GEOPHYSICAL INVESTIGATION OF MBEU IRON ORE DEPOSIT IN
MERU COUNTY USING GRAVITY METHOD
ABUGA VINCENT ONYANCHA [B.Ed. (Sc.)]
I56/CE/15208/2008
A research thesis submitted in partial fulfillment of the requirements for the award of the
degree of Master of Science in the school of Pure and Applied Sciences of Kenyatta
University
SEPTEMBER 2013
ii
DECLARATION
This thesis is my original work and has not been presented for the award of a degree or
any other award in any other university
Abuga Vincent Onyancha
Signature
Date
Department of Physics
Kenyatta University
…………………..
…………………………
I/We confirm that the work reported in this thesis was carried out by the candidate under
our supervision
Dr. W. J. Ambusso
Signature
Date
Department of Physics
Kenyatta University
…………………..
Dr. C. M. Migwi
Signature
…………………………
Date
Department of Physics
Kenyatta University
…………………..
…………………………
iii
DEDICATION
This thesis is dedicated to my Mother Euniah Moraa and my late Father Geoffrey Abuga
iv
ACKNOWLEDGEMENTS
The completion of this research would not have been had it not been the contribution of
others who contributed financially, critically, logistically and morally. First and foremost,
I thank the Almighty Lord for leading the way for me throughout the research project and
His grace in making meet the favour of people in the study area who were very
benevolent and very supportive.
I thank the Department of Physics for providing the GPS, gravimeter and other
equipment and also for the laboratory facility needed. I express my most sincere gratitude
to my supervisor Dr. Migwi for his positive criticism, suggestions, and encouragement.
My special thanks go to in particular to Dr. Ambusso for providing logistic support, for
his encouragement and high expectations throughout the research.
And to all my
colleagues particularly Bernard Adero, Moustafa Khassim and Rose Mose
who
supported in one way or another, am very grateful. I will also not forget my workmates
Petronillah Omari for and John Ocharo for their immeasurable support. God bless you all.
v
TABLE OF CONTENTS
Content
page
Title
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
TABLE OF CONTENTS
v
LIST OF TABLES
ix
LIST OF FIGURES
x
ABBREVIATIONS, ACRONYMS AND SYMBOLS
xii
ABSTRACT
xiii
CHAPTER ONE
1
INTRODUCTION
1
1.1
Background to the study
1
1.2
Regional geological setting
5
1.3
Statement of research problem
7
1.4
Objectives of the research project
7
1.4.1
Main objective
7
vi
1.4.2
1.5
Specific objectives
Rationale of the study
7
8
CHAPTER TWO
9
LITERATURE REVIEW
9
2.1
Introduction
9
2.2
Iron ore and metallic ore deposits
9
2.3
Mineral exploration
11
2.4
Modeling of gravity data
13
CHAPTER THREE
15
FIELD STUDIES
15
3.1
Introduction
15
3.2
Theory of gravity method
15
3.3
Gravitational potential
16
3.4
Units of gravity
16
3.5
Gravity instrumentation
17
3.5.1
Sodin gravimeter
17
3.5.2
Positioning equipment
18
3.5.3
Forward modeling
19
3.5.4
Spherical object
20
vii
CHAPTER FOUR
23
DATA REDUCTION AND PROCESSING
23
4.1
Introduction
23
4.2
Field methods
23
4.3
Reductions applied to gravity data
25
4.3.1
Drift correction
25
4.3.2
Latitude correction
26
4.3.3
Free air correction
27
4.3.4
Bouguer correction
28
4.4
Rock density
29
4.5
Data processing
30
4.6
The Bouguer anomaly map
30
CHAPTER FIVE
37
DATA INTERPRETATION
37
5.1
Aims and limitations of gravity data interpretations
37
5.2
Quantitative interpretation
39
5.2.1
Selection of profiles
40
5.2.2
Gravity profile zz’
41
5.2.3
Gravity profile vv’
42
5.2.4
Gravity profile yy’
44
viii
5.2.5
Gravity profile xx’
45
5.3
Modeling
46
5.4
Rock samples
55
CHAPTER SIX
57
CONCLUSIONS AND RECOMMENDATIONS
57
6.1
Conclusions
57
6.2
Recommendations
59
REFERENCES
60
APPENDIX 1: ROCK SAMPLES
63
APPENDIX II: DATA FOR THE PROTILES
65
APPENDIX III: DATA USED
68
ix
LIST OF TABLES
Table 1: The rock succession, major geological events and correlation with adjacent areas
(Mason, 1952) ..................................................................................................................... 4
Table 2: Parameters for profile xx' ................................................................................... 47
Table 3: parameters for profile yy' .................................................................................... 48
Table 4: Parameters for profile zz' .................................................................................... 49
Table 5: Properties of model bodies for profiles vv’, xx’, yy’ and zz’ Mbeu mineral
prospect ............................................................................................................................. 55
Table 6: Percentage compositions of rock samples .......................................................... 56
x
LIST OF FIGURES
Figure 1.1: A map of Meru showing the study area. .......................................................... 1
Figure 1.2: The geological map of the study area (Mason, 1952). ..................................... 6
Figure 3.1: The structure of the sodin gravimeter............................................................. 17
Figure 3.2: Vertical gravity effect of a sphere at point P. ................................................. 20
Figure 4.1: Station distributions for the gravity survey in Mbeu area. ............................. 24
Figure 4.2: Drift curve for the work done on 11/05/2011 using B1 as the base station. . 26
Figure 4.3: Bouguer anomaly map of the Mbeu area (contour interval of 0.5 mGal). ..... 31
Figure 4.4: Contour map showing the topography of the study area. ............................... 32
Figure 4.5: A view of three dimensional representation from the South. ......................... 33
Figure 4.6: A view three dimensional representation from the Southwest. ...................... 34
Figure 4.7: A view three dimensional representation from the Northeast. ....................... 35
Figure 4.8: Three- dimensional surface map showing the topography of the study area. 35
Figure 5.1: Bouguer gravity anomaly profiles. Gravity measurement stations are indicated
by post marks (
). ........................................................................................................... 40
Figure 5.2: Observed Bouguer gravity anomaly along profile zz’ and the estimated trend.
........................................................................................................................................... 41
Figure 5.3: Residual Bouguer gravity anomaly along profile zz’. .................................... 42
Figure 5.4: Observed Bouguer gravity anomaly along profile vv’ and the estimated trend.
........................................................................................................................................... 43
Figure 5.5: Residual anomaly along gravity profile vv’. .................................................. 43
Figure 5.6: Observed Bouguer gravity anomaly along profile yy’ and the estimated trend.
........................................................................................................................................... 44
xi
Figure 5.7: Residual Bouguer gravity anomaly along profile yy’. ................................... 44
Figure 5.8: Observed Bouguer gravity anomaly along profile xx’ and the estimated trend.
........................................................................................................................................... 45
Figure 5.9: Residual gravity anomaly along profile xx’. .................................................. 45
Figure 5.10: Residual Bouguer gravity anomaly profile vv’ and two-dimensional model.
........................................................................................................................................... 46
Figure 5.11: Residual Bouguer gravity anomaly profile xx’ and two-dimensional model.
........................................................................................................................................... 47
Figure 5.12: Residual Bouguer gravity anomaly profile yy’ and two-dimensional model.
........................................................................................................................................... 48
Figure 5.13: Residual Bouguer gravity anomaly profile zz’ and two-dimensional model.
........................................................................................................................................... 49
Figure 5.14: Residual Bouguer gravity anomaly along profile vv’. ................................ 50
Figure 5.15: Residual Bouguer gravity anomaly along profile xx’. ................................ 51
Figure 5.16: Residual Bouguer anomaly along profile yy’. ............................................. 52
Figure 5.17: Residual Bouguer anomaly along profile zz’. .............................................. 53
xii
ABBREVIATIONS, ACRONYMS AND SYMBOLS
ANWR
Arctic National Wildlife Refuge
BC
Bouguer Correction
CAG
African Company of Geophysics
F
Force
FAC
Free Air Correction
GPS
Global Positioning System
G
Gravitational constant
gz
Vertical component of gravitational acceleration
IGF
International Gravity Formula
Me
Mass of the Earth
Re
Radius of the Earth
VLF-EM
Very Low Frequency Electromagnetic
∆M
Anomalous mass (either excess or deficient)
a
Density
xiii
ABSTRACT
Gravity survey was used to detect metallic bearing rocks and dense bodies of rocks
within host formations in Mbeu area of Tigania. From the study, there is a clear
indication of the presence of iron ore in the region. The ground based gravimeter was
used to precisely measure variation in the gravity fields at different points. A total of 86
gravity stations were surveyed. The data obtained was corrected for drift, latitude, Free
Air and Bouguer corrections from where the Free Air Anomaly and Bouguer Anomaly
were computed. The contour map was drawn to represent this information and the
profiles were created. Four profiles were chosen which were oriented in the directions
NE-SW, NW-SE, nearly E-W and N-S for the purpose of fitting model to the observed
data. Spherical model was employed to estimate the sought parameters of the anomaly.
These include: depth from the surface to the centre, Z, radius, R, depth to surface T and
the mass of the body, M. The depth from the surface was found to range from 0-140 m
and mass ranging from 8.6  10 9 to 3.2  1011 kg.
1
CHAPTER ONE
INTRODUCTION
1.1
Background to the study
Mbeu lies to the North of Meru town, 220km North-East of Nairobi. It is at an altitude of
1300m above the sea level (Figure 1.1).
Figure 1.1: A map of Meru showing the study area.
2
The area is within a chain of volcanic hills which forms spectacular scenery. The large
tracts of ancient rocks which were concealed by thick cover of natural vegetation, soil
and vast volcanic rock have since been exposed due to weathering and erosion. As a
result, indication of iron ore and other mineral deposit in the region has been seen; this is
the main reason of employing geophysical investigation to determine mineral viability of
the region.
Mbeu is an agricultural area and land use is very intense. Agriculture is the main source
of income for area residents. The population density is rather modest compared to other
parts of the country. At the present time this area is well known for its sands that are
commercially mined along river beds. The presence of iron would be a welcome
discovery as it would boost the local economy and provide for technical jobs that have
higher income.
The earlier studies carried out in the area indicated the presence of granitic intrusion on
the southern slopes of the Nyambeni range. This suggests the possibility of the
occurrence of valuable minerals (Mason, 1953). However, the study was of an
exploratory kind and was not adequately detailed; therefore, it did not find any mineral.
Also the area is rich in inlier of quartzo-felspathic biotite gneisses and granitoid gneisses
of Precambrian age surrounded much more recent lavas and thick brown soils. At lower
levels the contact between the Archaean rocks and later volcanic rocks is obscured by
recent sandy deposits, derived from the basement systems inliers and black cotton soil
3
described a gneiss inlier (Parkinson, 1920). Thus geophysical method can help establish
the structure of subsurface (Murthy et al., 2009).
This study proposed to undertake a comprehensive investigation of the mineral bearing
potential of the rocks and soil sediments in Mbeu. The gravity geophysical technique was
employed since it has played a very important role in the search for new reserves of iron
ore and other valuable minerals elsewhere. This has been enhanced by the development
of the highly portable gravimeter capable of high degree precision and which has got
wide application. The technique exploits the fact that the physical properties of in-situ
rocks give rise in some physical quantity which may be measured remotely at the surface
of the ground or above it without the need to touch, see or disturb the rock itself. The
success of gravity method depends on bodies having different masses which are caused
by the bodies having greater or lesser density than the surrounding material. The Earth’s
gravitational field strength (the vertical component of gravitational acceleration, gz.) was
measured at selected locations on the Earth’s surface to determine sub-surface density
variations. Gravitational fields occur naturally but their local variation can indicate areas
of variable density particularly those that have clear centers. Analyzing and interpreting
the contrast between expected and observed values, gravity techniques revealed the
physical properties of geologic material and provided data on deep parts of the subsurface
that is otherwise inaccessible.
4
Table 1: The rock succession, major geological events and correlation with adjacent areas
(Mason, 1952)
Chronology
Rift
faultin
g
(Kent,
1994)
RECENT
-
PLEISTOCENE
R
Meru-Isiolo
Embu- Meru
(Schoeman, 1951)
Earth movements
and erosional
phases
Black cotton soil
and kunkar
Silts and gravels
Nyambeni parasitic
volcanic activity
Upper Nyambeni
lavas
Soils, laterites and
calcretes
Lower Nyambeni
basalts
Parasitic cones of
Mt. Kenya
Lake beds
Lower Nyambeni
basalts
Mount Kenya
volcanic series}
2. upper olivine
basalts
1.Lower basalts
Mount Kenya
volcanic series
End- Tertiary
penetration
(disturbance)
-
River gravel and
sands
Gravel beds
(disturbance)
PLIOCENE
-
MIOCENE
R
-
-
EARLY
TERTIARY
-
-
-
MESOZONE
-
-
-
ARCHEAN
-
Basement System
Basement System
R= Major Rifting faulting
Sub-Miocene
peneplanation
(disturbance)
End cretaceous
peneplain
-
5
1.2
Regional geological setting
The geological framework needs to be well understood in order to successfully apply
gravity method. This is because the interpretation of gravity potential anomalies is
inherently ambiguous. The ambiguity arises because any given anomaly could be caused
by a large number of possible causes, for example, a large deep body can give the same
anomaly as a small shallow body. Concentric spheres of constant mass but differing
density and radius would all produce the same anomaly. Thus understanding the geology
can guide interpretation of the gravity data.
The regional geological setting of Mbeu (Figure 1.2) is dominated by the Archaean or
Basement System rocks and comparatively young Tertiary, Pleistocene and Recent
extrusive rocks and subordinate sediments (Mason, 1953). The Mbeu area is largely
covered by the Mt. Kenya volcanic rocks (Schoeman, 1948). The plains consist of mafic
rocks and rest on the Sub-Miocene. Also some parts are covered predominantly by
ferromagnesian mineral. It has also been found that finely granular iron ore make a
considerable portion of ground mass in some parts. The indication of the presence of iron
is found in soil sediments weathered from iron bearing rocks. Anciently it was averred
that these large track of ancient rocks do not contain any mineral deposits, as the volcanic
rocks were concealed beyond reach and the remnants of the old rocks that protruded were
devoid of such occurrences.
6
Figure 1.2: The geological map of the study area (Mason, 1952).
The Basement System of Mbeu forms the floor upon which all the remaining rocks of the
