Groundwater Modeling, Inverse Characterization, and Parallel Computing
TITLE PAGE FORWARD AND INVERSE MODELING OF …
Transcript of TITLE PAGE FORWARD AND INVERSE MODELING OF …
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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
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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
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DEDICATION
This thesis is dedicated to all the exploration geophysicist.
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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.
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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.
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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
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CHAPTER FIVE: RESULT, CONCLUSION AND RECOMMENDATION
5.1 Results - - - - - - - - - - 55
5.2 Discussion - - - - - - - - - - 57
5.3 Conclusion - - - - - - - - - - 57
5.4 Recommendation - - - - - - - - - 58
REFERENCES
APPENDIX
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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
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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
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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.
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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
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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
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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).
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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.
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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.
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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
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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).
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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)
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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.
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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:
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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.
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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.
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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.
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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).
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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
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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.
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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.
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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
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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