Examination of Geology

1. PART I
ELECTRICAL METHODS

2. Introduction
Geophysical methods can be classed as either:
I. Passive (involving measurements of naturally
existing fields) or
II. active, if the response of the ground to some
stimulus is observed.
 Passive methods include measurements of
magnetic and gravity fields, naturally occurring
alpha and gamma radiation, and natural electrical
fields (SP and Magnetotellurics).
 All other electrical and electromagnetic
techniques, seismic methods, and some down hole
methods that use artificial radioactive sources are
active.

3. Introduction
 Electrical prospecting involves the detection of
subsurface effects produced by electric current flow in
the ground.
 Using electrical methods, one may measure potentials,
currents, and electromagnetic fields which occur
naturally or are introduced artificially in the earth.
 Electrical methods are often classified, by the type of
energy source involved, into Natural or Artificial.

4. Introduction
Those utilizing the natural field of the earth
Self potential, etc
Methods utilizing the artificial sources
Electrical resistivity, induced polarization, etc
 Electrical methods are more frequently used in
searching for metals, groundwater, archaeology,
engineering and environmental problems because
most of them have proved effective for shallow
exploration, except telluric method which penetrate to
the depths where oil and gas are normally found.

5. Introduction ----Cont
The electrical methods of prospecting are more
diversified than the other geophysical methods
and comprise the following:
 Electrical Resistivity Method
 Induced Polarization
 Self potential

6. Electrical prospecting relates to three properties of earth
i. Resistivity (ρ): which governs the amount of current
passing through a rock for a given tame.
ii. Electrochemical Activity: relates the effect of electrolytic
behavior to current flow.
iii. Dielectric constant : provides information on the capacity
of rock material to store charge.
Application of Electrical Methods:
 Mineral Exploration
In search of for metallic/ non-metallic deposits
Mapping of mineralized zones

7. Ground Water Exploration
a. For horizontal stratified zones
b. Depth to the saturated horizons
c. For contacts/vertical that may control the
movement of ground water
d. For mapping of structural discontinuities like
faults, dykes, vein, fissures and fractures which
may be:
-Zones of segregated mineralization
-Conduits for flow of fluids like ground water
 Zones of weakness when the area is desired for
engineering

8. e. For mapping basement surfaces underlying
weathered top layers or sedimentary- basis
(depth to the bed rock)
f. For Geothermal exploration (especially for
shallow depth rock) to map high conductivity
zones
g. For Archaeological site investigation
h. locate narrow mine shafts or other forms of buried
cavities.
 Environmental

9. Basic resistivity theory
 The relative abilities of materials to conduct electricity
where a voltage is applied are expressed as
conductivities.
 Conversely, the resistance offered by a material to
current flow is expressed in terms of resistivity.

10. Basic definition of resistivity
across a homogenous Block of
side length L with an applied
current I and potential drop
between opposite faces of V
The material within the cube
resists the conduction of
electricity through it, resulting
in a potential drop (V) between
opposite faces.
R α L
R α 1/A
R α L/A
R = ρ (L/A) , Where ρ, the constant of proportionality is known
as the electrical resistivity
The resistance (R) is directly proportional to
its length (L) of the resistive material and
inversely proportional to its cross sectional
area (A) that is:

11.  According to Ohm's law: R = Δ V / I
ρ = (Δ V/I) (A/L)
R = ρ (L/A) ,
This Equation is used to determine the
resistivity (ρ) of homogeneous and isotropic
materials in the form of regular geometrical
shapes such as cylinders, cubes, ….

12.  In a semi-infinite material, the resistivity is defined
using Ohm's law that states; the electrical field
strength (E) at a point in a material is proportional to
the current density (J) passing that point:
E α J
E = ρ J
ρ = E/J ……. (Ohm's law)

13.  In an isotropic medium the current density J and the
potential gradient E have the same direction.
 From Ohm’s law; the resistance of a conductor of
length l and cross section area A is given as:
 Considering an elementary cube( )of
homogeneous rock ,oriented with Δz in the
direction of J.