area rest, and consists of schist, granulites and heterogeneous gneisses of varying
composition. The rocks are monotonous, consisting essentially of quartzo- feldspathic
gneisses containing varying proportions of biotite content. The rocks are frequently
intensely veined by stringers of quartz and feldspar, while some layers and lenses are
typically pegmatitic in texture.
7
1.3
Statement of research problem
Iron is regarded the backbone of many economic activities and the per-capita iron
consumption is an internationally recognized indicator of the level of development of the
country. The iron industry in Kenya is dependent on imported raw materials. Local
deposits of iron ore have been identified at various places in the country but not much has
been done to determine whether the deposits are viable in quantity and quality for
commercial exploitation. To establish the occurrence of commercial quantities of iron ore
mineral in Mbeu area, would be welcome news to the locals, to scholars and the nation at
large. The immediate economic benefits of such deposits will greatly improve the
economic activities in this area and create technical jobs and also job opportunities will
arise from the sectors of mining, transport and manufacturing, hence steering our country
towards realization of several principal millennium development goals.
1.4
1.4.1
Objectives of the research project
Main objective
The main objective of this research study was to determine the distribution of iron
bearing rocks and sediment in Mbeu area of Meru region using gravity method.
1.4.2
Specific objectives
The specific objectives were;
8
i)
To carry out ground gravity measurement of Mbeu area in order to determine
variations in gravity that would indicate the presence of iron ore and other
mineral deposits;
ii)
To determine the shape, sharpness of gravity anomaly location and form of
the structure which causes the gravity variations;
1.5
iii)
To determine possible depth extent of ore deposit;
iv)
To estimate the amount of iron quantity.
Rationale of the study
The information about the subsurface geology is important in that it associates variations
with the difference in distribution of densities and rock types (Sherriff, 1994). The
gravity technique delineate best geological features related to natural hazards, natural
resources and tectonic events on the upper crust of the Earth to a depth of approximately
20 kilometers. Relative to most geophysical techniques, acquisition of land gravity data,
processing and interpreting is straight forward, is also cost effective. A particularly nice
aspect of gravity technique is that the instrumentation and interpretative approaches
employed are mostly independent of the scale of investigation, thus this technique can be
employed in a wide variety of application. Maps of gravity anomaly also reveal structure
and trend that may control the location of ore bodies even when the bodies themselves
produce little or no gravity anomaly. This research there will therefore provide
information which will be very useful in updating the geology of Meru and its environs
especially Mt. Kenya region as a whole.
9
CHAPTER TWO
LITERATURE REVIEW
2.1
Introduction
Gravity has been used in mineral exploration since the early 1900’s due to its ability to
delineate highly dense geologic features from the surrounding host rock. This method is
even better nowadays because of the improved gravimeters which are in use than the
olden day’s torsion balances. Application of gravity to mineral deposition environmental
considerations includes identification of lithologies, structures and at times ore bodies
themselves (Wright, 1981). Historically, gravity has been used in oil exploration in any
places involving salt because of the large density contrast of salt, at almost all depths,
with surrounding sediments; positive when shallow, negative when deep (Greene and
Bresnahan, 1998). Gravity and magnetic methods have been used for deposit-scale ironformation studies. Most iron formation is associated with positive, high-amplitude gravity
anomalies because it contains elevated abundances of high-density iron minerals,
including magnetite and hematite. The magnetic signature of iron-formation is usually
one to two orders of magnitude greater than that of its host rock (Bath, 1962; Sims,
1972). Remote sensing imaging spectroscopy can also be used in regional exploration
(Hook, 1990) because iron ore minerals and their alteration products have distinct
spectral signatures (Clark et al., 1993).
2.2
Iron ore and metallic ore deposits
Michus (2008) carried out regional analysis of Burkina Faso using gravity method with
the aim of locating metallic ore deposits. The study was prompted by the fact that the
10
area is well endowed with metallic ore deposits (Bourges et al., 1998; Sattran and
Wenmenga, 2002; Schwartz and Melcher, 2003). The study used the available data to
determine the regional geologic environment. The three thousand five hundred gravity
data was obtained from the U.S National Geospatial and Imaging Agency. The data was
evenly distributed throughout the country with the data concentrated along most major
roads and tracks at station spacing 2-5m. Free Air and Bouguer gravity corrections were
made using see level as a datum and 2.67 g/cm3 as a reduction density. The Bouguer
anomaly data were gridded and contoured to produce gravity anomaly map. The gravity
analysis suggested that a majority of known metal deposits were associated with low
amplitude, short wavelength gravity maxima within Birimian belts, except BouroumYologo belt deposit located to the northern edge which, had a large amplitude gravity
maximum caused by a 5 km thick ultramafic complex. Such studies have never been
conducted in Kenya and it is because of this that we purpose to undertake this venture to
determine its viability and profitability.
Shendi et al. (2008) used gravity and magnetic methods for locating probable areas of
metallic mineralization in South Sinai, Egypt. The study delineated near surface
structures which host metallic mineral deposits. The sites for gold, copper, silver, iron
and manganese mineralization were discovered. Four sites were selected for modeling by
using the Gramond software (Geosoft, 1994). The density contrast between the causative
structures and its surrounding at the four sites were estimated as being 0.30, 0.31, 0.23
and 0.27gcm-3 and the depths to the causative anomalies for the sites were calculated as
being 1.45, 1.43, 1.88 and 1.23 km, respectively.
11
Pal et al. (2006) used geological interpretation to determine the cause of gravity highs
and lows. The gravity highs are associated with iron ore group and metamorphic group of
rocks. The iron ore group rocks overlie the basement rocks and are exposed over vast
areas in the east. The gravity lows are associated with anticline structures of granitic
masses which clearly indicate the intrusive natures of the granitic masses.
2.3
Mineral exploration
Ugbor and Okeke (2010) carried out a geophysical investigation in the lower section of
Benue trough of Nigeria using the gravity method to determine the depth of the suspected
mineral body and the lateral extent. Ninety eight gravity stations were occupied. The
geometry of the buried body was determined from the interpretation of residual anomaly
data. The Spherical model was assumed for the anomalous body based on the local
geology and the residual gravity anomaly. A density contrast of 0.32 gcm-3 was
calculated for the body. Interpreted gravity profiles yielded results that reveal low
Bouguer gravity anomalies. The result from their analyses helped in ascertaining the
depth to the suspected mineral body and lateral extent of the body. Further the geologic
and geophysical features were revealed.
Jaffal et al. (2010) carried out gravity and magnetic investigation in the Haouz Basin,
Morocco. The study was intended to explore mineral potentiality of the region so that
mining could be done. One thousand five hundred and forty-three gravity and magnetic
stations were collected using a LaCoste and Romberg gravity meter and a Magnetometer
12
measuring the total magnetic field. Euler deconvolution method was applied to
characterize the highlighted structures. This method provided automatic estimates of
source location and depth. The method uses magnetic or gravity and its orthogonal
gradients to compute anomaly source locations (Thompson, 1982). The study found out
that the outcrops of the basement fitted with highs, the lows were due to local
sedimentary thickening generated by depressions of the Hercynian Basement. The areas
of magnetic and gravity highs were found to be rich in sulphide ore deposits.
Klasner et al. (1979) conducted geophysical studies to determine more precisely the size
and location of peridotite bodies at Northern Peninsula of Michigan. Studies were carried
out near known locations of peridotite plus more widely spaced new places. Gravity,
ground magnetic and very low frequency electro-magnetic (VLF-EM) techniques were
used in the detailed survey area. The combined use of all three geophysical techniques
greatly restricted the spectrum of possible geologic bodies responsible for the measured
anomalies and allowed a closer approach to a unique solution than would be possible
with any single technique. Gravity values were measured with a LaCoste and Romberg
model G land gravimeter. All readings were taken with a Geometrix model G816 proton
precession magnetometer in the backpack mode. VLF-EM coverage in the detailed study
area consisted of 16 lines. All readings were taken with a Geonics EM-16 unit facing
north. Gravity, ground magnetic, and VLF-EM surveys disclosed several other anomalies
nearby with the same trend as the peridotite.
13
The gravity survey for the whole of Kenya has been done by Khan and Swain (1977).
The duo examined the nature of the axial gravity high. They noted its association with the
prominent volcanoes similar to those in the southern part of the rift and showed that the
lift axis is associated with the intermittent narrow positive anomaly (gravity high).
Elsewhere the gravity method has found a frequent application in mapping bedrock
topography in glacial environments (Lenox and Carson, 1967; Ibrahim and Hinze, 1972;
Carmichael and Henry, 1977).
2.4
Modeling of gravity data
In the study of the San Francisco volcanic field crustal structure Mickus and Durrani
(1996), used gravity and magnetic methods. Data was obtained from National
Geophysical Data Centre and from a master’s thesis by Locrem (1983). The profiles were
chosen based on the amount of data available along the profile. For gravity modeling;
complete Bouguer anomalies were used while gridded data points were used for magnetic
modeling. The models were determined using a 2.5D forward modeling algorithm (Lai
1984) which calculates gravity and magnetic responses. The lateral positions of the
models were obtained from geologic maps and the final models were obtained by trial
and error process in which the body’s geometry were varied and or density / magnetic
susceptibility until the observed value matches the predicted value.
Williams et al. (2006) used the existing gravity data to draw Bouguer gravity anomaly
map of SW Pacific. Six profiles were drawn in their quest for causative body and
modeled along a series of those profiles using Interpex Magic XL (version 3) software. A
14
2.75D was constructed along each profile. For each profile modeled, the extent and the
orientation of the body from either side of the profile was estimated using the residual
gravity map and the 2.75 D models were correlated to ensure that they formed a coherent
overall 3D model. The best fit model comprised a body approximately 15 km wide and
had an average density 2.8Mg-3. Based on the extent of the Bouguer gravity anomaly
map, a reasonable estimate for the real extent of the whole ultramafic body was 15km
×10km.
Harbi (2005) carried 2-D modeling of southern Ohio. The Bouguer anomaly data set was
used to produce Bouguer gravity map for qualitative interpretation and for 2-D forward
quantitative modeling. The Bouguer data was re-gridded by surferTM software. Nine EastWest data profiles were extracted. Gravity and magnetic forward modeling software used
a simple idea to simulate the geologic sources from a complex system. The proposed
shape and physical parameters for a subsurface body were entered in the model.
Anomalies were calculated and then compared with observed magnetic and gravity
anomalies. The model was iterated until there was acceptable match between the
synthetic and actual data. The geologically feasible polygons and cylindrical bodies were
modeled for each profile.
15
CHAPTER THREE
FIELD STUDIES
3.1
Introduction
In gravity surveying technique, the subsurface geology is investigated with regard to
Earth’s gravitational field. The variation arises from differences of density between
subsurface rocks. The causative body anomaly has different density other than that of the
surrounding rocks and represents a subsurface zone of anomalous mass responsible for
gravity anomalies. Although referred to as the ‘gravity method’, it is actually the
difference in acceleration due to gravity that is measured.
3.2
Theory of gravity method
The Earth’s gravitational field is usually described by the vertical component of the
gravitational acceleration gz. The mean value of the field at a point on the Earth’s surface
is mostly determined by the mass of the Earth but small local variations mass perturb this
mean value. The basis on which gravity method is encapsulated is two laws derived by
Newton, namely his universal law of gravitation and his second law of motion. Newton’s
second law explains how a force acts on an object. The force per unit mass F/m2 defines
the gravitational field which the gravitational acceleration g. On Earth, gravity ought to
be constant but due to the ellipsoidal shape, its rotation, its irregular surface relief and its
internal mass distribution, gravity varies from place to place.
16
3.3
Gravitational potential
The gravitational potential at a point in a field can be defined as the work done in
bringing unit mass from infinity to that point or the potential energy of a unit mass placed
at that point in the field with the zero at infinity. Gravitational potential is a scalar
quantity, its first derivative in any direction gives the component of gravity in that
direction. Due its attractiveness in nature and zero at infinity, the gravitational potential is
negative. Therefore the concept of gravitational potential and potential energy enable us
to solve certain type of problems that are difficult to solve by other means.
3.4
Units of gravity
The centimeter–gram–second system (c.g.s.), unit of acceleration is referred to as Galileo
(Gal). One galileo is an acceleration of 1 centimeter per second per second (cm/s2). For
gravity surveys, smaller units; milligals (mgals) is normally used. The following
relationships among units hold;
1 Gal = 10-2 ms-2
1 mGal = 10-5 ms-2
1  Gal = 10-3 mGal
10 gu=1 mGal
17
3.5
3.5.1
Gravity instrumentation
Sodin gravimeter
The meter is designed to measure the vertical component, g z of gravity to a high order of
accuracy. In sodin gravimeter (Figure 3.1), the extension of the spring is related; to the
gravitational force a predictable, well-behaved and hence the meter is properly calibrated.
The size and play of the quartz springs is limited to ranges between 1,400 and 2,000 μms2
and hence this requires a mechanical range resetting screw to enable them to cover the
worldwide range of 50,000μms-2. The meter not being thermostatically controlled tends
to exhibit a diurnal drift curve.
Figure 3.1: The structure of the sodin gravimeter.
18
The simplest type of gravimeter is a mass-spring system. Its operation based on simple
harmonic motion in a spring. If you hang a mass on a spring the weight force (mg) acting
on the mass causes the spring to stretch a certain distance (x) from its unstretched length.
The length the spring stretches is dependent on the spring constant (  ) and the size of the
attached mass (m). The relationship that describes this stretching is.
x
m

