TITLE PAGE FORWARD AND INVERSE MODELING OF …

i

TITLE PAGE

FORWARD AND INVERSE MODELING OF AEROMAGNETIC DATA

FOR MINERALS AND INTRUSIVES IN ABAKALIKI AREA, EBONYI

STATE

BY

EZE, IFEOMA DORIS

PG/M.Sc./07/42862

A THESIS SUBMITTED TO DEPARTMENT OF PHYSICS AND

ASTRONOMY, UNIVERSITY OF NIGERIA NSUKKA IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF

MASTER OF SCIENCE (M.Sc.) IN GEOPHYSICS

MAY, 2011

ii

CERTIFICATION

Eze, Ifeoma Doris, a post graduate student with reg. number PG/M.Sc./07/42862 has

satisfactorily completed the requirement of course and research work for the degree of Master

of Science (M.Sc.) in Geophysics, in the Department of Physics and Astronomy, University of

Nigeria, Nsukka.

This research work is original and has not been submitted in full or part for any other

diploma submitted in full or part in any other University.

…………………. ……………….. Dr. P. O. Ezema Date Supervisor

……………......... …………….. External examiner Date

…………………….… ....…………. Prof. C. M. I. Okoye Date Head of Department

iii

DEDICATION

This thesis is dedicated to all the exploration geophysicist.

iv

ACKNOWLEDGEMENT

My profound gratitude goes to Almighty God for His abundant grace. I also

acknowledge the role played by my able supervisor, Dr. P.O. Ezema. I sincerely appreciate his

encouragement, and guidance throughout the work. His prompt attention to the numerous

consultations and enquires, are commendable.

My appreciation also goes to my lecturers for the knowledge they have impacted on me.

Special thanks also go to my beloved husband and all the members of my family for

their financial and moral support.

I must not forget the effort of my dear friends, Blessing and Robert to mention but a

few whose encouragement helped me in this work.

v

ABSTRACT

Aeromagnetic data of Abakaliki in the Lower Benue Trough flown at an altitude of

80m with line spacing of 500m and cross tie of 2km was used for this study. The data

was made available in the digital form on the scale of 1: 50, 000. The data was

processed using computer software (Potent). Polynomial fitting was used to remove the

regional fields from the observed data while forward and inverse modeling technique

was used to model the profiles. Three profiles were taken on the residual map and were

modeled. The results showed 5 intrusive bodies, granulites, pyrite, and igneous

basement. The depths of the intrusives and minerals ranged from 2.4km – 6.32km, with

areas around Abakaliki town having enough sedimentary thickness of 3.5km -4.7km for

hydrocarbon generation. Dolerite intrusives were mainly found at areas around Idemba

–Iza, and Abba Omega at depths of 2.4km, 2.7km, and 3.6km respectively. The range

of depths of the anomalies at Abakaliki town makes the area favorable for hydrocarbon

generation and potential for mineral deposits.

vi

TABLE OF CONTENTS

Title page - - - - - - - - - - i

Certification - - - - - - - - - - - ii

Dedication - - - - - - - - - - iii

Acknowledgment - - - - - - - - - iv

Abstract - - - - - - - - - - - v

Table of contents - - - - - - - - - vi

List of figures - - - - - - - - - - viii

List of tables - - - - - - - - - - - ix

CHAPTER ONE: INTRODUCTION

1.1 Background of study - - - - - - - - - 1

1.2 Purpose of the study - - - - - - - - - 5

1.3 Geology of the area - - - - - - - - - 5

1.4 The stratigraphy of lower Benue Trough - - - - - - 7

1.5 Mineralization in Benue Trough -- - - - - - - 9

1.6 Fundamental and basic concept of magnetic prospecting - - - 11

1.7 Magnetic anomalies - - - - - - - - - 17

1.8 The Geomagnetic field - - - - - - - - - 18

CHAPTER TWO: LITERATURE REVIEW

Review of previous geological and geophysical studies in the area - - - 22

CHAPTER THREE: THEORY OF MAGNETIC METHODS

3.1 Introduction - - - - - - - - - - 26

3.2 Magnetic effects of simple shapes - - - - - - 27

3.3 Methods of aeromagnetic data interpretation - - - - - 33

CHAPTER FOUR: DATA ANALYSIS AND MODELING

4.1 Data source - - - - - - - - - 41

4.2 Data analysis - - - - - - - - - - 41

4.3 The potent computer modeling program - - - - - - 45

4.4 Modeling of selected profiles - - - - - - - - 50

vii

CHAPTER FIVE: RESULT, CONCLUSION AND RECOMMENDATION

5.1 Results - - - - - - - - - - 55

5.2 Discussion - - - - - - - - - - 57

5.3 Conclusion - - - - - - - - - - 57

5.4 Recommendation - - - - - - - - - 58

REFERENCES

APPENDIX

viii

LIST OF FIGURES

Fig 1.1 Map of study area - - - - - - - 2

Fig. 1.2: Geology map of Benue Trough - - - - - 7

Fig. 1.3: Alignment of atoms and molecules in the presence of magnetic field 12

Fig. 1.4: Vector representation of the geomagnetic field - - - 18

Fig. 1.5: The elements of geomagnetic field - - - - - 19

Fig. 3.1: Relationships and notations used to derive the magnetic effect of a Single pole - - - - - - - - 28

Fig. 3.2: (a,b) Relationships and notations for a magnetic field of a dipole - 30

Fig. 3.3: Notation used for the derivation of magnetic field anomalies over a Uniformly magnetized sphere - - - - - 32

Fig. 3.4 Idealized magnetic profile showing measurements for slope (S) and half slope (P) - - - - - - - 35

Fig. 3.5: Schematic magnetic profile with quantities measured in Grant and

Martins’s system of depth estimation. - - - - 36 Fig.3.6: Co-ordinate Axes - - - - - - - 40

Fig. 4.1: Sheet 303, Abakaliki aeromagnetic contour map - - - 42

Fig. 4.2: 2008 aeromagnetic digital data for Abakaliki - - - 43

Fig. 4.3: Residual map of Abakiliki - - - - - - 45

Fig. 4.4: Definition of a Slab - - - - - - - 46

Fig. 4.5: Definition of a Dyke - - - - - - - 46

Fig. 4.6: Definition of a Cylinder - - - - - - 47

Fig. 4.7: Definition of an Ellipsoid - - - - - - 47

Fig. 4.8: Definition of a Lens - - - - - - - 48

Fig. 4.9: Definition of a Polygonal Prism - - - - - 48

Fig. 4.10: Definition of a Sphere - - - - - - 49

Fig. 4.11: Residual map of the study area showing 3 profiles - - 51

Fig. 4.12: Modeled profile A - - - - - - - 52

Fig. 4.13: Modeled profile B - - - - - - - 53

Fig. 4.14: Modeled profile C - - - - - - - 54

ix

LIST OF TABLES

Table 1.1: Stratigraphic sequence of the Lower-Middle-Upper Benue and

Chad basins - - - - - - - - 9

Table 1.2: Magnetic susceptibilities of selected rocks and minerals - - - 14

Table 5.1: Summary of the results - - - - - - - 56

1

CHAPTER ONE

INTRODUCTION

1.1: Background Study

Magnetic surveying investigates the subsurface based on variations in the Earth’s magnetic

field that result from the magnetic properties of the underlying rocks. It is the oldest method of

geophysical prospecting but has become relegated to a minor importance because of the advent

of seismic exploration. The studied area is located within and around Abakaliki area in Ebonyi

state (Fig.1.1). It is situated within the lower Benue Trough and is bounded by latitudes 60N

and N0360 and longitudes E08 and E0380 . The aerial extent covers 3080.25 2km . In the

present study, forward and inverse modeling technique was used to determine susceptibilities

‘k’ and depth ‘z’ to the centre of the anomalies observed on the aeromagnetic map of the

study area. Thus, the study shows the relationships between surface and subsurface features.

Therefore, the aeromagnetic survey helps to investigate the depth to magnetic basement rocks

in the sedimentary basin. With aeromagnetic survey major basement surface structure is

indicated which reveal encouraging exploration areas that can be studied in detail using more

costly but more concise and more specific seismic method of geophysical exploration.