14.  Accordingly;
But,
For which follows
Then:
where V is the electric potential

15.  The fundamental physical law used in resistivity surveys is
Ohm’s Law that governs the flow of current in the ground.
 The equation for Ohm’s Law in vector form for current flow in
a continuous medium is given by
……….(1.1)
where is the conductivity of the medium, J is the current
density and E is the electric field intensity.
 In practice, what is measured is the electric field potential.
 In geophysical surveys the medium resistivity (ρ), which is
equals to the reciprocal of the conductivity (σ) is more
commonly used.

16.  The relationship between the electric potential and the
field intensity is given by
(1.2)
 Combining equations (1.1) and (1.2) , we get
 This is the basic equation that gives the potential
distribution in the ground due to a point current source.

17. Electric Current flow in homogeneous earth
 For the conservation of charge;
And for stationary charge:
According to ohm’s law:
Then: , which is the fundamental
equation for electrical
prospecting with direct
current.

18.  When the medium is homogeneous and isotropic, the
resistivity is constant in all direction and becomes;
In such a medium J and E have the same
direction ,in other words, the resistivity is a
scalar function of place

19. One current electrode at surface
 Consider a single current electrode on the surface
of a medium of uniform resistivity (Fig. below).

20.  The circuit is completed by a current sink at a large
distance from the electrode.
 Current flows radially away from the electrode so that
the current distribution is uniform over hemispherical
shells centered on the source.
 At a distance r from the electrode the shell has a
surface area of , so the current density j is given
by;

21.  The current flows radially away from the source, and
the potential varies inversely with distance (r) from the
current source.
 The equipotential surfaces have a hemisphere shape,
and the current flow is perpendicular to the
equipotential surface.
 The potential in this case is given by:

22. The potential in this case is given by:
Where, r is the distance of a point in the medium
(including the ground surface) from the electrode.
 In practice, all resistivity surveys use at least two current
electrodes, a positive current and a negative current source

23. There are three ways in which electric current can be
conducted through a rock (materials of the Earth):
i. Electronic (ohmic) (conduction in metals and
crystals)
ii. Electrolytic, ( Conduction in liquids) and
iii. Dielectric conduction ( conduction in insulators).
 The conductivity of the rock is a combination of the
conductivity of the rock material (matrix) itself and
that of the fluid in its pores

24.  Electronic conductivity resulting from electron
motion in rock matrix. It is the process by which
metals, allow electrons to move rapidly, so carrying
the charge.
 Electrolytic conduction (in liquids) occurs by the
relatively slow movement of ions within an
electrolyte and depends upon the type of ion, ionic
concentration and mobility, etc. It is this
conductivity that determines the conductivity of
the rocks

25.  It varies with;
the pore volume
the pore shape
the % of pores filled with fluid and
with the conductivity of the pore fluid
 Dielectric conduction occurs in very weakly conducting
materials (or insulators) which contain no free
electrons. when an external alternating current is
applied, so causing atomic electrons to be shifted
slightly with respect to their nuclei.

26.  The electrons are distributed symmetrically about a
nucleus. However, an electric field displaces the
electrons in the direction opposite to that of the field,
while the heavy nucleus shifts slightly in the direction
of the field.
 The atom or ion acquires an electric polarization and
acts like an electric dipole. The net effect is to change
the permittivity of the material from 0 to a different
value , given by



27.  In most rocks, conduction is by way of pore fluids acting
as electrolytes with the actual mineral grains contributing
very little to the overall conductivity of the rock (except
where those grains are themselves good electronic
conductors).
 Archie developed an empirical formula for the effective
resistivity of a rock formation which takes into account the
porosity (Φ) , the fraction (S) of the pores containing water,
and the resistivity of the water (ρw). Archie's Law is used
predominantly in borehole logging
W


28. Archie's Law is given as:
where and are the effective rock resistivity, and the
resistivity of the pore water, respectively; is the
porosity; S is the volume fraction of pores with water;
a, m and n are constants ;where, and
 The ratio is known as the Formation Factor (F).
 The purpose of electrical surveys is to determine the
subsurface resistivity distribution by making
measurements on the ground surface.

29. All substances act to retards the flow of electric current.
The extent to which a substance restrains this movement
is described as electrical resistivity
The ground resistivity is related to various geological
parameters such as:
the mineral and fluid content
porosity and
degree of water saturation in the rock
 Electrical resistivity surveys have been used for many
decades in hydrogeological, mining and geotechnical
investigations.
 More recently, it has been used for environmental
surveys.