g
(3.1)
Where x is the extension of the string,  is the spring constant, m is the mass of the
attached object and g is the gravitational constant of the place. In other words the
stretching is proportional to the weight force acting on the spring. If the mass and spring
are kept the same but moved to a number of different locations where the g varies then
the length of stretching due to the constant mass hanging off the end of the spring will
vary as the weight force varies. The change in the relative stretching of the spring ( x ) is
a direct result of any changes in g.
3.5.2
Positioning equipment
The GPS is a satellite based navigation system that can be used to locate positions
anywhere on Earth, it consists of satellites, control and monitor stations, and receivers.
GPS receivers take information transmitted from the satellites and uses triangulation to
calculate a user’s exact location. GPS is used on incidents in a variety of ways, such as:
to determine position locations; to navigate from one location to another; to create
digitized maps and to determine distance between two points or how far you are from
another location.
19
3.5.3
Forward modeling
The vertical gravity anomaly is given by:
g z 
GMz
GMz
cos  
2
h
h3
(3.2)
This idea can then be extended to an arbitrary body and then the vertical component of
the gravity anomaly which is extremely small was found by the gravimeter. To determine
the gravity anomaly the body is divided into small ‘point masses’ at each position along
the profile then the anomaly due to each point mass is calculated then all the anomalies
are added together. For a full 3 D problem we get the integral equation:
g z   G
z