2

Fig. 1.1: Map of study area (Modified from geology map of Nigeria, 1994)

In principle, magnetic surveying is similar to gravity, i.e. we are dealing with the potential

fields. However the application of gravity and magnetic methods in oil exploration is quite

different. While gravity effects are caused by sources which may vary in depth within the

subsurface, the sedimentary rocks which are the ones in which oil may occur, are always less

3

magnetic than the underlying basement usually igneous or metamorphic rocks. There are three

fundamental differences between the two fields;

We are dealing with vector fields, not scalar. We cannot always assume that the

magnetic field is vertical as we can for gravity.

Magnetic poles can be repulsive or attractive. They are not always attractive as in

gravity.

The magnetic field is dependent on mineralogy or grain properties, not bulk properties.

Thus, what may be a trivial change in composition can have a large effect on the

magnetic field.

In terms of line-km measured each year, it is the most widely used survey method. The

problems involved in interpreting magnetic anomalies greatly limit their use. These problems

are:

(1): The geometry of the body

(2): The direction of the earth field at the location the body

(3): The direction of polarization of the rocks forming the body

(4): The orientation of the body with respect to the direction of the earth’s field

(5): The orientation of the line of observation (flight line) with respect to the axis of the body

Magnetic survey can be carried out on land, air and sea. In our case we will focus on

magnetic survey in air, commonly called aeromagnetic survey. The aeromagnetic survey is a

powerful tool in delineating the regional geology (lithology and structure) of buried basement

terrain. The detailed aeromagnetic map is proven to be very effective in cases where the

geology of the studied area is clearly known (Aero-service, 1984). According to Reford (1962),

the earth’s magnetic field, acting on magnetic minerals in the crust of the earth induces a

4

secondary field, which reflects the distribution of these minerals. The main magnetic field

varies slowly from one place to another. However, the crustal field, which is the portion of the

magnetic field associated with the magnetism of crustal rocks and from remanent

magnetization, is the chief interest in magnetic prospecting, and is referred to as magnetic

anomaly. Airborne measurements are made high enough above the surface to eliminate the

effects of small, near surface intrusions of magnetic material or of cultural objects (buildings,

pipelines, railways etc). The airborne magnetometer records variations in the total magnetic

field. The regional correction removes the greater part of the primary field of the earth, so that

the local variations are emphasized. Although several familiar minerals have high

susceptibilities (magnetite, ilmenite, and pyrrhotite), magnetite is by far the most common.

Rock susceptibility is directly related to the percentage of magnetite present. Spatial variations

of the crustal field, is usually smaller than the main field, nearly constant in time and place

depending on the local geology. The local magnetic anomalies are the targets in magnetic

prospecting. The very high gradient on an aeromagnetic map usually indicates the difference in

magnetic susceptibility such as that between granite (acidic rock), andesite (intermediate rock)

and basalt (basic rock). The shape of the causative body may be inferred as in the case of

circular contours with vertical magnetization, where the body may be a plug. In ca of elongated

closed contours, the source may be a dyke and the direction of elongation should indicate its

strike. However, in the case of elongated zone of steep gradient without well-defined closures,

it is quite possible that its pattern results from subsurface faulting, which has displaced

magnetized rocks (Dobrin and Savit, 1988).

5

1.2: Purpose of the study

Abakaliki was chosen as the study area because it has a lot of potentials for hydrocarbon and

minerals such as Lead, Zinc, Silver, Salt, Limestone, and Dolerite. The Abakaliki anticlinorium

is flanked by two synclines one to which coincides with the Anambra valley while the other

one passes through Afikpo. Also Nigeria is currently intensifying surveys in eight basins in the

country with a view to opening frontier exploration for hydrocarbon mapping. These basins

include Bida, Dahomey, Gongola/Yola, and Sokoto basins, alongside with Middle/Lower

Benue Trough. Abakaliki falls within the Anambra basin in the lower Benue Trough.

The purpose of this work is to use forward and Inverse modeling technique to interpret the

anomalous features in the study area. The study is aimed at providing information on the

following;

(a): Types of intrusive bodies in the area (b) : Depth to the centre of the anomalous bodies(z in km) (c) : Shape, position(X,Y in meters),dip, plunge and strike of the anomalies (d) : Susceptibilities of rocks and minerals in the study area. This detailed information will help

to determine ore bodies and hydrocarbon potential in the area.

1.3: Geology of the Area

The sequence of events that led to the formation of the Benue Trough and its component units

(Fig. 1.2 and Table1) are well documented (Burke et al, 1975; Benkhelil, 1982, 1988;

Nwachukwu, 1972; Olade, 1975; Ofoegbu, 1984, 1985; Onuoha and Ofoegbu, 1988). The

lower Benue Trough is underlain by a thick sedimentary sequence deposited in the Cretaceous.

6

The Precambrian basement complex is made up essentially of granitic and magmatic rocks

which outcrop in the eastern portion of the study area. (Ofoebgu and Onuoha, 1990).

The sediments that occur in the Abakaliki Anticlinoriun belong to four geological formations:

Awgu shale(Caniacian); Nkporo shale(Campanian); Eze-Aku shale(Turonian); and Asu River

Group(Albian).

The Albian Asu River Group consists of bluish black shales with very minor sandstone

units. The shales are fissile and highly fractured. In the vicinity of Abakaliki, these shales are

associated with pyroclastic rocks.

The Eze-Aku Formation consists of a sequence of calcareous sandstones Reyment (1965). The

Awgu shales consist of marine fossiliferous grey bluish shales, limestone and calcareous

sandstones of Caniacian age. These are overlain by the Nkporo shales (Campanian), which are

also mainly marine in character.

These sedimentary sequences were affected by large scale tectonic activities which

occurred in two phases and culminated in the folding of the sediments (Nwachukwu, 1972).

The folding episode that took place during the Santonian strongly affected the development

of Abakaliki Anticlinorium. The predominantly compressional nature of the fold that

developed during this period is revealed by their asymmetry and the reversed faults associated

with them.

Benkhelil (1988) in a detailed report on the geology of the Abakaliki domain likened its

geological development to that which occurs in a complete orogenic cycle including

sedimentation, magmatism, metamorphism and compressive tectonics. He suggests that the

scale folding and cleavage was directed N 1550E. The magmatism that occurred resulted in the

injection of numerous intrusive bodies into the shales of Eze-Aku and Asu River Group.

7

Intermediate intrusive outcropped in some parts of the study area, for example in Abakaliki

town and also around Odomoke. These intrusives occur mainly as sills (Ofoegbu, 1985; Eze

and Mamah , 1985).

Fig. 1.2: Geology map of Benue Trough (Peters, 1982)

1.4: The stratigraphy of Lower Benue Trough

The study area falls within the lower Benue Trough (Table1.1). The stratigraphic succession in

the lower Benue Trough has been discussed by several authors (Reyment, 1965, Murat, 1972;

Peters, 1978a; Agagu, 1978; and Agagu et al., 1985). The sedimentation in the Benue Trough

8

was controlled by two dominant factors namely: the progressive ecstatic rise in sea level from

Albian and the consequent widespread drowning of the continental margins, and the creation of

vast interior seaways during the Cenomanian and Turonian times and local diastrophism. Both

processes resulted in the transgressive - regressive cycles that characterized depositional

pattern.

Calcareous shales were deposited in the structural depressions during trangressive phase while

shoal carbonates developed on submerged structural highs (platforms,) protected from clastic

influx. Extensive deltaic sediments, filling the subsiding basin and by predominantly fine

clastic (shallow marine shales) deposits over the structural highs dominated the regressive

phases. Agagu (1978) recognized five respective cycles depositing marine shales and

limestones and fluvio-deltaic sandstones and shales in the Upper Cretaceous sequence while

the Tertiary has only one cycle. The local geology is made-up of a cyclic sequence of

fossiliferrous upward fining shales and limestone beds. The limestone beds thicken southwards

and grade laterally into shale (Umeji, 1984).

9

1.5: Mineralization in Benue Trough

Occurrence of lead, zinc, silver and barites have been recorded in parts of the Lower Benue

Trough of Abakaliki, Ishiagu, and Arufu/Akwana areas.