30. Electrical Properties of Earth Materials
 The resistivity (ρ) of rocks and minerals displays a wide
range. For example, graphite has a resistivity of the order
of 10-5 ohm-m, whereas some dry quartzite rocks have
resistivity of more than 1012 ohm-m.
 Igneous rocks tend to have the highest resistivity,
sedimentary rocks tend to be most conductive due to their
high pore fluid content. Metamorphic rocks have
intermediate but overlapping resistivity
 The age of a rock is an important consideration: a
Quaternary volcanic rock may have a resistivity in the range
10-200 Ωm while that of an equivalent rock but Pre-
Cambrian in age may be an order of magnitude greater.

31.  Some minerals such as pyrite, galena and magnetite
are commonly poor conductors in massive form yet
their individual crystals have high conductivities.
 Hematite and sphalerite, when pure, are virtual
insulators, but when combined with impurities they
can become very good conductors (with resistivity as
low as 0.1 Ωm).
 Resistivity for sandy material are about 100 Ωm and
decrease with increasing clay content to about 40 Ωm.

32. The resistivity of rocks, soils and minerals

33. Factors controlling the resistivity of earth materials
 The electrical current is carried through the earth
material by either :
1) Motion of free electrons or ions in the solid. This is
important when dealing with certain kinds of minerals
such as graphite, magnetite or pyrite.
2) Motion of ions in the connate water, come from the
dissociation of salts such as sodium chlorite,
magnesium chloride. This is important when dealing
with engineering and hydrogeology.

34.  For water bearing rocks and earth materials, the
resistivity decreases with increasing:
1) Fractional volume of the rocks occupied by water
2) Salinity or free ion content of the connate water
3) Interconnection of the pore spaces (i.e. permeability
and porosity).
 From the proceeding, we may infer that:
A. Materials which lack pore spaces will show high
resistivity such as:
i) Massive limestone.
ii) Most igneous and metamorphic rocks such as
granite and basalt.

35. B. Materials whose pore spaces lacks water will show high
resistivity ( dry sand or gravel)
C. Materials whose connate water is clean (free from salinity)
will show high resistivity, even if water saturated.
D. Most other materials will show medium or low resistivity,
especially if clay is present, such as: clay soil and weathered
rocks.
 The presence of clay minerals tends to decrease the resistivity
because:
i) The clay minerals can combine with water.
ii) The clay minerals absorb cations in an exchangeable state on
the surface.
iii) The clay minerals tend to ionize and contribute to the supply
of free ions.

36.  As a rough guide, we may divide earth materials
into:
a) Low resistivity less than 100 Ωm.
b) Medium resistivity 100 to 1000 Ωm
c) High resistivity greater than 1000 Ωm.

37.  The resistivity of common rocks, soil materials and
chemicals is shown in Figure above.
 Igneous and metamorphic rocks typically have high
resistivity values.
 The resistivity of these rocks is greatly dependent on
the degree of fracturing, and the percentage of the
fractures filled with ground water.
 Sedimentary rocks, which are usually more porous and
have higher water content, normally have lower
resistivity values compared to igneous and
metamorphic rocks.
 Unconsolidated sediments generally have even lower
resistivity values than sedimentary rocks.

38.  The resistivity value is dependent on the porosity
(assuming all the pores are saturated) as well as the clay
content.
 Clayey soil normally has a lower resistivity value than sandy
soil. However, note that there is the overlap in the
resistivity values of the different classes of rocks and soils.
This is because the resistivity of a particular rock or soil
sample depends on a number of factors such as the
porosity, the degree of water saturation and the
concentration of dissolved salts.
 Chemicals that are strong electrolytes, such as potassium
chloride and sodium chloride, can greatly reduce the
resistivity of ground water to less than 1 Ωm even at fairly
low concentrations.

39.  As shown in the following Figure the potential
distribution is caused by a pair of electrodes.
C1 C2
rc2p2
rc1p1
P1 P2
rc1p2 rc2p2
where and are distances of the point from the first and second current
electrodes.
 The convectional practice in electrical resistivity surveying is to use
source and sink electrodes connected to a battery to compel current
to flow in the ground.