z ' ' '
dx dy dz
h3
'
(3.3)
where  is the density difference relative to the surrounding rocks
x, y, z, x’, y’ and z’ is the local coordinate with the body and
h
x' x2   y' y 2  z' z 2
(3.4)
for simple geometric shapes such as sphere or cylinder, the (Equation.3.3) is written in
simplified form.
20
The geology of the area plays a very important role with regard to the model to be
employed to estimate the sought parameters of the anomaly. The parameters include:
depth from surface to centre Z, radius R, depth to surface, T and the mass of the body, M.
The choice of the model depends on the fact that the cylinder anomaly falls off more
slowly than the sphere, 1/z rather than 1/z2 and that the anomaly is broader than that of
the sphere. While it may be difficult to distinguish between the two bodies in a survey
profile, a map will show the parallel linear contours of the cylinder versus the circular
contours of the sphere.
3.5.4
Spherical object
Gravity due to spherical object buried below the earth’s surface is given by:
g sphere 
G 4R 3  GM
GM

 2
2
2
3r
r
x  z2


Figure 3.2: Vertical gravity effect of a sphere at point P.
From figure 3.2 we have
(3.5)
21
g sphere 
GM
GMz
Cos 
2
2
3
x z
x2  z2 2




(3.6)
Since
g Max 
GM
z2
We get
g Sphere  g Max
x
z3
2
 z2

3

2
g Max
 x 2 2 
  1 
 z 



3
2
(3.7)
the maximum, gMax is at the point directly above the centre of the sphere (x=0 m) and gz
decreases rapidly as you move away from the sphere, then ;
 x  2 
g Max
g Max

    1
3
2

 x 2  2
 z 
    1
 z 



3
2
2
thus
z
x1
2
2
3
2
1
 1.305 x 1
2
(3.8)
The radius of the anomaly can be obtained by employing the equation:
 3z 2 g Max 