The Trough, which is believed to have originated as a failed arm of an aulacogen at the time of

the opening of the South Atlantic Ocean during the separation of African plate and the South

American plate, is partitioned into the lower, middle and upper region with lead-zinc

mineralization occurring in almost the entire Trough.

The lead-zinc strata is localized along the northeast-southwest trending belt of slightly

deformed volcanic and sedimentary cretaceous sequences (Albian Asu River group) which is

about 500m thick, and they occur in the form of veins and veinlets associated with the host

rock.

Table 1.1: Stratigraphic sequence of Lower – Middle –Upper Benue and Chad basin (Kogbe, 1981)

10

Lower Benue Trough Lead-Zinc Mineralization

The general geology of lower Benue Trough in Abakaliki is made up of thick sequence 500m

(Ofoegbu,1985). There is presence of volcanic and pyroclastic materials forming elongated

conical hills in the cores of the anticlinal structures. The Abakaliki lead-zinc is believed to be

of hydrothermal origin emplaced at a high temperature of about 140oC , and it is found in

Ishiagu, Enyigba, Ameri and Ameka in the lower Benue Trough.

Middle Benue Trough Lead-Zinc Mineralization.

The middle Benue trough veins are located mainly in Akwana and Arufu. This mineralization

is hosted in silicified limestone sequence and also belongs to the Asu River Group. Dips of

these veins are generally steep to vertical with a width of between 0.5m – 10m and length of

approximately 100m along the strike length of the bodies. Limestone at Arufu and Akwana is

highly silicified, which appears to be related to the mineralization processes as the intensity of

the silicification decreases away from the vein.

Upper Benue Trough lead-Zinc Mineralization:

This Trough is made up of sedimentary sequences consisting of medium to fine grained

sandstone which is divided into Bima sandstone (upper Albian Age); and yolde sandstone

(Cenomanianan age) shales of yolde formation which underlies the alluvium which is

associated with the sandstones as intercalations. These mineralization zones are located in and

around Isamiya, Diji and Gidan Dari in Bauchi state.

11

1.6: Fundamental and Basic Concept of Magnetic prospecting

1.6.1: Magnetic Force

Magnetic Force is defined in terms of monopoles:

If two magnetic poles of strength m1 and m2 are separated by a distance r, the magnitude of

force between them is given by:

221

rmmF

1.1

Where is magnetic permeability of medium and depends on the magnetic properties of the

medium in which the poles are situated. The force is repulsive if the poles have the same sign,

attractive if they are of opposite sign.

1.6.2: Magnetic Field Strength H

Magnetic field strength vector H is defined as force per unit pole strength which would be

exerted upon a small pole of strength m, if placed at that point.

21

2

rm

mFH

1.2

Magnitude of H represents "closeness" of flux lines. The unit of H is tesla in SI which is the

magnetic field such that a force of 1 Newton is exerted on a pole with a strength of 1 ampere-

meter.(1ᵞ= 10-5 gauss=10-9 tesla=1nano tesla).

1.6.3: Intensity of Magnetisation or polarization (M or I)

A body placed in a magnetic field can become magnetized as atoms and molecules align in the

direction of the external applied field. The induced magnetization /polarization are proportional

to the strength of the external field.

12

Fig. 1.3: Alignment of atoms and molecules in the presence of magnetic field

The intensity of magnetization is the same as the magnetic dipole moment per unit volume.

The magnetic field strength within a body is made up of the external field H and the resulting

intensity of magnetization of the body.

If polarization has the same amplitude and direction throughout the body, the body is said to be

uniformly magnetized.

1.6.4: Total Magnetic Field B (Magnetic induction)

The Total Magnetic Field B represents the sum of the magnetizing field strength and the

magnetization of the medium:

HHkIHB 000 )1()( 1.3

Thus

HB

0

Where 0 is magnetic permeability of free space (4 x10-7 H/m)

B is also called the magnetic flux density or magnetic induction.

13

Magnitude of B represents "closeness" of flux lines. Direction of B is along flux lines.

Magnetic field is measured in volt. s /m2 = weber/m2 = teslas (T) in SI units. is measured in

weber/ (amp.m) = henry/m (H/m)

In geophysics, magnetic fields are small and measured in nT. Earth’s magnetic field varies

between 20,000nT in the equator and 60,000 nT at the poles.

1.6.5: Magnetic Susceptibility k and Permeability

The inherent magnetism of rocks called magnetic susceptibility is caused by changes in the

subsurface geologic structures. Placing a magnetizeable body in the influence of a magnetizing

force tends to align the dipole moment within the body in the direction of the magnetizing

force. The body thus takes on a degree of magnetization which is proportional to the

magnetizing force and also depends on the cause of magnetization of the body. The

susceptibility is a measure of the number of elementary magnet per unit volume of the material

and of their mobility or the ease with which they can be oriented. The Magnetic susceptibility

is the ratio of magnetization (i.e., magnetic moment per unit volume) in a substance to the

corresponding magnetic force H. It is mathematically expressed as

HI

1.4

Where I= intensity of magnetization

H= magnetizing force

The factor k, is the magnetic susceptibility. In SI units, k is “dimensionless”, since I and H

have the same unit (A/m).

14

Magnetic susceptibilities of rocks are the fundamental parameter in the applications of

magnetism for oil and gas exploration (Table 1.2). In every, case, the susceptibility of rocks

depends on the amount of magnetite (Fe204).

Table 1.2: Magnetic susceptibilities of selected rocks and minerals (modified from Dobrin and Savit, 1988).

Rock/Mineral Magnetic Susceptibility(SI unit)

Rocks Salt 0 – 0.001 Slate 0 – 0.002 Limestone 0.00001 –

0.0001 Granulite 0.0001 – 0.05 Rhyolite 0.00025 – 0.001 Greenstone 0.0005 – 0.001 Basalt 0.001 – 0.1 Gabbro 0.001 – 0.1 Dolerite 0.01 – 0.15 Basic igneous 0.0326 Minerals Pyrite 0.0001 – 0.005 Hematite 0.001 – 0.0001 Pyrrhotite 0.001 – 1.0 Chromite 0.0075 – 1.5 Magnetite 0.1 – 20.0

Magnetic permeability: here the magnetic force H and the resulting magnetic induction B are

usually parallel and proportional. The proportionality factor is called the “relative magnetic

permeability”. From the definition of B, it is evident that:

0

15

1.6.6: Rock Magnetism

Most common rock-forming minerals have very small magnetic susceptibilities. Anomalies in

the geomagnetic field are mainly caused by variations in the presence of a small proportion of

magnetic minerals found in the underlying rocks. There are two geochemical that contain these

minerals, the iron-sulphide group. The first group contains the mineral magnetite (Fe204) and a

solution between ilmenite (Fe Ti 03 ) and hematite (Fe203) (Blatt and Tracy, 1995). Magnetite

and ilmenite are ferromagnetic minerals and have a relative high magnetic susceptibility.

Hematite, on the other hand, is anti-ferromagnetic and does not give rise to any anomalies. The

second group provides the mineral pyrrhotite. The magnetic susceptibility of pyrrhotite is

dependent upon the actual composition of the mineral and is also a ferromagnetic mineral.

Magnetite content in rocks can vary dramatically, which makes direct correlation between

lithology and susceptibility very difficult. However, magnetic behaviour of rocks can be

classified according to their overall magnetite content. Basic igneous rocks have a relatively

high magnetite content, which causes them to be highly magnetic. The proportion of magnetite

in igneous rock tends to decrease with increasing silica content, making acid igneous rocks

generally less magnetic than basic igneous rocks. Metamorphic rocks also vary greatly in their

magnetite content. The abundance of iron and the partial pressure of oxygen, along with the

degrees of metamorphism, control the amount of magnetite and subsequently the degree of

susceptibility that is formed in the rock.

16

Sedimentary rocks are rarely magnetic, and most anomalies observed over sediment – covered

areas are caused by underlying igneous or metamorphic basement, or by intrusions into the

sediments. Other cause may include buried volcanic flows and man-made ferrous material.

