5 m station spacing along profile.

Examples of Resistivity Data

Vertical Electrical Sounding

Apparent resistivity usually plotted on
logarithmic scale against electrode half-separation

Constant Separation Traversing

Resistivity values plotted on linear scale
against location of centre of array along profile.

- Clay filled (more conductive) dissolution
feature in limestone

Qualitative CST Interpretation: In-Line Array

As array moves toward lower resistivity medium, current flow
lines converge on interface:

i.
Current density increased at boundary, but decreased at potential
measurement electrodes, so r_{a} falls.

ii.
r_{a} falls until C_{2} at boundary when r_{a} reaches a minimum

iii.
When C_{2} crosses boundary, current density increases
close to boundary in medium 2, and is at a maximum when first potential
electrode reaches boundary

iv.
When entire array has crossed boundary, current density highest in
resistive medium, and r_{a} falls sharply at potential dipole.

v.
When C_{2} crosses boundary, current density deflected
from medium 1, increasing potential gradient slightly at potential dipole.

Qualitative CST Interpretation: Cross-Line Array

If array is oriented perpendicular to profile, current flow
changes smoothly, and cusps in r_{a} curve do not occur.

r_{a} varies smoothly from resistivity of medium 1 to
value of medium 2

Qualitative CST Interpretation: Pseudosections

A single CST survey produces a profile of r_{a} vs. distance.

Increasing the electrode separation, increases
depth of penetration.

Repeating the same profile with different electrode spacing,
allows construction of a __pseudosection__
of apparent resistivity.

Pseudosection is constructed by plotting measured
value at intersection of lines drawn at 45^{o} from current and
potential dipoles, and contouring result. (Discussed in detail in IP section)

Vertical axis is electrode spacing **NOT**
depth, but does give a very
approximate idea of the depth variation of r_{a}

Example of Pseudosection (Faulted Bedrock, UK)

Qualitative VES Interpretation: Two Layers

Basic Idea: Can consider current flow to refract in
subsurface at layer boundaries, like light at a boundary.

Two Layer Earth

Consider Wenner array over two layer Earth:

Depth of current penetration increases with electrode
separation a

For small a:

Current flows almost entirely in layer 1: r_{a} ~ r_{1}

As a increases:

Current flow lines reach interface, and are refracted
towards interface as less resistive path is more attractive to current.

r_{1} > r_{a} > r_{2}

For large a:

Almost all current flows in lower less resistive layer: r_{a} ~ r_{2}

Only two possibilities in two layer case: r_{a} increases or decreases

Qualitative VES Interpretation: Three Layers

In three layer case, more variations in sounding
curves exist

1. First part of curve at small
electrode separations can be analysed as two layer case to see if r_{a} increase or decreases into second
layer.

2. Comparing curve at small and large
spacings indicates resistivity of lower layer relative to upper.

3. Character of mid-part of curve
indicates nature of middle layer:

- Types H & K have distinct maximum/minimum
and indicate anomalously high/low resistivity respectively.

- Types A & Q show steady change indicating
middle layer has r intermediate between upper and
lower layer

Layer only shows up in curve if it is
sufficiently thick, and resistivity sufficiently different from others, e.g. D with small h_{2}.

Qualitative VES Interpretation: Four Layers

Many more combinations possible in four layer
case

Two Examples:

- In general, number of detectable layers equal to
number of turning points in sounding curve plus one.

- Turning point due to interface, so number of
layers is one greater.

- Electrode separation, at which
turning points occur, has no connection with depth to interface.

Example: Interface location plotted on electrode
separation axis

Quantitative VES Interpretation: Master Curves

Layer resistivity values can be estimated by matching to a
set of __master curves__ calculated assuming a layered Earth, in which layer thickness increases
with depth. (seems to work well)

For two layers, master curves can be represented
on a single plot

Master curves:
log-log plot with r_{a} / r_{1} on vertical axis and a / h on horizontal (h is depth to interface)

- Plot smoothed field data on log-log graph
transparency.
- Overlay transparency on master curves keeping
axes parallel.
- Note electrode spacing on transparency at which
(a / h=1) to get interface depth.
- Note electrode spacing on transparency at which
(r
_{a}/ r_{1}=1) to get resistivity of layer 1. - Read off value of k to calculate resistivity of
layer 2 from:

Quantitative VES Interpretation: Inversion

Curve matching is also used for three layer models, but book
of many more curves.

Recently, computer-based methods have become common:

- forward modelling with layer
thicknesses and resistivities provided by user
- inversion methods where model parameters
iteratively estimated from data subject to user supplied constraints

Example (Barker, 1992)

Start with model of as many layers as data points and
resistivity equal to measured apparent resistivity value.

Calculated curve does not match data, but can be perturbed
to improve fit.

Application to Bedrock Depth Determination

Both VES and CST are useful in determining bedrock depth

- Bedrock usually more resistive than
overburden

Example (South Wales)

For sewer construction wanted to avoid having to blast into
sandstone bedrock.

CST profiling with Wenner array at 10 m spacing and 10 m
station interval used to map bedrock highs

- Location where bedrock close to
surface shown by CST profile.

- Depth to bedrock determined at
specific locations by VES survey.

Application to Location of Permafrost

Permafrost represents significant difficulty to construction
projects due to excavation problems and thawing after construction.

- Ice has high resistivity of
1-120 Mohm-m

Example (Fairbanks, Alaska)

Need to identify permafrost prior to construction of road
cutting

- Dashed line data acquired in spring are dashed
line

- Solid line is data acquired in autumn and has lower
resolution due to layer of thawed ground.

Application to Landfill Mapping

Resistivity increasingly used to investigate landfills:

- Leachates often conductive due
to dissolved salts

- Landfills can be resistive or
conductive, depends on contents

Example (Yorkshire, UK)

VES survey carried out over landfill. Resistivities in
ohm-m.

Three/Four layer VES analyses made at each sounding location
depending on shape of r_{a} curve.

Results plotted side by side to constuct 2-D model of
landfill.

- Landfill shows as 10 m thick layer with 20 ohm-m
resistivity

- Bedrock shows as much higher 200 ohm-m layer

- Contaminated sandstone beneath landfill seen as
anomalously low resistivity layer with value of ~9 ohm-m.