R  

 4G 
1
3
(3.9)
Using equation 3.8 and 3.9 the depth from the surface is given by:
T Z R
(3.10)
22
Therefore the excess mass (∆M) of the sphere can be calculated by
∆M=density × volume, thus;
M 
4R 3 
3
Where R= radius of the sphere
 =density
(3.11)
23
CHAPTER FOUR
DATA REDUCTION AND PROCESSING
4.1
Introduction
In order to produce a gravity map reflecting lateral variations in the density, raw gravity
measurement were reduced. These reductions removed the effects that are not of interest
to us to yield the Bouguer anomaly. Analysis of gravity data shows that most of the ore
deposits are located on the gravity highs.
4.2
Field methods
A total of 83 gravity stations were surveyed as shown in the figure 4.1. The data was
collected along the road, footpath and in regions which were accessible using sodin type
gravimeter. The base station was first established from where gravity differences along
the other stations were measured. Stations were sited at 5-20 meters intervals, spaced
closely near the anticipated region of high accumulations of the ore and far apart in other
regions. The gravimeter was first oriented by leveling and this was done by first setting it
stable on the ground on a tripod stand. The tripod was made to stand firm and the legs
pushed deep enough into the soil. Gravity data was collected data in loops by remeasuring base stations at less than 2 hours intervals. This was done so as to enable us to
check for the drift. An umbrella was used to protect the gravimeter bubble levels from
24
being warped in the sun as this could lead to errors in the reading taken.
361800
361700
361600
Grid North
361500
361400
361300
361200
361100
12200 12300 12400 12500 12600 12700 12800 12900 13000 13100 13200
Grid East
0
200
400
600
800 Metres
Figure 4.1: Station distributions for the gravity survey in Mbeu area.
The gravity meter was then leveled over the survey mark before making the reading. The
time, date, dial reading and station number were recorded. Also recorded was the
elevation of the station with sea level as the reference point and also the station’s exact
position in terms of northings and eastings using the Global Positioning System (GPS).
25
4.3
Reductions applied to gravity data
The parameters obtained were used to reduce the readings to standard reference
conditions before the data analysis.
4.3.1
Drift correction
If the gravimeter is left undisturbed for an hour or so after a reading and a second reading
is taken, the gravity value will be different. If additional readings are taken over a period
of time, the points tend to fall on a smooth curve. But this is not always the case as there
can be jumps. Hence the conclusion that the readings of all gravimeters drift more or less
with time, due to elastic creep in the quartz springs.
Gravity data was corrected in several steps. An initial dial correction was applied to
convert dial readings to milligals (mGals). Next empirical drift correction was applied
using base station readings. This removed the effects of earth’s tides and mechanical drift
of the gravity meter. We applied an offset correction to match each data from the base
station. This produced a data set that would have been obtained if we had measured every
station at the same time. A drift was taken and the corrections read from it (fig 4.2). The
drift curve was determined by a least square adjustment which is straight forward since
the modern gravimeters drift linearly with time.
26
Figure 4.2: Drift curve for the work done on 11/05/2011 using B1 as the base station.
4.3.2
Latitude correction
The gravity acceleration on the earth’s surface is not uniform. The gravitational
acceleration is more at the poles as compared to the equator. This is because at the poles
distance from the centre of the earth is less than it is at the equator caused by the
maximum centrifugal acceleration here. The earth’s shape can be approximated by an
oblate spheroid, the surface that is generated by revolving an ellipse about its minor axis.
The latitude correction takes care of both the effect of oblate spheroid shape of the earth
and the centrifugal acceleration created by the earth’s spin. As a function of latitude, the
theoretical gravity attraction decreases from the pole to the equator and can be calculated
from the formula (Dobrin, 1988; Keary and Brooks 1984; Telford et al,. 1990)
27
g  978013.5(1  0.05278895 sin 2   0.000023462 sin 4  )(mGal)
(4.1)
where g = theoretical gravity
  Latitude of gravity station
Equation 3.8 was used to give the gravity value that would result if the Earth were a
perfect spheroid. This gravity value was first calculated for each base station and then
subtracted from all other values tied to that station to find the relative latitude correction.
For instance, the latitude correction for station A13 relative to the base station is
978048.2681-978048.2844= -0.0163
4.3.3
Free air correction
Gravity varies with elevation because a point at a higher elevation is farther away from
the centre of the earth and therefore has a lower gravitational acceleration than one at a
lower elevation. The gravity at a point on the surface of a spherical earth is:
g1 
GM
r2
(4.2)
where M is total mass of the earth and r its radius and G is the gravitational constant
Then at a height h above it is given by
g1  
GM
( r  h) 2
 g  g1 (1 
where powers of
2h
)
r
h
higher than first are neglected
r
(4.3)
28
From the above equation it is clear that the correction from the elevation known as free
air correction (FAC) is then;
FAC  
2 gh
 3.086h
R
(4.4)
For each of the field stations free air correction was calculated using equation 3.11. The
value of FAC at the base station was subtracted from all other stations to give the relative
FAC. For A6 FAC = 397.4768 - 386.9844 = 10.4924mGal. FAA is given by Relative
gravity minus relative corrected gravity Plus FAC. For A6 FAA = -5.40-(-0.0255) +
10.4924 = 5.1179 mGal.
4.3.4
Bouguer correction
The attraction of the material between a reference elevation and that of the individual
station is taken care of by the Bouguer correction. In moving from a valley to a plateau
the gravity decreases due to the increasing distance from the centre of mass but also is
increased by the attraction of the slab of rock whose thickness is the change in elevation.
The correction per meter (elevation) for the effect is called the Bouguer Correction (BC)
and is given as:
BC  2Gh  0.4191hg.u
where ρ=density; g = acceleration due to gravity
h = depth and g.u = gravity units
(4.5)
29
The BC takes into account the material between the station levels if a given station is
higher than the reference elevation. The BC therefore is a function of thickness h and
density of the material between h datum level and station. It is also subtracted from FAA
to arrive at the Simple Bouguer Anomaly (SBA) and always positive in sign to the free
air correction and is given as:
SBA  FAA  BC
(4.6)
Equation 3.12 was used in computing BC with a density value of 2.67 gcm-3. For each
station this effect was calculated. It is a function of thickness h of the infinite horizontal
slab and the density ρ of the material between the datum level and the field stations. The
value of BC calculated for the base station was then subtracted from all other stations tied
to that base station to give relative BC. The relative BC was then subtracted from FAA to
yield SBA, thus for A6, SBA=5.1179-3.8064=1.3115mGal.
4.4
Rock density
Density and density contrasts of rocks not only controls gravity anomalies but also aid in
the identification of rocks , estimation of ore abundance and assessing rock conditions
( Amigun at al., 2009). Therefore gravity anomalies are caused by lateral variations in the
density of the Earth materials. The samples were collected in the study area at the
selected gravity stations. Given that the shapes of the rock samples were irregular, their
density values were determined using the Archimedes principle. The density contrast was
calculated by the relation    a   c . Where  a is the average density of the rocks
30
collected from the study area and  c is the mean density of surrounding crustal rock
taken as 2.67g/cm3. The density contrast was found to be 2.52g/cm3 and this was
employed for modeling.
4.5
Data processing
Column 14 and 16 (Appendix III) shows the corresponding relative BC and SBA for all
the stations. The data were manipulated using Microsoft ExcelTM. The gravity data were
gridded using surfer software in the X and Y directions using Kringing method. Data
were saved as grid files (GRD format). The grid files were then important by surfer
software using the Grid Node Editor and saved as DAT files. The DAT files were ready
to be imported into Grav 2 dc.
4.6
The Bouguer anomaly map
A contour map, constructed using a computer program surfer, shows simple gravity data
as gathered in the field (Figure 4.3). The Bouguer anomaly map with a contour interval of
0.5 mGal and a maximum of 2.5 mGal and a minimum of -5 mGal was drawn.
There is measure of correlation between several of mapped geological features and
gravity values. The relatively large anomaly has a shape which roughly follows
Northeast- Southwest trend of the study area. The maximum amplitude of the gravity
high is of order 2.5. This is high to relate to either surface geology or the topography of
the area.
31
361800
361750
361700
361650
361600
361550
361500
361450
mGal
2.5
Grid North
361400
2
1.5
361350
1
0.5
361300
0
-0.5
361250
-1
-1.5
361200
-2
-2.5
361150
-3
-3.5
361100
-4
-4.5
361050
-5
12200
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
Grid East
Figure 4.3: Bouguer anomaly map of the Mbeu area (contour interval of 0.5 mGal).
The Bouguer anomaly map reveals both positive and negative anomalies northern part of
the study area. To the north western part, a positive gravity anomaly is adjacent to the
negative gravity anomaly. The central part of the study area generally reveals positive
gravity anomaly. Some positive gravity anomalies were revealed in dry river valleys.
After free air and Bouguer correction have been made, the Bouguer anomaly contained
the information about the subsurface density only. The Bouguer anomaly map gives a
32
very good impression of the sub surface density; a low (negative) value of Bouguer
anomaly indicated a low density beneath the measured point. This was not of our interest
at the moment. High (positive) value of Bouguer anomaly indicates higher density
beneath the measured point.
meters
361800
1330
1325
361700
1320
1315
361600
Grid North
1310
1305
361500
1300
1295
361400
1290
1285
361300
1280
1275
361200
1270
1265
361100
1260
12200 12300 12400 12500 12600 12700 12800 12900 13000 13100 13200
1255
Grid East
Figure 4.4: Contour map showing the topography of the study area.
We used SurferTM to generate a two-dimensional grid for our Bouguer gravity using a
Kriging interpolation with an anisotropy of 2 to 1 aligned Northwest parallel to the trends
of major faults. The shaded surface (contour map) and a perspective plot surface of the
gridded data.
33