1.6.7: Remanent Magnetism

Any rock containing magnetic minerals may posses both an induced magnetization vector Ji

and a remanent vector Jr. Induced magnetization is a direct result of the present-day

geomagnetic field and would be lost if the geomagnetic field could be removed. Natural

remanent magnetization (NRM) is a permanent magnetization of a rock and is dependent upon

the magnetic history of the rock. The total magnetization of a rock J is the vector sum of the

induced magnetization and remanet magnetization.

ri JJJ 1.5

There are several mechanisms by which natural remanent magnetization forms in rocks and

some of them are;

Chemical remanent magnetization (CRM): This is acquired as a result of chemical

grain accretion or alteration, and affects sedimentary and metamorphic rocks.

Detrital remanent magnetization (DRM) is acquired as particles settle in the presence of

Earth’s field. The particles tend to orient themselves as they settle.

Isothermal remanent magnetization (IRM): is the residual magnetic field left when an

external field is applied and removed, e.g. lightning.

Thermoremanent magnetization (TRM) is acquired when rock cools through the Curie

temperature, and characterizes most igneous rocks.

17

Viscous remanent magnetization (VRM) is acquired after a long exposure to an

external magnetic field.

The remanent magnetization can be measured using an astatic or spinner magnetometer, which

measures the magnetism of samples in the absence of the Earth’s field.

1.7: Magnetic Anomalies

All magnetic anomalies are superimposed on the geomagnetic field and are the result of

variations in the presence of magnetic minerals in the near surface crust. Common causes of

magnetic anomalies include dikes, faulted, folded or truncated sills and lava flows, massive

basic intrusion, metamorphic basement rocks and magnetite Ore bodies. The normal elements

of geomagnetic field at any point are related by

222 1.6

Where B HH 1 is the total geomagnetic field intensity and H and Z are the horizontal and

vertical components of B, respectively (figure 1.4a). if a magnetic anomaly is superimposed on

the geomagnetic field, there may be a change B in the strength of the total field vector B. At

any point, the anomaly produces a vertical component Z and a horizontal component H at

an angle α to H. Only the part of H in the direction of H, will contribute to the change in B

(figure 1.4b). Thus

HCosH 1 1.7

A vector sum of the magnetic anomaly and the geomagnetic field at any point is given by:

222 1.8

If equation 1.8 is expanded and ignoring insignificant terms in ∆2, it reduces to;

)()( 1

1.9

18

Substituting 1.7 and angular descriptions of geomagnetic element ratios into 1.9, we have

CosiCosSini 1.10

Where i is the inclination of geomagnetic field.

At any point on the Earth’s surface, the effects of all magnetic dipoles in the material can be

summed to give a net change B in the total geomagnetic field. In geomagnetic element ratio

B = Z sin i + H cos i cos 1.11

Where i = inclination of the geomagnetic field and = angle of inclination to H.

The figure 1.4 below shows the vector representation of the geomagnetic field with and

without a superimposed magnetic anomaly (Keary and Brooks, 1991).

I

Fig.1.4: Vector representation of the geomagnetic field with and without a superimposed

magnetic anomaly ( Keary and Brooks, 1991).

1.8: The Geomagnetic Field

The Earth’s main magnetic field, the geomagnetic field, is believed to be caused by a dynamo

action produced by the circulation of charged particles in coupled convection cells located

within the outer part of the Earth’s core. Since these circulation patterns within the outer core

change slowly with time, there is a slow, progressive, temporal change in the geomagnetic field

I

α

Magnetic North

(b)

H + 1H

B + B

Magnetic North

H

1H H

Z+Z

Z B

H

(a)

(c)

I Magnetic North

19

called secular variation. This change is evident in the observed gradual rotation of the north

magnetic pole around the geographic pole.

In addition to the secular variations of the geomagnetic field, there are magnetic effects of

external origin that change the field much more rapidly. These changes are due to magnetic

field induced by electrical currents in the ionized layer of the upper atmosphere. There are

diurnal variations in the geomagnetic field that range in amplitude from about 20-80 nano

Telsa (nT), with maximum variation at the polar regions. There is also far less regular and

much stronger short term variation in the geomagnetic field with amplitudes of up to 1000nT.

These disturbances are referred to as magnetic storms and are caused by intense solar activity.

Fig.1.5: The elements of geomagnetic field

The Earth’s magnetic field is described by seven parameters (Fig.1.5). These are;

20

Declination (D), Inclination (i), Horizontal intensity (H), Vertical

Intensity (Z), Total intensity (F) and the North (X) and East (Y) components of the horizontal

intensity.

The parameter most frequently requested and most often misunderstood is magnetic

declination or variation, D. This is the angle made between the trace of the total magnetic field

in the horizontal plane, H, and true north. D is considered positive when the angle measured is

east of true north and negative when west. The inclination or dip, i, is the angle between the

horizontal plane and the total magnetic field. Inclination, also called magnetic dip, is

considered positive when downward pointing. These elements, D, i and H give a full vector

representation of the total magnetic field, F. Vertical intensity is the trace of the total intensity

in the vertical plane and is considered positive when i, is positive, that is downward pointing.

The east component, Y, is considered positive when pointing east and the north component, X,

is positive when pointing towards geographic north.

At any specific point, the values of the magnetic elements are changing. The changes are not

uniform over area or time. Some types of change are distinguishable. Three important,

classifiable changes are the diurnal, secular and storm variations. The small regular

fluctuations in the magnetic field that occur more or less regularly every 24 hours are called

diurnal variations. Secular changes extend over years with generally smooth increases or

decreases in the field. Magnetic storms are sudden and potentially large disturbances in the

magnetic field which may last hours or days. Of these changes, the least understood is the

long-term change that occurs over years in the main magnetic field. The magnetic field can be

approximated by mathematical models over short periods of time, but because the secular

21

change is not predictable, the potential for error increases the further in time from the base

epoch the calculations are. For this reason, it is important to use the most current accepted

models of the magnetic field.

The International Geomagnetic Reference Field (IGRF) defines the theoretical undisturbed

geomagnetic field at any point along the Earth’s surface. Variations in the geomagnetic field

can be determined by subtracting the IGRF from observed magnetic field data. These

variations are referred to as magnetic anomalies.

22

CHAPTER TWO

LITERATURE REVIEW

Review of Previous Geological and geophysical Studies in the Area

Benue Trough of Nigeria is a major structure in West Africa which has attracted the attention

of geologists, geophysicist, and hydrogeologists. The Trough is characterized by the existence

of interesting geological structures and the presence of zones of mineralization of economic

importance. Intense geophysical investigations have been carried out for some time in different

parts of the Benue Trough. The first major geophysical survey carried out in the Benue trough

was done by Cratchley and Jones (1965). Most of the published works on the area were

reported on a regional basis. However, the area has been mapped by a lot of geologists like

(Reyment ,1965; and Okezie ,1965). Shell-Bp Development Company, in 1938-1958 carried

out an extensive geological and geographical survey of Abakaliki area prospecting for oil. In

1957, they carried out some geological mapping of the area using aerial photographs and

ground control to produce 250,000 geological maps. Reyment (1965) investigated the

ammonites found in shale of southern Nigeria and assigned the shale to Albian age. Okozie

(1965) studied and described the volcanic rocks of the Abakaliki area, as being made up of

dominantly tuffs and agglomerate lavas of andesitic composition. He also identified intrusive

diorite within Abakaliki area.Uzuakpunwa (1974) described the volcanic rocks of Abakaliki as

basic to intermediate pyroclastics of pre-Albainage overlain by the Abakaliki shale of the Asu-

river group.Ehinola ( 2010) in his preliminary studies on the lithostratigraphy and depositional

environment of the oil shale deposits of the Abakaliki folded belt indicates that three

lithostratigraphic units of Albian to Coniacian age are present; namely: Abakaliki, Eze-aku and

Awgu shales. He also noted that Abakaliki unit contains light brown to dark grey massive

23

shales and forms part of the Asu River group. The Eze-Aku shale is dark grey to black, while

the Awgu shale is dark grey and well bedded with limestone interbands. The mineralogical

analyses he carried out revealed that the principal mineral components of the area are quartz,

calcite, kaolinite and pyrite with field pars, muscorite and illite as secondary components.

Geochemical analysis indicates high values for the Si02, Ca0 and Fe203. He concluded that high

content of Ca0 indicates calcareous shale with marine condition prevailing. An assessment,

based on organic facies characteristics, has been carried out also by Ehinola (2010) on the

middle Cretaceous black shales in order to determine their hydrocarbon source potential,

thermal maturity, and depositional environment.

