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CHAPTER 3 LITERATURE REVIEW

3.1       Groundwater Exploration

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The
use of geophysical methods for groundwater exploration depends on the
understanding of the geology, hydrogeology, the topography of the study area
and a good interpretation of reliable geophysical data (Appiah,
2002). Geological factors primarily consider geological structures which
control potential groundwater sources in the study area and physical properties
namely; density, resistivity, electrical conductivity. These factors inform the
selection of the appropriate geophysical methods to be employed in a particular
area (Daly, 1987). In major alluvial plains with
sufficient rainfall, groundwater may be developed at relatively shallow depths
and hence little or no geophysical investigations is required for groundwater
exploration and are highly successful wherever they are developed. However, for
a geologically heterogeneous formation, investigations ranging from simple
field observation to a more expensive exploratory drilling of boreholes may
become necessary to ensure such successes. In certain formation, studying the
geomorphology is an excellent way for groundwater exploration (MacDonald et al,
2005).

According
to (MacDonald et al, 2005), the
following factors are normally considered for groundwater exploration in a
geologically heterogeneous formation:

i.       
Valleys follow the lines of major faults,
so the valleys may be a good place to explore for groundwater.

ii.      Some
basement location where the topography is undulating, groundwater may be
explored halfway down slope towards the bottom of the valleys. The bottom of
the valleys is mostly clayey, and the top of the interfluves are unweathered to
support aquifers.

iii.    Inselbergs
(also known as bornhardts, kopjes, tors) in basement rocks offer
good conditions for groundwater exploration where gravels could be found around
the base of these large and rounded hills.

iv.    Sedimentary
areas, where sandstones and mudstones are interbedded, sandstones can often be
identified by slight ridges or high grounds.

 

3.1.2    Water Dowsing

Water
dowsing is the practice of using of forked stick, rod, pendulum etc. to locate groundwater, minerals and
lost substances (USGS, 1988). The dowsing method works by using a forked stick
in each hand with the palms upwards. The bottom of the forked stick is pointed
skyward at an angle of about 45o. The dowser then walks back and
forth over the area to be tested and when its passed over a water source, the
bottom of the forked stick is supposed to rotate or attracted downwards (USGS,
1988). Dowsers believe that the attraction of the water may be so great that
the bark of the forked stick is able to peel off as the rod twists in the
hands.

Water
dowsing however is mainly practiced in rural or suburban communities where
settlers are uncertain as to how to locate the best and cheapest supply of
groundwater (USGS, 1988). Most homeowners resort to water dowsing due to the
cost involved in the drilling a dry well. Compared to geophysical methods,
water dowsing is unscientific and the use of it has received unanimous
condemnation by geologist.

 

3.2       The Electromagnetic Method

The
electromagnetic geophysical method measures the subsurface conductivity variations
to delineate aquifers. Several electromagnetic geophysical methods exist and
each have the advantage of being rapid as none requires the penetration of
electrodes into the ground (Fetter, 2001). Electromagnetic surveys can be
conducted in either Frequency Domain (FEM) or Time Domain (TEM). The Frequency
Domain survey is a continuous excitation method whilst the Time Domain survey
measures the electrical response of the subsurface to a pulsed waves of
different times of the order of micro to milliseconds after the transmitter
current has been turned off (Hitzig et al., 1997).

Applications
of both the Time Domain and Frequency Domain methods are common and popular in
mineral exploration (Anon., 2018a). The major difference in its application in
both groundwater and mineral exploration is the conductivity contrast being
much smaller in groundwater exploration than in mineral prospecting (Anon.,
2018a).

Frequency
Domain method is used as a reconnaissance and for delineating aquifers and for
the selection of sites for drilling of water wells. Electromagnetic magnetic
methods however are often used in conjunction with electrical resistivity
methods.

A
small conductive mass within a poorly conductive environment has a greater
effect on induction than on direct current resistivity and hence
electromagnetic methods focuses on conductivity which is a measure of the
reciprocal of resistivity rather than on measuring resistivity directly (Kearey
et al., 2002). Ground conductivity is
measured in milliSiemens per metre (mS/m or mhos/m).

 

3.2.1    General Principle of the Electromagnetic
Method

The
electromagnetic method primarily measures the ground or terrain conductivity by
low frequency electromagnetic induction. The electromagnetic method uses
electromagnetic field generated by a transmitter coil through which an
alternating current is passed (Fetter, 2001). A transmitter coil radiates a
primary electromagnetic field which propagates above and below the ground (Figure).

 

Source: Kearey, 2002

For
a homogeneous subsurface, there is no significant difference between the
propagated field above the surface and the subsurface except a small decrement
in the amplitude of the surface with respect to the subsurface (Kearey et al., 2002).