A three-dimensional representation of this data, as viewed from three points of
perspective, shows how this high and low relate to gravity value trends over in the study
area (Figure 4.5 through figure 4.7).
Figure 4.5: A view of three dimensional representation from the South.
34
Figure 4.6: A view three dimensional representation from the Southwest.
35
Figure 4.7: A view three dimensional representation from the Northeast.
Figure 4.8: Three- dimensional surface map showing the topography of the study area.
36
Topographic lows with gravity high represent the best target for drilling investigation.
37
CHAPTER FIVE
DATA INTERPRETATION
5.1
Aims and limitations of gravity data interpretations
The geologic interpretation of gravity data is more difficult and involve more
uncertainties that that for seismic records. Gravity maps have more resemblance to
structural maps than one can easily fall into mental trap of identifying gravity contours
as being indicative of structures. In evaluating gravity maps’ it’s important that one keeps
in mind the true nature of the contours: especially one must not forget that they depict a
potential field rather than a subsurface structure.
The accuracy of gravity data for geophysical interpretation depends both on the accuracy
of gravity observations themselves and on the accuracy of other quantities, namely
station location, elevation, and density of near surface rocks, that must be used to reduce
the gravity observations to form a suitable interpretation. Thus, the interpretation of the
gravity data properly begins at the very earliest stage of survey planning, and survey must
be designed with the definite goals clearly in mind. Accurate gravity data measured along
a few well-spaced and detailed profiles may be better suited for determining important
characteristics of a concealed body or structure than a large data set spreading uniformly
over a wider area.
Most of gravity investigations are undertaken with specific goals in mind; detection of
salt domes, determination of altitude of faults, mapping of plutons, definition of the size
and shape of hot bodies or ore bodies (Dobrin, 1988). Researchers can consult case
38
histories and find the ranges of widths and amplitudes of gravity anomalies found under
similar features in other places.
Any interpretation of potential field anomalies (gravity, magnetic and electrical) is
inherently ambiguous. The ambiguity arises because any given anomaly could be caused
by an infinite number of possible sources, hence an infinite number of solutions (Keaary
and Brooks, 1984). For example, concentric spheres of constant mass act as though as
located at the centre of the sphere. This ambiguity represents the inverse problem of
potential field interpretation which states that although the anomaly of a given body may
be calculated uniquely, there infinite number of bodies that could give rise to any
specified anomaly. Therefore, it is vital in interpretation to decrease this ambiguity by
using all available external constraints on the nature and form of the anomalous body.
Such constraints include geological information derived from surface outcrops, borehole
and mines and from other geophysical techniques.
There exist two characteristics of the gravity fields which make interpretation almost
impossible. The measured value of gravity and hence the superimposed effects of many
mass distribution of different sources are isolated. The second difficult in gravity
interpretation occurs when sources are approximately the same size and buried at about
the same depth are so close together and they appear to come from a single source rather
than from two separate sources. Resolution for that individual source is not always
possible but when it is rather complex, filtering techniques may be applicable with useful
results.
39
Thus, the interpretation of gravity anomalies for the determination of subsurface geologic
mass distribution is somewhat a subjective practice. There is no unique mass distribution
to satisfy a given gravity anomaly. The interpretation needs, in addition to knowledge of
gravity and potential theory, fundamental knowledge of geology coupled with logic.
These together with other information such as density or depth of the geologic features
often rule out solutions of many forms.
5.2
Quantitative interpretation
Quantitative interpretation involves analysis of gravity anomaly profiles. This enables the
interpretation of data as recorded. The magnitude and form of gravity anomalies are
interpreted as having been caused by bodies of simple shapes such as an infinitely long
thin conductor, a sphere and an infinitely long thin conductor (Parasnis, 1986).
An initial model for the source body was constructed based on geologic and geophysical
intuition. Values for the model’s gravitational field were calculated and compared with
the observed values, and model parameters was adjusted in order to improve the fit
between the two sets of values. This three-step process of body adjustment, calculation,
and comparison was repeated until calculated and observed values match.
In this interpretation, the depth to the body, depth extent, radius of the anomaly and the
anomalous mass are determined. This is achieved through modeling where an attempt is
made to match the observed anomaly with the theoretical one calculated for a model by
making iterative adjustments to the model.
40
5.2.1
Selection of profiles
Using surfer software, a grid and contour map have been created and then sliced to obtain
the gravity profile. The profiles chosen were oriented in the directions NE-SW, NW-SE,
nearly E-W and N-S for the purpose of fitting model to the observed data. The profiles
which gave nearly symmetrical anomalies are shown in figure 5.1. The simple Bouguer
anomaly contour lines were used in plotting of the profiles. The regional was removed by
trend analysis and for our case it was approximated by a linear curve. This was subtracted
from the observed data and the resulting positive or negative anomalies were interpreted.
mGal
361800
Z'
361700
2.5
V'
X'
2
1.5
Northing(metres)
Y
1
361600
Y'
0.5
0
361500
-0.5
-1
361400
X
Z
V
361300
-1.5
-2
-2.5
-3
361200
-3.5
-4
361100
-4.5
12200 12300 12400 12500 12600 12700 12800 12900 13000 13100 13200
-5
Easting(metres)
0
200
400
600
800 metres
Figure 5.1: Bouguer gravity anomaly profiles. Gravity measurement stations are indicated
by post marks (
).
41
5.2.2
Gravity profile zz’
This is a N-S oriented profile which runs through a positive and negative anomaly. The
residual profile plotted was obtained by subtracting the estimated regional value from the
observed gravity at all points along the gravity profile zz’.
2
Relative gravity anomaly (mGal)
1.5
1
0.5
0
12370
-0.5
12380
12390
12400
12410
12420
12430
SBA
Regional Trend
-1
-1.5
-2
-2.5
-3
Easting
Figure 5.2: Observed Bouguer gravity anomaly along profile zz’ and the estimated trend.
42
4
3.5
Relative gravity anomaly (mGal)
3
2.5
2
1.5
Residual
1
0.5
0
12370
-0.5
12380
12390
-1
12400
12410
12420
12430
Easting
Figure 5.3: Residual Bouguer gravity anomaly along profile zz’.
5.2.3
Gravity profile vv’
Figure 5.4 show relative gravity, regional and residual anomalies along gravity profile
VV’. The anomaly profile is taken along NE-SW direction. After the removal of regional
from the observed gravity we get the residual anomaly (figure 5.7) which was used for
modeling in order to determine the parameters of the causative body.
43
Relatieve gravity anomaly (mgal)
1.5
1
0.5
0
12650 12700 12750 12800 12850 12900 12950 13000
-0.5
SBA
Regional
-1
-1.5
-2
Easting
Figure 5.4: Observed Bouguer gravity anomaly along profile vv’ and the estimated trend.
3
Relative gravity anomaly (mGal)
2.5
2
1.5
Residual
1
0.5
0
12650 12700 12750 12800 12850 12900 12950 13000
-0.5
Easting
Figure 5.5: Residual anomaly along gravity profile vv’.
44
Gravity profile yy’
5.2.4
Figure 5.6 show relative gravity, regional and residual anomalies along gravity profile
yy’. The anomaly profile is taken along E-W direction.
Relative gravity anomaly
(mgal)
2
1
0
12000
-1
12500
13000
13500
SBA
Regional Trend
-2
-3
-4
Easting
Figure 5.6: Observed Bouguer gravity anomaly along profile yy’ and the estimated trend.
Relative gavity anomaly (mGal)
4
3
2
1
0
12200
Residual
12400
12600
12800
13000
13200
13400
-1
-2
Easting
Figure 5.7: Residual Bouguer gravity anomaly along profile yy’.
45
Gravity profile xx’
5.2.5
3
Relative gravity anomaly (mGal)
2
1
0
12400
12600
12800
13000
13200
SBA
Regional Trend
-1
-2
-3
-4
Easting
Figure 5.8: Observed Bouguer gravity anomaly along profile xx’ and the estimated trend.
Residual gravity anomaly (mGal)
4.5
4
3.5
3
2.5
2
1.5
Residual
1
0.5
0
-0.512400
-1
12600
12800
13000
13200
Easting
Figure 5.9: Residual gravity anomaly along profile xx’.
46
5.3
Modeling
Using the subsurface imaging software Grav2DC, designed by Dr. Gordon Cooper, twodimensional gravity models were made. The SBA data were plotted with their horizontal
distance. This computer program allows us to input the virtual buried rock bodies,
specifying their density contrast with the host rock, depth with and shape. Therefore the
parameters were adjusted, altering the factors determinant of the observed gravity
anomaly as it would be detected on the surface, until the observed and modeled gravity
anomalies resembled each other. The models below show possible configuration of the
subsurface using different density contrast and depth of contrast.
Figure 5.10: Residual Bouguer gravity anomaly profile vv’ and two-dimensional model.
Density contrast=2.52 g/cm3; Depth=121.48 m, Width=310.723 m
47
Figure 5.11: Residual Bouguer gravity anomaly profile xx’ and two-dimensional model.
Table 2: Parameters for profile xx'
Parameters
Body 1
Body 2
Density contrast
2.52g/cm3
1.58 g/cm3
Depth
12.98m
37.02 m
Width
311.68m
116.42 m
48
Figure 5.12: Residual Bouguer gravity anomaly profile yy’ and two-dimensional model.
Table 3: parameters for profile yy'
Parameters
Body 1
Body 2
Density contrast
2.52 g/cm3
2.10 g/cm3
Depth
10.10m
120.10 m
Width
433.82m
155.05 m
49
Figure 5.13: Residual Bouguer gravity anomaly profile zz’ and two-dimensional model.
Table 4: Parameters for profile zz'
Parameters
Density contrast
Depth
Width
Body 1
Body 2
3
2.52 g/cm
2.89 m
139.20 m
2.51 g/cm3
16.83 m
95.95 m
The residual Bouguer anomalies along the profiles suggest the presence of anomalous
body within the region. The geology of the area suggests a spherical body and hence, a
spherical model was employed to estimate the sought parameters of the anomaly. These
include: depth from the surface too the centre z, radius R, depth to surface T and the mass
of the body, M
50
2.5
2.45
2.0
1.5
mGal
1.29
1.0
0.5
0.0
-0.5
0
100
200
300
400
500
Distance (m)
Figure 5.14: Residual Bouguer gravity anomaly along profile vv’.
From figure 5.14 half-width
x 12 =183.82  2.98m
Depth from the surface to the centre of the anomaly is given by equation 3.8
Thus,
z =1.305× 183.82=239.89  3.89m
Radius of the anomaly is estimated using equation 3.9
 3(238.89) 2  2.45  10 5 
R