Furthermore, he carried out an extensive geological mapping and geochemical studies of the

oil shale deposit in the Abakaliki anticlinorium to determine the areal extent, reserve estimate,

recovery techniques and possible environmental impacts. He estimated an aerial extent of

72.7km2, reserve estimate of 5.76109 tonnes and recoverable hydrocarbon reserve estimate of

1.7109 barrels. Low concentration of sulphur (0.33-0.74%) and trace elements such as Ba,

Cd, Cu, Cr, Ni, Pd and Zn supports the economic viability of the oil shales as refinery feed

stock. In the Abakaliki Anticlinorium, exploration activities were originally geared towards the

search for lead-zinc deposits ( Bougue and Reynolds, 1951; Farrington, 1952), and for coal

deposits (Simpson, 1955; De Swardt and Casey, 1963). Early geophysical investigation in the

Benue Trough were mainly centred on the measurement and interpretation of gravity field

(cratchley and Jones, 1965; Ajakaiye and Burke, 1972; Adighije, 1979, 1981a, b, Ajakaiye,

1981, 1986) .Cratchley and Jones (1965) carried out on extensive gravity survey in the Benue

Trough and suggested a mantle uplift of 10-12km having a width of 190-220km under the

Trough. They further found out that the gravity field on the Trough was characterized by an

24

axial positive anomaly in the centre of the basin with negative anomalies on either flanks. The

central positive anomaly in the Trough was interpreted in terms of the combined effects of

zones of mafic/intermediate intrusions occurring either in the basement or within the

sedimentary basin (Adighije, 1981a; Ajayi and Ajakaiye 1981). The existence of several

basement ridges and basinal structure within the Trough as well as the folding and faulting of

sediments and the basement has been shown from the study of gravity field over the Benue

Trough (Fairhead and Okereke, 1987; Osazuwa et al ,1981) through an analysis of gravity

anomalies over the upper Benue Trough estimated the thickness of sediments in the upper

Benue Trough to vary between 0.9km and 4.6km. Ofoegbu and Onuoha (1989) in a review of

geophysical investigations in the Benue Trough have reported that the crustal extension from

gravity data in the middle Benue Trough ranges from 95-130km. Since the release of

aeromagnetic data collected over the Benue Trough by the Geological Survey of Nigeria (Now

called Nigerian Geological Survey Agency, NGSA), there has been an upsurge of interest in

the quantitative interpretation of aeromagnetic data. Ofoegbu (1984a, c) carried out an

interpretation of aeromagnetic anomalies over the Lower and Middle Benue Trough using

Non-Linear Optimization Technique. He interpreted the anomalies in the area in terms of basic

intrusive bodies which occur either within the Cretaceous sediments or within the metamorphic

basement or both and found the sediment thickness to vary between 0.5km to 7km. Ofoegbu

(1985b) has also interpreted long wavelength magnetic anomalies over parts of the Benue

Trough as being due to the variable position of the Curie isotherm of about 18-27km.The

knowledge of the depth to the Curie surface and its variation is of obvious interest and can be

related to the thermal history of the area. Ofoegbu and Onuoha (1991), through spectral

analysis of aeromagnetic data estimated the thickness of the Cretaceous sediments over the

25

Abakaliki Anticlinorium to vary between 1.2km and 2.5km. Also, Ahmed Nur et al. (1994)

carried out a Two-dimensional Spectral Analysis of Aeromagnetic Data over the Middle Benue

Trough to determine the depth to magnetic sources in the area. The result of the analysis shows

that the depth to the deeper sources varies between 1600 – 5000m, while the shallower depth

source model lies between 60-1200m.

Obi et. al. (2010) carried out Aeromagnetic Modeling of Subsurface Intrusive and its

implication on Hydrocarbon Evaluation of the Lower Benue Trough. Their result showed the

presence of 12 intrusive bodies with sediment thickness that range from 1.0km – 4.0km in

areas around Nkalagu, Abakaliki, Ikot Ekpene and Uwet. He concluded that these intrusive

have enough sediment thickness (greater than 2km) for hydrocarbon generation.

26

CHAPTER THREE

THEORY OF MAGNETIC METHODS

3.1 INTRODUCTION

The purpose of magnetic surveying is to identify and describe regions of the Earth’s crust that

have unusual (anomalous) magnetizations. In the realm of applied geophysics, the anomalous

magnetizations might be associated with local mineralization that is potentially of commercial

interest, or they could be due to subsurface structures that have a bearing on the location of oil

deposits Lowrie (2004).

The surveying of magnetic anomalies can be carried out on land (Ground survey), at sea

(marine borne) and in the air (air borne).

In practice, the surveying of magnetic anomalies is most efficiently carried out from an

aircraft. As the aircraft flies, the magnetometer records tiny variations in the intensity of the

ambient magnetic field due to the temporal effects of the constantly varying solar wind and

spatial variations in the Earth's magnetic field, the latter being due both to the regional

magnetic field, and the local effect of magnetic minerals in the Earth's crust . Aeromagnetic

data was once presented as contour plots, but now is more commonly expressed as coloured

and shaded computer generated pseudo-topography images. The apparent hills, ridges and

valleys are referred to as aeromagnetic anomalies. Geophysicist can use mathematical

modeling to infer the shape, depth and properties of the rock bodies responsible for these

anomalies.Air borne surveying is extremely attractive because of low cost and high speed. Also

the flight elevation may be chosen to favour structures of certain size and depth. Aeromagnetic

survey can be used over water and in regions inaccessible for ground work.

27

3.2 Magnetic Effects of Simple Shapes

3.2.1. The isolated pole (monopole):

Although an isolated pole is a fiction, in practice it may be used to represent a steepy dipping

dipole whose lower pole is far away that has a negligible effect. A very long and thin body

oriented vertically and magnetized along its length essentially functions as a monopole, as the

top surface has a pole strength of –m and the bottom surface (+m) is sufficiently far removed

for its effect to be eligible.

From fundamental principle of magnetic method, magnetostatic potential:

rmV ,

AkFIAm E ,

where k is susceptibility, EF is the earth’s magnetic field, A is the area and I is the magnetic

intensity

Where m = pole strength and from the figure below; 2/122 cr

But magnetic intensity is equal to magnetic moment per unit volume.

Thus, V

Magnetic field is determined by taking the negative of the derivative in that direction.

28

Fig. 3.1: Relationships and notations used to derive the magnetic effect of a single pole (H.R.

Burger, 1992).

Using the relations for magnetostatic potential, intensity of magnetization and susceptibility we

have:

2

3222 zyx

AkFr

AkFrmV EE

3.1

But

23222

212

zyx

AkFzdzdv E

23222 zyx

AkFz E

3.2

Where FE is the inducing field and A is the cross-sectional area .HAx and HAy which are the

horizontal components of the anomalous field parallel to X and Y of the earth’s field can also

be determined using the same approach.

r

αθ

+x

-x

+y -y

-m

z

p

y

c x

-x

+x Magnetic North

29

2

3222 zyx

AkFxdxdV E

Ax

3.3a

23222 zyx

AkFydydVH E

Ay

3.3b

But AXH represents the component of the horizontal anomalous field in the direction of

magnetic north, the total anomalous field can be written as in equation (1.10) where ATFB ,

= AZ and = AH respectively and 1Cos therefore,

CosiSiniZF xAAT 3.4

Magnetic Effect of a dipole:

Dipole behavior is contained within bodies of geologic interest. A small three – dimensional

structure containing anomalous concentrations of magnetic materials and varying section from

rod-like to spherical often may be represented by a dipole model.

(a)

+FE

θ Φ2 Φ1

rp

L

-m

+m

Zp

rn Zn

X=0 p

x

+x -x Magnetic North

30

(b)

Fig. 3.2 (a,b) :Relationships and notations for a magnetic field of a dipole (H.R. Burger, 1992).

Using R as the magnetic field intensity at P due to the negative and positive pole for the

negative pole.