40. A conventional array with four electrodes to
measure the subsurface resistivity

41. The Resistivity Method
 The most common used methods for measuring earth
resistivity are those in which current is driven through
the ground using galvanic contact.
 Four – terminal electrode arrays are used since the
effect of material near the current contacts can be
minimized.
 Current is driven through one pair of electrodes (A &
B) and the potential established in the earth by this
current is measured with the second pair of electrodes
(M & N).

42. Current flow through earth

43. Electrodes
A. Current Electrodes:
 They are generally steel, aluminum or brass.
 They are Stainless steel is best for combined strength
and resistance to corrosion.
 They are driven a few inches into the ground
 In dry ground , the soil around the electrodes may
have to be moistened or watered to improve contact
 To reduce the contact resistance, many stakes driven
into the ground a few feets apart and connected in
parallel.

44. B. Potential Electrodes
 Contact resistance is not important in case of potential
electrodes as in case of current electrodes.
 Potential electrodes must be stable electrically.
 Stable electrode may be obtained by using a non-
polarizing electrode.

45. Apparent Resistivity:
 All resistivity techniques in general require the
measurement of apparent resistivity
 In making resistivity surveys a direct current or very
low frequency current is introduced into the ground
via two electrodes (A & B) and the potential difference
is measured between a second pair of electrodes (M &
N).
 If the four electrodes are arranged in any of several
possible patterns, the current and potential
measurement may be used to calculate apparent
resistivity

46.  If the measurement of (ρ) is made over a semi-infinite
space of homogeneous and isotropic material, then
the value of (ρ) will be true resistivity of the
material.
 If the medium is in-homogenous and or anisotropic,
the resistivity is called apparent resistivity ( ).

47. Electrode configuration
 For field practice a number of different surface
configurations are used for the current and potential
electrodes .
 When two current electrodes A and B and Two
measuring electrodes (potential probes) M and N
arranged as follows, then the potential difference
between M and N is given as:
A M N B

48.  There are three main types of electrode configuration
1) Wenner array
 For the Wenner array, so that
, Where is geometric factor

49. 2) Schlumberger Array
A M N B
l
r1 r2
L
Where and are distances from the midpoint of MN
to respectively A and B, and

50. For the symmetric Schlumberger array,
For
and
where

51. 3) Dipole – Dipole array (Double – dipole system)
 In a dipole – dipole array, the distance between the
current electrodes A and B (current dipole) and the
distance between the potential electrodes M and N
(measuring dipole) are significantly smaller than the
distance (r) between the centers of the two dipoles.

52. If each pair has a contact separation ‘a’ and ‘na’ is
the distance between the two innermost
electrodes (B & M), then
ρa = K .ΔV/I
ρa = {πn (n + 1) (n +2) a } (ΔV/I)

53. o A conventional array with four electrodes to measure the
subsurface resistivity

54.  Where the ground is uniform, the resistivity calculated
should be constant and independent of both electrode
spacing and surface location.
 When subsurface inhomogeneities exist, however, the
resistivity will vary with the relative positions of the
electrodes.

55.  In resistivity survey low-frequency alternating current is
employed rather than direct current, for two main reasons:
 Firstly, if direct current were employed there would
eventually be a build-up of anions around the negative
electrode and cations around the positive electrode; that is,
electrolytic polarization would occur, and this would inhibit
the arrival of further ions at the electrodes. Periodic reversal
of the current prevents such an accumulation of ions and thus
overcomes electrolytic polarization.
 Secondly, the use of alternating current overcomes the effects
of telluric currents, which are natural electric currents in the
ground that flow parallel to the Earth’s surface and cause
regional potential gradients. The use of alternating current
nullifies their effects since at each current reversal the telluric
currents alternately increase or decrease the measured
potential difference by equal amounts

56.  Summing the results over several cycles thus removes
telluric effects .
 The frequency of the alternating current used in
resistivity surveying depends upon the required depth of
penetration.
 For penetration of the order of 10m, a frequency of 100Hz
is suitable, and this is decreased to less than 10 Hz for
depths of investigation of about 100m.
 For very deep ground penetration direct currents must
be used, and more complex measures adopted to
overcome electrolytic polarization and telluric current
effects.
 Many modern instruments make use of a square wave
current input to overcome the polarization.