11
 4  6.67  10  2520 
1
3
 126.04  3.20m
The depth to surface of anomaly was estimated using equation 3.10, i.e.
T Z R
51
 239.89  126.04  113.85  7.09m
Mass of the anomaly is
M 
4R 3  a 4  126.04 3  2520

 2.11  0.24  1010 kg
3
3
4
3.89
3
mGal
2
1.74
1
0
-1
-100
0
100
200
300
400
500
600
700
Distance (m)
Figure 5.15: Residual Bouguer gravity anomaly along profile xx’.
From figure 5.15 Half width
x 12 =98.62  2.54m
Depth from the surface to the centre of the anomaly is given by equation 3.8
Thus,
z =1.305× 98.62= 128.70  3.32 m
Radius of the anomaly is estimated using equation 3.9
52
 3(128.70) 2  3.89  10 5 
R

11
 4  6.67  10  2520 
1
3
 97.09  3.04m
The depth to surface of anomaly was estimated using equation 3.10, that is;
T Z R
 128.4  97.09  31.61  6.36m
Mass of the anomaly is
4R 3  4  97.09 3  2520

 (9.66  1.29)  10 9 kg
3
3
.
M 
3
2.79
2
1
mGal
0.55
0
-1
-2
0
200
400
600
800
Distance (m)
Figure 5.16: Residual Bouguer anomaly along profile yy’.
From figure 5.16,
1000
53
Half width
x 12 =194.34 194.34  10.43m
Z=1.305× 1.305 194.43  253.61  13.62m
Radius of anomaly:
 3(253.61) 2  2.79  10 5 
R