22n

E

n rAkF

rmR

An and R due to the positive pole is given as

22P

E

pAp r

AkFr

mR

Thus, horizontal and vertical component of the magnetic field at P due to each of the pole (-m

and +m)

1 SinRZ nAn, 2 SinRZ pAP

1 CosRAnAn , 2 CosRApp

But

ApAnA , and pAnA

+

+

θ

θ - 90 b zp

zn a

L

31

The total field anomaly is calculated as in the case of monopole;

CosiSiniZF AAAT

CosiHHSiniZZ pnApAn 3.5

Where,

pp

p

nn

nnp

pp

n

rax

rz

rx

rzbzz

zaxrLbzxrLa

)(cos and , sin

cos ,sin ,

])[( ),180sin(

)( ),180cos(

22

11

2/122

2/121

3.3.3: Magnetic Effect of a sphere

When a finite body becomes magnetized the magnetic dipoles within the body becomes

aligned with the applied field. Magnetic poles of one polarity appear on some surfaces, whole

poles of the other polarity appear on the other surfaces. Within the body, the positive poles

cancel with the negative poles.

To compute the total field anomaly of this body, all the dipoles or surface poles are being

summed. Poisson’s approach is used which consider all the positive poles to form an imaginary

positive body, while all the negative poles form an imaginary negative body.

To obtain the magnetic field anomaly using Poisson’s approach, contribution of the monopoles

of an imaginary body is summed to find the mathematical expression and the expression is

differentiated along the direction of magnetization to obtain the magnetic formula. Poission’s

relation states that the magnetic potential V is proportional to the derivative of the gravity

potential U in the direction of magnetization (Dobin and Savit, 1988 ).

32

dwdU

GIV

3.6

Where I = magnetic field intensity

U = Gravitational potential

ρ = density

w = direction of magnetic polarization

G = universal gravitational acceleration

Fig. 3.3: Notation used for the derivation of magnetic field anomalies over a uniformly

magnetized sphere

Vertical and horizontal field anomaly of a sphere is defined as;

2

21dz

UdGdz

dVZ A ,

dz

dUdxd

GdxdV

1

The Gravitational potential of sphere is;

Z

x = 0

R x

n r

i x

FE

33

2

122

34

zx

RGr

Gvr

GMU

3

Thus, for the vertical anomaly

1cos)(

3)(

3sin

34

2/1222/122

2

2/522

3

izxxz

zxz

zx

ikBRZ A

3.7

Where,

i = inclination

r = radius of the sphere

z = depth to the centre of the sphere and x is the horizontal distance on the earth surface from

the point above the centre of the sphere.

For horizontal anomaly

izxxz

zxx

zx

ikBRH A tan

)(31

)(3

cos34

2/1222/122

2

2/322

3 3.8

But total field anomaly FAT is given as CosiSiniZ A

3.3 Methods of Aeromagnetic Data Interpretation

3.3.1. Direct detection of structural trends

Interpretation of the aeromagnetic survey data aims to map the surface and subsurface regional

structures (e.g. faults, contacts bodies and mineralization). This could be performed

quantitatively or qualitatively. Thus, detection of structural trends is done qualitatively. The

qualitative interpretation of the shapes and trends of magnetic anomaly begins with a visual

inspection of the structural trends, and a closer examination of the characteristic features of

each individual anomaly is carried out. Some of these features Sharma (1976) are;

34

(a): The relative location and amplitudes of the positive and negative contour parts of the

anomaly.

(b): The elongation and aerial extent of the contour and

(c): The sharpness of the anomaly as seen by the contour spacing.

Accordingly, those features are taken into considerations during qualitative interpretation of

aeromagnetic map.

3.3.2. Estimation of depth

Since the magnetization is primarily a tool for subsurface mapping and detection, it follows

that determination of the depths as well as other physical properties of bodies causing

anomalies are important in its application to geological exploration and search.

Knowledge of the depth of a particular formation or source may have considerable geological

significance as it determines the nature of configuration for a formation. The depth to various

points on the surface of crystalline rock or magnetic basement allows one to map that surface

and its topography and to infer thickness of sediments or conformable sedimentary ores deposit

or ground water. Placer deposits are gold, diamond, etc. Areas underlain by sediments or other

sedimentary deposits may be ruled as economic or uneconomic according to their depths.

Several methods have been developed to estimate depths to magnetic sources using profile

data. Some of these methods are half – slope method and Grant and Martin method.

(a): Slope and half-slope methods for estimating basement depths The principles of the half-slope and maximum-slope distance parameters are indicated in

(Fig.3.4). A drafting triangle is set with one-half of this maximum slope and slid along another

triangle to determine the point of tangency P1 above and P2 below the point of inflection. The

half-slope parameter P is the horizontal distance between these two points.

35

It is quite usual in actual practice to find that the maximum slope coincides very closely with

the magnetic profile for a certain distance and then break away from the straight line at

consistently measurable positions, S1 and S2. The distance S between these points is the slope

parameter. The principal objective of this method was to determine the factors by which these

and some other parameters should be multiplied to give the depth to the magnetic source. The

system is very straightforward: a series of total magnetic-intensity and second –derivative

contour maps was calculated for prismatic bodies of rectangular form with their tops at unit

depth and bottoms at infinity. The lengths of the interpretation parameters could then be

measured on the calculated maps and the ratios of these lengths to the unit depth determined.

From these measurements and from extensive practice in their application it has been

determined that, as a general rule, the depth to the prism source is approximately equal to S and

also approximately equal to P/2.

Fig. 3.4: idealized magnetic profile showing measurements for slope (S) and half slope (P)

(Nettleton, 1976)

Curve of Magnetic Intensity Half Slope

Half Slope Maximum Slope

0

p1

S

s1

s2

P2

P

36

(b): Grant and Martin (1966)

Grant and Martin describe a system which uses certain depth “estimators” derived from

measurements on a map and on a profile across the anomaly. These are used with charts of the

variation of certain ratios of this estimator, depending on the form of the models used to

approximate the magnetized body, Grant and West (1965). An example of one estimator is

given by (Fig. 3.5). This is applicable to an intrabasement prismatic block such as those of

Vacquier et al. (1951). The example is for near-vertical magnetization.

Fig. 3.5: Schematic magnetic profile with quantities measured in Grant and Martin’s system of

depth estimation, Grant and Martins, (1966)

The quantities measured are the maximum slopes, S1 and S2 on the two sides of the anomaly,

the half-width W 1/2, and the total amplitude .minmax TT

SLOPE =S1

2T

H N S

minT

maxT

T SLOPE =S2

minmax21 TT

21W

37

One estimator, here called E1, is the ratio of apparent length to width of the anomaly, with

these dimensions determined by the distance between half-amplitude contours in the long- and

short-axis directions of the anomaly.

Another estimator, here called E2, is the average slope multiplied by the half-width and divided

by the amplitude, i.e.

minmax

2/1212 2 TT

WSSEE

3.10

Auxiliary charts are made for ratios of certain estimators. On one such chart curves are plotted

of E1 versus E2 for a range of values of H/T and L/T which make an approximately orthogonal

family of curves, where H, L, and T are the depth, half-length, and half-width of the model

body.

3.3.3: Automatic depth calculations

Automatic depth calculation techniques available today rely on the fact that magnetic field

(gravitational field) are three-dimensional potential fields. The three-dimensional automated

dept-to-source interpretation technique used in this study is forward and inverse modeling

technique. Other automated methods are;

(a): The Spector and Grant Method (1970) This system depends on a two-dimensional spectral analysis of a given map or region. The

physical basis is that the magnetic map represents the effect of a group of magnetic sources and

that the individual sources are rectangular parallelepipeds. By varying the relative sizes of

length, width, thickness, depth, polarization angle, etc., any of the various shapes, such as

sphere, slap, thin plate, bottomless prisms, vertical dike, etc., can be approximated. The group

38

of such blocks is treated by statistical theory and reduced to a power spectrum. The result of

the analysis is plotted on a logarithmic scale against the frequency. On such a plot, if a group

of sources has a similar depth, they will fall into a line of constant slope. Thus, if there are

groups of sources with the individual groups at widely different depths, such as shallow

volcanic over a deep basement, the slope is a measure of depth.