57. FIELD PROCEDURES RESISTIVITY METHOD
 There are only two basic procedures in resistivity work.
 The procedure to be used depends on whether we are
interesting in lateral or vertical variations in resistivity.
i) Vertical Electrical Sounding (VES or drilling)
ii)Electrical horizontal profiling (mapping )

58. i. Vertical Electrical Sounding
 VES , is by which the variation of resistivity with depth
below a given point on the ground surface is deduced
and it can be correlated with the available geological
information in order to infer the depths (or thicknesses)
and resistivity of the layers (formations) present.
 VES is based on the fact that the current penetrates
continuously deeper with the increasing separation of
the current electrodes.
 When the electrode separation, C1 C2 , is small
compared with the thickness, h, of the upper layer, the
apparent resistivity as determined by measuring (ΔV)
between the potential electrodes, P1P2 , would be
virtually the same as the resistivity of the upper layer (ρ1)

59.  The values of apparent resistivity are plotted on a
graph (field curve), the x- and y-axes of which
represent the logarithmic values of the current
electrode half-separation (AB/2) and the apparent
resistivity (ρa), respectively
 Schlumberger sounding ;

60.  The potential electrodes (M & N) are kept at a fixed
spacing (b) which is no more than 1/5 of the current
electrode half spacing (a).
 The current electrodes (A & B) are moved outward
symmetrically in steps
 It is advisable then to have an overlap of two or three
readings with the same AB and the new as well as the
old MN distance
 The ρa values with the two MN distances but the same
AB distance sometimes differ significantly from each
other.

61. In this case, if the results are plotted as (ρa )
against AB (or AB/2) on a double logarithmic
paper, each set of (ρa ) values obtained in the
overlapping region with one and the same MN
will be found to lie on separate curve segments,
displaced from each other.

62. Dipole – Dipole sounding
The distance between the two dipoles (i.e. AB &
MN) is increased progressively to produce the
sounding.
Once the dipole length has been chosen (i.e. the distance
between the two current electrodes and between the two
potential electrodes), the distance between the two dipoles
is then increased progressively to produce the sounding

63.  Applied when the ground is layered(determine the depth to
the different layers).
 The method consists of observing the changes in potential
difference between the potential probes when the distance
between the current electrodes are gradually increased.
 The current and potential electrodes are in one line and the
center part of the array remains fixed. The center point of
the electrode array remains fixed, but the spacing between
the electrodes is increased to obtain more information
about the deeper sections of the subsurface.
 The depth of penetration depends upon the electrical
properties of the layers and in particular of the surface
layers.

64.  Roughly the penetration depth, as an average, is half of the
current electrode distance. However, for reliable
observations the electrode spacing should be about four
times the desired depth of penetration.
 The measured apparent resistivity values are normally
plotted on a log-log graph paper.
 To interpret the data from such a survey, it is normally
assumed that the subsurface consists of horizontal layers.
In this case, the subsurface resistivity changes only with
depth, but does not change in the laterally.
 This method has given useful results for geological
situations (such the water-table) where the one-
dimensional model is approximately true.

65.  The greatest limitation of the resistivity sounding method
is that it does not take into account lateral changes in the
layer resistivity. Such changes are probably the rule rather
than the exception. The failure to include the effect of such
lateral changes can results in errors in the interpreted layer
resistivity and/or thickness.
 The technique is extensively used in geotechnical surveys
to determine overburden thickness and also in
hydrogeology to define horizontal zones of porous strata.
 A sounding can be rapidly accomplished by switching
between different sets of four electrodes.

66. Electrical horizontal profiling (mapping )
 In profiling method, the spacing between the electrodes
remains fixed, but the entire array is moved along a straight
line. This gives some information about lateral changes in the
subsurface resistivity, but it cannot detect vertical changes in
the resistivity. Interpretation of data from profiling surveys is
mainly qualitative. The most severe limitation of the
resistivity sounding method is that horizontal (or lateral)
changes in the subsurface resistivity are commonly found.
This method is employed
 in search for ore bodies or geological mapping.
 in mapping an area by moving a fixed electrode array along
traverses and observing the potential variations.

67.  in mineral prospecting to locate faults or shear zones
 to detect localized bodies of anomalous conductivity.
 It is also used in geotechnical surveys to determine
variations in bedrock depth and the presence of steep
discontinuities.
 Results from a series of electrical profiling (CST) traverses
with a fixed electrode spacing can be employed in the
production of resistivity contour maps.