11
 4  6.67  10  2520 
1
3
 136.60m
Depth to surface,
T  518.20  219.95  117.01  20.48m
Mass of anomaly;
M 
4  136.60 3  2520
 (2.69  0.51)  1010 kg
3
Residual Bouuguer gravity anomaly (mGal)
4
3.5
3
2
1.5
1
0
-1
50
100
150
200
250
300
350
400
450
Distance (m)
Figure 5.17: Residual Bouguer anomaly along profile zz’.
54
From figure 5.17 half-width
x 12 =35.26  2.21m
Depth from the surface to the centre of the anomaly is given by equation 3.8
Thus,
z =1.305× 35.26 =46.01  4.19m
Radius of the anomaly is obtained using equation 5.7
 3(46.01) 2  3.5  10 5 
R

11
 4  6.67  10  2520 
1
3
 47.21  3.54m
The depth to surface of anomaly was estimated using equation 3.10
T Z R
 46.01  47.21  1.2  7.73m
Mass of the anomaly is given by equation 3.11
4R 3  a 4  47.213  2520
M 

 (1.11  0.25)  10 9 kg
3
3
55
Table 5: Properties of model bodies for profiles vv’, xx’, yy’ and zz’ Mbeu mineral
prospect
Profile Z(m)
R(m)
T(m)
T’(m)
M(kg)
(Calculation) (Grav2DC)
vv’
240  4
124  3 114  7
121.48
(2.1  0.2)  1010
xx’
129  3
97  3
12.98
(9.6  1)  10 9
yy’
253  14 137  7 117  21
120.10
(2.7  0.5)  1010
zz’
46  4
2.89
(1.1  0.3)  1010
5.4
Rock samples
47  4
32  6
-1  8
Some rock samples (Appendix I) exposed was corrected from the gravity stations
especially where gravity readings were high, they were analyzed in the laboratory and
their average density was obtained.
Major element analysis (Table 6) reveals that the ore contains very little amount of SiO2,
Al2O3, CaO MgO Na2O, K2O, TiO2, MnO, Pb and Zn.
56
Table 6: Percentage compositions of rock samples
Samp
les
SiO2
Al2O3
Ca
O
MgO
Na2O
K2O
TiO2
MnO
Fe2O3
LO
I
Pb
ppm
Zn
ppm
1
ND
0.50
0.12
0.01
0.02
0.01
0.44
1.40
92.00
-
9.00
35.4
2
6.60
2.90
0.03
0.03
0.01
ND
0.40
1.30
86.00
-
8.60
30.6
3
6.40
3.20
0.07
0.50
0.10
0.13
0.60
0.30
84.00
-
8.40
28.8
4
87.01
0.80
0.06
0.05
0.04
0.06
0.03
0.30
11.00
0.16
7.00
39.4
5
57.00
-
7.40
2.70
4.24
2.40
1.20
0.30
11.80
4.09
6.00
349.6
6
45.00
-
0.15
6.80
0.10
5.80
0.76
0.50
22.50
6.42
12.0
62.0
7
51.10
23.63
8.00
6.80
3.10
3.60
0.80
0.20
0.80
2.10
8.00
64.0
57
CHAPTER SIX
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusions
The purpose of this research work was to determine the overall distribution of mineral
bearing rocks and sediment using gravity method. Specifically, the research was geared
toward carrying out ground gravity measurement of the study area in order to determine
variations in gravity. The gravity method exploits the fact that the variations in physical
properties of in-situ rocks give rise to variations in some physical quantity (density
contrast) which was measured remotely above the ground. Gravity was measured
accurately using a sodin gravimeter ad from the analysis gravity peaks indicated where
the dense iron rich material is best developed or concentrated. This research has not only
established that the hilly areas of Mbeu are the source of magnetite found in the alluvial
sands in the lowlands but has also revealed that the iron ore is possibly part of a larger
and existence resource below the hills within the area.
This study has not been able to establish the source of the magnetite. There has been no
evidence of hydrothermal activity within these volcanic complexes and the iron in Mbeu
is most likely derived from recent volcano-magmatic activity that could have taken place
after the Miocene period. From the immediate evidence it is apparent the deposit is not a
classic bedded iron formation. However, they are dark and mixed with almost pure silica
indicating some form of fractionation of a felsic magma. The weathered and limited
lateral extent do however point to dyke like intrusives that may be derived form a deeper
lying intrusive.
58
Based on the data presented in the previous sections, the following conclusions can be
made: The gravity modeling resulted in four cross sections that model the lithology and
structure of the study area (Figure 5.8 through figure 5.15). Gravity survey was able to
detect anomalies that likely show evidence for a buried dense body which for our case is
iron ore. The ore body (iron ore) responsible for the anomaly is buried in varied depths
from the surface. The analysis and interpretation of the gravity data revealed some
aspects about the structure of the Mbeu area which are useful for supplementing other
data in the geological synthesis.
A key factor in determining the economics of any discovery is the quality of iron ore
there is some course of optimism in this regard, based on surface samples containing 65
% Fe, alluvial accumulations found in valleys below the iron bearing hills from where
they have been found 25 Fe, 33 ,40 magnetite , 64% Fe.
The gravity anomalies seen in the field can only be interpreted as being due to the iron
ore that generally has a higher density than local rocks. Gravity highs corresponded to
high density magnetite bodies. The visibility of sandy iron is widespread and indicates
that there is potential for large scale alluvial accumulations found in valleys below the
iron bearing hills. Further geological and geophysical studies will need to be under taken
to establish if the Mbeu iron is part of an iron rich region or localized resource. Gravity
alone cannot distinguish between a strong density contrast at depth and a more diffuse
59
contrast shallow. Nevertheless, large scale gravity anomalies generally originate from
deep seated variation in density.
6.2
Recommendations
Extra information from seismic surveys is necessary to resolve the fundamental
ambiguity of detailed gravity interpretation. This is because any exploration geophysics
requires complementary geophysical surveys integrated with geochemical, environmental
geophysics and geologic insight, therefore further investigations of the Mbeu area by
other geophysical methods and finally drilling will assist in confirming the presence and
exact location in depth of the main iron ore which might have potential economic value.
There is need to re-assess and update the geology of the Meru area and the greater Mount
Kenya region as a whole. Based on the current knowledge of geology of the region no
valuable minerals were expected in the study area (Mason, 1953). The dominant
geological activity being associated with the volcanic eruptions that led to the formation
of Mount Kenya and the Nyambeni domes during the Oligocene and Miocene periods
respectively.
It is equally important to establish if the Mbeu iron is localized deposit or part of an iron
or mineral rich belt.
60
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63
APPENDIX 1: ROCK SAMPLES
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
64
Sample 7
65
APPENDIX II: DATA FOR THE PROTILES
Profile vv’
Distance Residual
0 0.00148
8.45098 -0.03253
15.54087 -0.06689
23.04712
-0.1011
35.81358 -0.11985
37.64326 -0.12385
52.2394 -0.10545
56.08629 -0.07892
66.83554 -0.03253
76.359
0.1105
81.43168 0.18005
96.02782
0.7701
96.63171 0.80027
110.624 1.64916
116.9044 1.95475
125.2201 2.29172
137.1771 2.45387
139.8163 2.45149
154.4124 2.27425
157.4498 2.23825
169.0085 2.05325
177.7226 1.96506
183.6047
1.8866
197.9953
1.7539
198.2008 1.75169
212.797 1.62676
218.268 1.59052
227.3931 1.52526
238.5407 1.46542
241.9892
1.4474
256.5854 1.39415
258.8134 1.38846
271.1815 1.36677
279.0861 1.35821
285.7777 1.35996
299.3588
1.3588
300.3738 1.36069
314.9699
1.3677
319.6315
329.5661
339.9042
344.1622
358.7584
360.1769
373.3545
380.4497
387.9506
400.7224
402.5468
417.1429
420.9951
431.7391
432.363
1.3634
1.37796
1.381
1.39116
1.408
1.40684
1.39528
1.30606
1.16895
0.75991
0.70856
0.10469
0.02218
0.00151
0.00832
Profile yy’
Distance
Residual
177.64008
1.2084375
189.46457
1.3128842
201.28906
1.4097131
213.11355
1.5320056
224.93804
1.7019787
236.76253
1.9320748
248.58702
1.9873504
260.41151
1.8577604
267.57773
1.8253799
272.236
1.8025252
284.06049
1.8235246
295.88499
1.9121057
307.70948
2.0011127
319.53397
2.036331
331.35846
2.0895022
343.18295
2.1565699
355.00744
2.2324392
366.83193
2.3129711
0.0003289
378.65642
2.3940773
0
390.48091
2.4717718
0.2727141
0.0009367
402.3054
2.5426022
12.097205
0.0335071
414.12989
2.6039099
23.921696
0.0610666
425.95439
2.653977
35.746187
0.0464598
437.77888
2.6926205
47.570678
449.60337
2.7228706
461.42786
2.7531146
473.25235
2.7934067
485.07684
2.8308909
496.90133
2.8222538
508.72582
2.7370463
520.55031
2.5936639
532.3748
2.4318029
118.51762
0.0132707
0.1134724
0.3861081
0.6610016
0.6983396
0.5740546
0.4942175
544.19929
2.2575128
130.34211
-0.352683
556.02378
2.062034
142.1666
0.3190919
567.84828
1.8212579
153.9911
0.7774484
579.67277
1.5416378
165.81559
1.0502486
591.49726
1.2543769
603.32175
0.975914
59.395168
71.219659
83.04415
94.868641
106.69313
66
615.14624
0.7148172
626.97073
0.4763291
630.66771
0.4100005
958.05647
638.79522
0.263041
964.60715
650.61971
0.0773261
0.0800672
0.2103036
0.3158704
0.3998893
0.4653185
0.5146872
0.5507635
0.5781848
0.6057679
0.6484835
662.4442
674.26869
686.09318
697.91767
709.74217
721.56666
733.39115
745.21564
757.04013
768.86462
780.68911
792.5136
804.33809
816.16258
827.98707
839.81157
851.63606
863.46055
875.28504
887.10953
898.93402
910.75851
922.583
934.40749
-0.726641
0.8596906
1.0555996
1.2974268
1.5331173
1.6955013
1.7559066
1.7365077
1.6705974
1.5779426
1.4617827
1.3288496
1.2299503
1.0031655
946.23198
0.5346676
0.1169873
Profile xx’
Distance
Residual
260.75492
3.889952
273.48511
3.8947653
274.31549
3.8901028
287.87606
3.7581664
297.66933
3.6384329
301.43663
3.5856289
314.9972
3.3710971
321.85356
3.2427289
0.0017756
328.55777
3.1131937
0
342.11834
2.8036075
3.104089
0.068041
346.03778
2.7008262
7.4586366
0.0958406
355.67891
2.4429385
16.664659
0.1731487
369.23948
2.033605
30.225229
0.2255709
370.222
2.0017664
31.642861
0.2299176
382.80005
1.590232
43.785799
0.2685535
394.40623
1.1945465
55.827086
0.3331147
396.36062
1.1284133
57.346369
0.3405264
409.92119
0.680894
70.906939
0.5142977
418.59045
0.4160839
80.01131
0.6964095
423.48176
84.467509
0.8001093
98.028079
1.117579
104.19553
1.2552996
442.77468
0.2772439
0.0376798
0.1288969
111.58865
1.4241405
450.6029
125.14922
1.7103614
128.37976
1.7742753
138.70979
1.976646
152.27036
2.2264564
152.56398
2.2315769
165.83093
2.4621583
491.14313
176.74821
2.6442677
491.28461
179.3915
2.6883424
192.95207
2.9076661
200.93243
3.0349062
206.51264
3.1246703
518.40575
220.07321
3.3444294
531.96632
225.11666
3.4281625
233.63378
3.561513
539.51158
247.19435
3.7652325
545.52689
249.30088
3.7931669
437.04233
464.16347
466.9589
477.72404
504.84518
515.32735
-0.243017
0.3526148
0.3624803
0.4021903
0.4173529
-0.417506
0.4105905
-0.397541
0.3930364
0.3659356
0.3491975
0.3340144
67
636.24847
0.2975638
0.2846671
0.2566962
0.2134691
0.2079287
0.1647318
0.1196618
0.1144932
0.0547782
0.0018214
640.45088
0.0243128
648.91668
0.0825297
559.08746
563.6958
572.64803
586.2086
587.88002
599.76917
612.06425
613.32974
626.89031
Profile zz’
184.94909
3.0764202
196.92669
2.239289
Residual
204.54524
1.7420381
208.90429
1.4357659
5.2851112
0.0005318
0.0528422
220.88189
0.7464027
17.26271
0.0221141
232.85949
29.240309
0.063629
244.83709
35.900711
0.0311483
41.217908
256.81469
101.1059
0.0163337
0.1156297
0.2927632
0.4321506
0.4745864
0.3007944
0.2632953
0.0404657
0.2266056
113.0835
0.9707088
316.70268
120.22298
1.9079215
328.68028
125.0611
2.5156956
137.0387
3.4972749
149.0163
3.0259695
160.9939
2.8380194
172.9715
3.0595211
Distance
0
53.195507
65.173106
77.150705
89.128303
268.79229
340.65788
-0.335828
0.3899706
0.3967946
0.4012672
0.3758167
0.3139299
0.2188487
0.0948199
348.43318
0.000534
280.76989
288.86751
292.74748
304.72508
68
APPENDIX III: DATA USED
Station
Elevation
Northing
Easting
Time
Dial
reading
Relative
gravity in
scale/div
Relative
gravity
in
mGals
A1
1254
361794
12129
1212
508.000
0.000
0.00
A2
1266
361796
12177
1230
512.000
4.000
0.40
A3
1259
361747
12257
1239
505.000
-3.000
-0.30
A4
1274
361656
12323
1300
489.500
-18.500
-1.85
A5
1275
361577
12392
1323
483.000
-25.000
-2.50
A6
1288
361510
12385
1340
454.000
-54.000
-5.40
A7
1279
361530
12415
1348
478.500
-29.500
-2.95
A8
1282
361506
12562
1909
469.500
-38.500
-3.85
A9
1293
361555
12729
1522
454.500
-53.500
-5.35
A10
1296
361590
12748
1533
446.500
-61.500
-6.15
A11
1307
361678
12955
1545
406.000
-102.000
-10.20
A12
1316
361619
13186
1602
406.500
-101.500
-10.15
A13
1299
361605
13194
1609
413.500
-94.500
-9.45
A14
1304
361616
13171
1612
407.000
-101.000
-10.10
A15
1308
361603
13223
1623
413.000
-95.000
-9.50
A16
1318
361698
13273
1637
388.000
-120.000
-12.00
A17
1318
361642
13170
1700
389.000
-119.000
-11.90
A18
1311
361649
13080
1732
416.000
-92.000
-9.20
A19
1307
361696
12943
1741
393.000
-115.000
-11.50
A20
1277
361514
12746
1750
458.000
-50.000
-5.00
A21
1288
361441
12788
1801
456.000
-52.000
-5.20
A22
1277
361534
12576
1817
471.000
-37.000
-3.70
A23
1273
361614
12568
1823
475.000
-33.000
-3.30
69
Cont.
Station
LC
relative
to base
mGals
F A C
Relative
to base
(mGals)
Latitude
in
degrees
LC mGals
A1
3.2343182
978048.2844
0.0000
386.9844
0.0000
0.0000
0.0000
0.0000
A2
3.2343398
978048.2847
0.0003
390.6876
3.7032
4.1029
1.3434
2.7595
A3
3.2339081
978048.2803
-0.0041
388.5274
1.5430
1.2471
0.5598
0.6874
A4
3.2330998
978048.2721
-0.0123
393.1564
6.1720
4.3343
2.2390
2.0953
A5
3.2323990
978048.2650
-0.0194
393.465
6.4806
4.0000
2.3510
1.6490
A6
3.2317995
978048.2589
-0.0255
397.4768
10.4924
5.1179
3.8064
1.3115
A7
3.2319807
978048.2607
-0.0237
394.6994
7.7150
4.7887
2.7988
1.9899
A8
3.2317777
978048.2587
-0.0257
395.6252
8.6408
4.8165
3.1347
1.6819
A9
3.2322288
978048.2632
-0.0212
399.0198
12.0354
6.7066
4.3662
2.3404
A10
3.2325432
978048.2664
-0.0180
399.9456
12.9612
6.8292
4.7020
2.1272
A11
3.2333461
978048.2746
-0.0098
403.3402
16.3558
6.1656
5.9335
0.2321
A12
3.2328368
978048.2694
-0.0150
406.1176
19.1332
8.9982
6.9411
A13
3.2327123
978048.2681
-0.0163
400.8714
13.8870
4.4533
5.0379
A14
3.2328088
978048.2691
-0.0153
402.4144
15.4300
5.3453
5.5976
2.0571
0.5846
0.2524
A15
3.2326967
978048.2680
-0.0164
403.6488
16.6644
7.1808
6.0455
1.1354
A16
3.2335498
978048.2766
-0.0078
406.7348
19.7504
7.7582
7.1650
0.5932
A17
3.2330411
978048.2715
-0.0129
406.7348
19.7504
7.8633
7.1650
0.6983
A18
3.2330966
978048.2720
-0.0124
404.5746
17.5902
8.4026
6.3813
A19
3.2335060
978048.2762
-0.0082
403.3402
16.3558
4.8640
5.9335
A20
3.2318636
978048.2595
-0.0249
394.0822
7.0978
2.1227
2.5749
2.0212
1.0695
0.4522
A21
3.2312143
978048.2529
-0.0315
397.4768
10.4924
5.3239
3.8064
1.5175
A22
3.2320291
978048.2612
-0.0232
394.0822
7.0978
3.4210
2.5749
0.8461
A23
3.2327436
978048.2685
-0.0159
392.8478
5.8634
2.5793
2.1271
0.4522
FAC
FAA
BC
Relative to
base(mGals)
SBA