When
a conductive medium is present within the subsurface, the magnetic component of
the incident electromagnetic wave induces eddy currents within the conductor
(Reynolds, 1997). The eddy currents produce secondary electromagnetic field
which is detected by a receiver coil. The receiver responds to the resultant of
the arriving primary and secondary fields so that the response differs in both
phase and amplitude from the response to the primary field alone. The
difference between the transmitted and received electromagnetic fields reveal the
presence of the conductor and provide information on its geometry and electric
properties (Kearey et al., 2002).

 

3.2.2    Theory of the Electromagnetic Method

Electromagnetic
method measures the response of the ground to the propagation of electromagnetic
fields, which are composed of an alternating electric intensity and magnetizing
force in a plane perpendicular to the direction of travel (Kearey et al., 2002). The strength and
direction of the magnetic field component can be expressed in terms of the magnetic
flux density or magnetic induction (Reynolds, 1997). The strength and direction
of the magnetic field can also be expressed in terms of the magnetic field or
magnetizing force (Reynolds, 1997).

Source:

A
transmitter coil placed on the earth surface is assumed to generate a primary
magnetic field which induces eddy currents within the earth and consequently
generate secondary magnetic field which is detected at the receiver together
with the primary field by the receiver coil. This secondary coil is generally a
complicated function of the inter-coil spacing, operating frequency and the
ground conductivity (McNeil, 1980).

The
ratio of the amplitude of the secondary magnetic field to amplitude of the
primary magnetic field is directly proportional to the apparent ground
conductivity at low induction number (Kearey et al., 2002). According to Kearey at al., 2002, apparent conductivity measurements taken at a low
induction number is expressed mathematically as:

…………………………. eqn 3.1

Where
Hs = amplitude of the secondary electromagnetic field

Hp
= amplitude of the primary electromagnetic field

s=ground
conductivity

 
where f is the frequency(Hz)

µo
=
the magnetic permeability of vacuum

s
= the inter-coil separation and

 and its presence indicates the quadrature
component being measured.

Since
the ratio Hs/Hp is proportional to the ground
conductivity, the above equation allows the construction of electromagnetic
instructions and hence provide a direct reading of ground conductivity to a
predetermined depth (Kearey at
al., 2002).

 

3.2.3    Physical Quantities and Field Equations

The
Maxwell equations explain the propagation and attenuation of electromagnetic
field using a set of differential equations. The Maxwell equations are space
and time dependent. These equations are:

i.       
Gauss Law for electricity. Expressed as r=V.
D

Where D is the electric displacement (C/m2)

r= volume charge density (C/m3)

 

ii.      Gauss
law of magnetism. Expressed as V. B = 0

Where B is the magnetic flux density
(Tesla, T)

V= divergence operator (1 per metre)

 

iii.    Faraday’s
law of induction.

Expressed as

Where E is the electric field (V/m)

Faraday’s
law of induction indicates that an electric field is generated by a change in
magnetic field with respect to time.

 

iv.  Ampere
law. Expressed as

Where H is the magnetic field
strength(A/m)

j= free current density (A/m2)

Ampere’s
law indicates that a magnetic field produced by a free current density and an electric
displacement.

For
a homogeneous or linear media, the electric displacement is expressed as

 and

 where

 is
dielectric constant and

 is
the magnetic permeability. Also, the Ampere law explains that an external
current density is the source of the electromagnetic waves and hence the
antenna in the system (Anon., 2018b).

 

3.2.4    Depth of Penetration of Electromagnetic
Fields

The
criteria used to estimate the depth of penetration of electromagnetic waves is
the skin depth (Telford et al., 1990). The skin depth is defined as the distance
which the amplitude electromagnetic wave signals falls to

 (where

 is
the base of natural logarithm)of its original value (Milson, 2003). The skin
depth is also defined the reciprocal of the constant of attenuation constant
and decreases almost two-thirds over a single skin depth (Milson, 2003).

Let
Ad
be the amplitude of electromagnetic wave as a function of the depth of
penetration d, then mathematically:

   
…………………………………eqn 3.2

Where

Amplitude of the field

 is
the surface amplitude

The
depth of penetration is then expressed mathematically as:

………………………………………eqn 3.3

Where

 is
the skin depth in metres

 is
the ground conductivity in S/m

 is
the frequency of the field in Hz

Equation
3.3 is theoretical and also represent as inverse relationship between the skin
depth and frequency and ground conductivity and hence the depth of penetration
increases as the frequency of the field decreases (Kearey et al. 2002). Also magnetic permeability is approximated to unity
as most materials related to groundwater exploration cannot be magnetized
(Milson, 2003).

The
effective depth of penetration

is defined as the maximum depth at which
a conductor may lie and still produce a recognizable electromagnetic anomaly
(Kearey et al. 2002). Empirically the
effective depth of penetration is expressed as:

   ……………………………eqn 3.4

The
dependence of the depth of penetration on frequency is a constraint on the
electromagnetic method as very low frequencies are difficult to generate and
measure (Kearey et al. 2002).

 

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