68.  The electrode spacing of the array corresponds to the
required depth of penetrations.
 The electrode configuration used for resistivity surveys are
many, among these the very widely used are the Wenner
and Schlumberger configuration.
 To reduce the effect of spontaneous potentials, very low
frequency current is often used or reversible direct
currents.
 The frequency of the alternating current must be so low
that induction currents play no role i.e. of the order of
1Herz or lower. At higher frequencies the direct current
theory is no longer applicable.

69. Interpretation

70. Interpretation
 A Model layer is described by two fundamental
parameters: its resistivity ( ρ ) and its thickness (h).
 Longitudinal unit conductance ( S = h/ ρ = hσ)
 Transverse unit résistance ( T = h ρ)
 Longitudinal resistivity (ρL = h/S )
 Transverse resistivity (ρt = T/h )
 Anisotropy (λ = √ρt / ρL )
 For an isotropic layer ρt = ρL and λ = 1.

71. The parameters S, T, λ , ρt and ρL are derived from
consideration of a column of unit square cross-
sectional area of layers of infinite lateral extension as
follows in the figure shown:

72.  If current flows vertically total resistance of the
column of unit cross – sectional area will be :
T = T1 + T2 + T3 +…… Tn
= ρ1 (h1 + ρ2 (h2) +…… ρn (hn)
T= Σ ρi hi
If the current flows parallel to the bedding , the
conductance will be
S = 1/T = 1/T1 + 1/T2 + ……+ 1/Tn
S = h1/ρ1 + h2/(ρ2) + ….hn/ρn
S= Σ hi/ρi

73.  Example:
Assume that a geoelectric unit consists of an alternating
series of beds with a total thickness of 100m. the
individual beds being isotropic, one meter thick and
resistivity alternating between 50 and 200 ohmm.
 T = Σρihi = 50 x 50 + 200 x 50 = 12.500 ohm-m2
 ρt = T/H = 12.500 / 100= 125 ohm.m
 S = Σσihi = 50 x 1/200 = 1.25 mhos
 ρL= H/S = 100/1.25 = 80 ohm.m
 λ = √ρt / ρL = 125/80 = 1.25

74.  Homogeneous and isotropic medium (One layer
medium):
If the ground is composed of a single homogeneous
and isotropic layer of infinite thickness and finite
resistivity, the apparent resistivity curve will be a
straight horizontal line whose ordinate is equal to the
true resistivity (ρt) of the semi-infinite medium.
TYPES OF ELECTRICAL SOUNDING CURVES

75. Single layer medium

76. Two-layer Schlumberger curves

77. Three-layer medium

78.  There are four possible combinations between the
values of ρ1 , ρ2 , ρ3 . These are:
1) ρ1 > ρ2 < ρ3 …… H-type curve (minimum type)
2) ρ1 < ρ2 < ρ3 …… A-type curve (ascending type)
3) ρ1 < ρ2 > ρ3 …... K-type curve (maximum type)
4) ρ1 > ρ2 > ρ3 …… Q-type curve (descending type)

80. Eight possible types of sounding curves for
four-layer Earth models

81. 1. ρ1 > ρ2 < ρ3 < ρ4 ………… HA – type curve
2. ρ1 > ρ2 < ρ3 > ρ4 ………… HK – type curve
3. ρ1 < ρ2 < ρ3 < ρ4 ………… AA – type curve
4. ρ1 < ρ2 < ρ3 > ρ4 ………… AK – type curve
5. ρ1 < ρ2 > ρ3 < ρ4 ………… KH - type curve
6. ρ1 < ρ2 > ρ3 > ρ4 ………… KQ – type curve
7. ρ1 > ρ2 > ρ3 < ρ4 ………… QH – type curve
8. ρ1 > ρ2 > ρ3 > ρ4 ………… QQ – type curve

82. DaDU Exam
 Reason why silicate minerals are abundant in the earth's crust
 Facters affect the following
 Gravitational acceleration of earth
 Resistivity
 4) differentiate
 Intensity and magnitude of quake earth
 Active and passive geophysical methods
 Reverse and thrust fault
 Symmetrical and asymmetrical folds
 Induced and remnant magnetic
 Direct and indirect geophysical method.
 Wenner and Schlumberger electron configuration
 Positive and negative magnetic