CHAPTER 3 LITERATURE REVIEW

3.1 Groundwater Exploration

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).