(b): Forward and inverse Modeling technique

Forward modeling involves making numerical estimates of the depth of burial and the

dimension of the sources of anomalies. This process often takes the form of modeling of

sources which could in theory; replicate the anomalies recorded in the survey. In other words

conceptual models of the subsurface are created and their anomalies calculated in order to see

whether the Earth-model is consistent with what has been observed, that is given model that is

a suitable physical approximation to the unknown geology.

Inversion modeling is a mathematical process that automatically adjusts model parameters so

as to improve the fit between the calculated field and the observed field. The important word

here is "mathematical". The inversion algorithms take no account of geological issues; it is up

to you, the interpreter, to ensure that the inversion starting conditions are sensible, and to reject

any inversion results that are not geologically plausible.

Potent's inversion scheme is very flexible and one can invert on:

any combination of parameters from any number of bodies;

multiple datasets (eg. regional gravity and aeromagnetic);

39

Multiple components from within the same dataset such as three component down-hole

magnetic data (which can be inverted in conjunction with, for example, ground TMI

data).

There are two key items needed for inversion:

A set of model parameters that you want the inversion process to adjust;

A sample of observed data (X, Y, Z, and F) values, where Z is height and F is the

observed field. This has two functions. Firstly, the data points in the sample provide the

geographic (X, Y, Z) coordinates at which Potent will calculate the field due to the model.

Secondly, they provide the observed field values, F, against which the calculated field values

will be compared. The inversion algorithm (a mathematical process) will attempt to minimise

the root-mean-square (RMS) difference between the observed and calculated values. Potent

uses several types of axes for various purposes. Observations and model are positioned

relative to axes (X, Y, and Z) (Fig.3.6) where Z, the elevation of the observation, is directed

vertically upwards. The depth (or rather depth-below-datum) therefore corresponds to -Z.The

X and Y axes define a horizontal reference surface. It is generally convenient to choose

coordinates so that true north corresponds to +Y and true east to +X. A third horizontal axis P

is defined in the (X, Y) plane. This is the profile axis onto which observations are projected in

order to display them in profile form. The origin of the P axis is the projection onto it of the

first observation of the profile. Each profile line that is displayed on a plan is the P axis for

that profile. The field axis F also is directed vertically upwards from the (X, Y) plane. It is

used for plotting observed and calculated field values when they are displayed in profile form.

The shape of a body is defined in its own coordinate system (A, B, C), in which (0, 0, 0) is the

reference point about which the body is defined. The position of the body is defined as the (X,

Y, Z) coordinates, dip, strike and plunge of its reference.

40

Fig.3.6: Co-ordinate Axes X is the X co-ordinate of the body's reference point, Y is the Y co-ordinate of the body's

reference point and Z is the Z co-ordinate of the body's reference point. Strike is the body's

rotation about its C axis. Dip is the body's rotation about its B axis and Plunge is the body's

rotation about it’s A axis.

41

CHAPTER FOUR

DATA SOURCE, ANALYSIS AND MODELING

4.1: DATA SOURCE

Two sets of data were obtained as part of a nationwide aeromagnetic survey which was

sponsored by the Nigerian Geological Survey Agency, (NGSA) in 1974 and 2008 respectively.

However, for the purpose of this study, we used the 2008 data as stated above. The data was

digitized along flight lines and plotted with a contour interval of 2.5nT with average flight

elevation of about 80m; and cross tie of 2km which helped in leveling the data. The data was

made available in digital form on the scale of 1:50,000 shown as (Fig. 4.2).

4.2: DATA ANALYSIS

4.2.1: Removal of geomagnetic field

International Geomagnetic Reference Field (IGRF) was used to remove the geomagnetic

gradient from the field data that was used in this study. The result of the estimated field is as

follows;

Total field strength = 32920nT, Declination = -3deg, Inclination = -13deg.

IGRF is the most widely used mathematical models for fitting the main magnetic field of the

earth at a given time. They are used objectively to remove long wavelength components from

survey data to obtain anomalous magnetic field which contains the shorter wavelength

components of exploration interest.

42

Fig. 4.1: Sheet 303, Abakaliki aeromagnetic contour map (1974, source NGSA)

390000 395000 400000 405000 410000 415000 420000 425000 430000 435000 440000

665000

670000

675000

680000

685000

690000

695000

700000

705000

710000

715000

ABAKALIKI

Okpoduma

Ejibafun

ALEBO

MFUMA

OBUBRA

ABBA OMEGA

IDEMBA IZA

OGURUDE

ABAKALIKI

SCALE, 1: 100,000

MAGNETIC LOW

CONTOUR LINE

CONTOUR INTERVAL 2.5nT

0 1 2 3 4Km

43

Fig.4.2: 2008 Aeromagnetic contoured map of Abakaliki (Source NGSA)

4.2.2: Removal of regional gradient

Regional gradient in the field data was removed using polynomial fitting method. Observed

values often have a regional background field superimposed on anomalies of interest. Such a

N

44

background field might arise from deep sources that produce long-period anomalies that are of

no interest in the context of our interpretation. This background field is referred to as the

"regional" field. Whatever the actual cause of the "regional" field it is necessary to remove it

before effective modeling can be performed. Potent removes the background field as a

polynomial surface with a maximum degree of two. Although it is straightforward to generate

higher degree surfaces, they carry the danger of introducing significant features into our data.

First-degree surface is recommended (an inclined plane) as the safest regional surface that is

reasonably versatile as regards the direction of its slope. The equation used to generate the

algorithm for removal of regional data is given as:

refref aaar 210 4.1

Where

r is the regional field, Xref, Yref are the X and Y coordinates of the geographical centre of the

dataset respectively. They are used as X and Y offsets in the polynomial calculation to prevent

high order coefficients becoming very small, and a0, a1 and a2 are the regional polynomial

coefficients.

The polynomial fitting method is an analytical method for determining regional magnetic field.

In this method, matching the regional field by a low order polynomial surface exposes the

residual features as random errors. The fitting is also based on statistical theory since the

observed data are computed by least-square method to obtain a surface that has the closest fit

to the magnetic field. This surface is considered to be the regional field .While the residual is

the difference between the observed magnetic field value and the regional field value

computed. The regional field values were subtracted from the observed data to obtain residual

values which forms the input data for this study. The residual map is shown in (Fig. 4.2).

45

Fig. 4.3: Residual map of Abakaliki (Source NGSA)

4.3: The Potent computer modeling program:

Potent is a program for modeling magnetic and gravitational effects of subsurface. It was

written by Geophysical Software Solution (GSS) in Australia. The program consists of an

assemblage of simple 2-D and 3D geometric bodies such as slabs, dykes, rectangular, prisms

which are demonstrated in figure 4.3 to figure 4.9.

Residual TMI N

Residual TMI

46

Slab

Fig. 4.4: Definition of a Slab

Dyke

Fig. 4.5: Definition of a Dyke

47

Cylinder

Fig. 4.6: Definition of a cylinder

Ellipsoid

48

Fig. 4.7: Definition of an Ellipsoid

Lens

Fig. 4.8: Definition of a Lens

Polygonal Prism

Fig. 4.9: Definition of a Polygonal Prism which is a 3 sided body.

49

Sphere

Fig. 4.10: Definition of a Sphere

The software used in the analysis consists of four main concepts which are;

Observation

Model

Calculation

visualization

The primary function of the program is to bring these concepts in a coherent and intuitive way.

Observations

These are the measurements taken either as airborne data or ground data. They could be magnetic or gravity data.

Model

Model concept uses bodies in figures 4.3 – 4.9 to replicate the observed data.

50

My main task as an interpreter is to devise a model that is geologically plausible and also is

consistent with the observed physical values.

Calculation

The model is consistent with the observed physical values if its calculated field matches the

observed values to some (subjective) degree of precision.

This is done by calculating the field (TMI in this case) due to the model and comparing it with

the observed field.

Visualisation

Under visualization we subjectively assess the "match" between the observed and calculated

physical values by visualising them in the most appropriate manner. Visualisation is an

inherent part of the modeling process.

4.4: Modeling of selected profiles:

The residual map of the study area consists of many anomalies. Three (3) profiles were taken

across the major anomalies for modeling as shown in (Fig. 4.11). Forward and inverse

modeling technique as discussed in section (3.3.3b) was applied to the bodies that were used to

model each profile. Parameters of the bodies which were varied in order to obtain a close

match between the observed data and calculated data includes: Dip, Strike, Plunge,

Susceptibility (k) and Depth (z).All the data used in plotting the profiles are shown in the

appendix.

51

Fig. 4.11: Residual map of the study area showing 3 profiles.

4.4.1:3D forward and inverse modeling of profile A

Profile A (Fig.4.12) which cuts across Northeast and Southwest of the study area was modeled

using four different bodies, sphere, ellipse, dyke and rectangular prism. The model revealed

two intrusive bodies (dolerite), with susceptibilities 0.06 and 0.013 buried at depths 3.4km and

4.7km respectively. Granulites with susceptibility 0.0002 buried at depth of 3.5km and salt

with susceptibility -0.0001 buried at depth of 4.6km.

N

PROFILE B

PROFILE C

Residual TMI

52

Fig. 4.12: modeled profile A

4.4.2: Forward and inverse modeling of profile B

Profile B (Fig. 4.13) is a North-South profile. It was modeled with 3 bodies, two rectangular

prisms and a dyke. The model revealed presence of 3 intrusive bodies (dolerite) with

susceptibilities 0.016, 0.010 and 0.010 each and buried at depths of (2.4, 2.7, 3.6) km

respectively.

Observed data Calculated data

Observed data Calculated data

53

Fig. 4.13: modeled profile B

4.4.3: Forward and inverse modeling of profile C

Profile C (Fig. 4.14) is also a North-South profile. It was modeled with 3 bodies, two ellipsoids

and a rectangular prism. The model revealed one pyrite with susceptibility 0.003 buried at

depth 5.9km and two basic igneous intrusive with susceptibilities 0.0279 and 0.0329 each

buried at depths of 6.32km and 5.9km each. It shows a magnetic value of about 40nT and a

very low value of about – 80 nT.

Observed data Calculated data

54

Fig. 4.13: modeled profile C

55

CHAPTER FIVE

RESULTS, DISCUSSION, CONCLUSION AND RECOMMENDATION

5.1: Results:

Anomalous bodies in Abakaliki area have been modeled using 3-D modeling software (potent).

The forward and inverse modeling applied on Profile A (Fig.4.12) showed that depth to the

anomalous bodies in the area ranges from 3.4km – 4.7km, it has two intrusions of susceptibility

0.01 each, one granulite with susceptibility 0.0002 and one salt deposit of susceptibility -

0.0001. Profile B (Fig.4.13) showed a shallow depth which ranges from 2.4km -3.6km, it has

three intrusive bodies with susceptibility 0.01 each. Profile C (Fig.4.14) showed a deeper depth

which ranges from 5.9km - 6.3km, anomalies in this area revealed basic igneous intrusion

which is in the basement complex and their susceptibilities ranged between 0.0279 -0.0326.

The summary of the results are shown in (Table 5.1).

56

57

5.2: Discussion

In this work, 3-D forward and inverse modeling technique was used. Bodies were fitted to the

intrusive bodies and minerals in the area and subsequently adjusted until a good fit was

obtained between the observed residual values and calculated values. Profile A (Fig. 4.12) cuts

across Abakaliki town and it revealed two intrusive, granulites and salt with spherical,

ellipsoidal, dyke-like and rectangular prism shape respectively. The shape of theses bodies are

delineated by A (width), B (length) and C (height) as shown in Table: 5.1. From these values

the volume and area of these bodies can be calculated. Profile B (Fig. 4.13) passed through

Abba Omega and Idemba –iza and it revealed three intrusive with two rectangular prisms and

dyke-like shapes respectively. Profile C (Fig.4.14) cuts across Mfuma and it revealed one

pyrite and igneous basement with two ellipsoidal and rectangular prism-like shapes.

5.3: Conclusion:

Aeromagnetic data from Abakaliki has been analysed. The result of the analysis showed that

there are intrusive bodies (dolerite sills) around Abba Omega and Idemba – Iza and intrusive

rocks (basic igneous) which correlate well with the works of Ofoegbu (1985), Obi et. al.,

(2010). There is also availability of mineral (pyrite), granulites and salt at Mfuma which

corroborates the work of Ehinola (2010). The major source of the magnetic anomalies in

Abakaliki arises from the presence of intrusions and basic igneous in the sedimentary terrain.

Ofoegbu and Onuoha, (1991) used spectral analysis on aeromagnetic data of Abakaliki and

estimated a shallow sediment thickness which varies between 1.2km and 2.5km. In this study,

the range of depths which varies between 2.4km to 6.32km and the availabilities of intrusive

58

bodies makes the area suitable for mineral exploitation. With all the intrusives found, the area

is not favourable for hydrocarbon accumulation.

5.4: Recommendation:

The depth to the anomalous bodies in the Abakaliki town suggests that it is not favourable for

hydrocarbon generation. In this work the data used was flown at altitude of 80m, but using data

from ground survey will give a more detailed result. Such ground survey though limited in

aerial extent could be seismic, gravity or magnetic.

59

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64

APPENDIX

/ PROFILE A

/ X Y TMI

Line - PROFILE A

389400 663600 -5.09

390500 664900 -6.12

391600 666200 -7.19

392700 667500 -8.11

393600 667200 -6.98

394700 668500 -6.34

395800 669800 -6.51

396900 671100 -7.54

398000 672400 -8.82

399100 673700 -12.45

400000 673400 -8.67

401100 674700 -16.73

402200 676000 -30.96

403300 677300 -42.75

404400 678600 -46.27

405500 679900 -48.88

406600 681200 -49.39

407500 680900 -46.25

408600 682200 -41.78

409700 683500 -37.78

410800 684800 -34.36

411900 686100 -33.55

413000 687400 -32.3

413900 687100 -32.68

65

415000 688400 -32.6

416100 689700 -34.02

417200 691000 -37.45

418300 692300 -40.3

419400 693600 -43.45

420500 694900 -46.91

421400 694600 -46.2

422500 695900 -48.22

423600 697200 -48.57

424700 698500 -48.2

425800 699800 -47.74

426800 701100 -45.48

427800 702100 -46.48

428800 703100 -76.3

430200 704300 -44.5

431300 705600 -37.73

432200 705300 -37

433300 706600 -33.97

434400 707900 -27.35

435500 709200 -20.09

436600 710500 -16.42

437700 711800 -7.97

438600 711500 -7.04

439700 712800 1.37

440800 714100 8.78

441900 715400 9.2

443000 716700 -1.51

444100 718000 -0.62

/ PROFILE B

66

/ X Y TMI

Line - PROFILE B

394100 673700 -34.21

394300 675300 -54.59

393400 675600 -64.09

393600 677200 -80.76

393800 678800 -85.48

394000 680400 -76.3

393900 682100 -53.94

394100 683700 -28.95

394300 685300 -11.55

394200 687000 -5.55

394400 688600 -0.89

393500 688900 -3.94

393700 690500 -7.76

393600 692200 -19.35

393800 693800 -30.56

394000 695400 -43.96

393900 697100 -54.06

394100 698700 -59.92

394300 700300 -57.51

394400 701700 -50.69

394200 703000 -40.04

394000 704700 -29.21

394200 706300 -20.06

394400 707900 -10.55

394300 709600 -8.02

394500 711200 -7.36

393600 711500 -6.71

67

393800 713100 -18.85

393700 714800 -34.73

393900 716400 8.8

/ PROFILE C

/ X Y TMI

Line - PROFILE C

436600 666200 34.24

436800 667800 -9.71

435900 668100 0.12

436100 669700 -19.88

436300 671300 -13.08

436500 672900 -23.45

436700 674500 -20.56

436900 676100 -24.45

437100 677700 -6.55

437300 679300 -10.31

437500 680900 0.69

437700 682500 -18.65

437900 684100 -19.04

438100 685700 -20.26

438300 687300 -58.06

438500 688900 -41.36

438700 690500 -41.24

438900 692100 -45.96

439100 693700 -44.62

439300 695300 -46.48

438400 695600 -47.34

68

438600 697200 -39.01

438800 698800 -34.84

439000 700400 -30.72

439000 701800 -26.97

439900 704400 -20.63

440100 706000 -20.27

440300 707600 -18.47

69