MAPPING GEOTHERMAL HEAT SOURCE IN HOMA HILLS USING GRAVITY TECHNIQUE. ODEK ANTONY [B.Ed. (Sc)] I56/CE/11191/2007

MAPPING GEOTHERMAL HEAT SOURCE IN HOMA HILLS USING GRAVITY TECHNIQUE ODEK ANTONY [B.Ed. (Sc)] I56/CE/11191/2007 A thesis submitted as partial fulfillment of the requirement for the award of the Degree of Master of Science (Physics) in the school of Pure and Applied Sciences of Kenyatta University November 2012

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 All sources of information have been acknowledged by means of references Odek Antony Signature Date Department of Physics Kenyatta University P.O Box 43844-00100 NAIROBI-KENYA This thesis has been submitted for examination with our approval as University supervisors Dr. W.J. Ambusso Signature Date Department of Physics Kenyatta University P.O Box 43844-00100 NAIROBI-KENYA Dr. Githiri J. Gitonga Signature Date Department of Physics Jomo-Kenyatta University of Agriculture and Technology P.O Box 62000-00200 NAIROBI-KENYA

iii DEDICATION To my daughter Joy, wife Deurence, and my entire family members.

iv ACKNOWLEDGEMENTS I wish to acknowledge my supervisors Dr. W. J. Ambusso and Dr. J. G. Githiri for their great contributions at different stages of the research and development of this thesis. This great idea has become a reality because of the good professional relationship I had with them. They did not only contribute their valuable ideas but also assisted me in acquiring software for data processing and other logistics which enabled me to complete this programme within some considerable period of time. I also wish acknowledge Kenyatta University for availing the equipments which I used while collecting data, not to forget the Ministry of Environment and Mineral resources for availing the geological report of Homa Hills. I am also grateful to my colleague Mr. B. Adero for the quality time we shared throughout the field data collection, the useful discussions and the encouragement. Through this I was able to adapt a go getter spirit which became instrumental in achieving this academic height. I also want to acknowledge other Master of Science colleagues in geophysics, Mr. V. Abuga and Mr. K. Mustafa for their encouragement and moral support during my entire programme. I wish also to recognize the very important moral, spiritual and material support from my wife during my studies. I also wish to acknowledge my friends Mr. A. Orondo and Mercy Aliet for their moral and material support at different stages of this study. Most important I thank the almighty God for the gift of wisdom, knowledge and good health. Amen.

v TABLE OF CONTENTS DECLARATION... ii DEDICATION... iii ACKNOWLEDGEMENTS... iv TABLE OF CONTENTS... v LIST OF FIGURES... ix LIST OF TABLES... xi ABBREVIATIONS AND ACRONYMS...xii ABSTRACT... xiii CHAPTER ONE... 1 INTRODUCTION... 1 1.1 Background to the Study...1 1.2 Location, Physiography and Communication...5 1.3 Geological and Tectonic setting...8 1.4 Statement of Research Problem... 11 1.5 Thesis Objectives... 11 1.5.1 Main Objective... 11 1.5.2 Specific Objectives... 11 1.6 Rationale of the Study... 12 CHAPTER TWO... 13 LITERATURE REVIEW... 13 2.1 High Temperature Geothermal System... 13 2.2 MT/TEM Results of Homa Hills... 14

vi 2.3 Gravity Technique in a Geothermal Field... 15 CHAPTER THREE... 18 THEORY OF GRAVITY METHOD... 18 3.1 Introduction... 18 3.2 Principles of Gravity Method... 18 3.2.1 Gravitational force and gravitational potential... 18 3.2.2 Relative measurement of the gravity... 19 3.3 Gravity Reductions... 19 3.3.1 Need for correction... 19 3.3.2 Latitude correction... 20 3.3.3 Free air correction... 21 3.3.4 Bouguer correction... 21 3.3.5 Terrain correction... 22 3.3.6 Tidal correction... 23 3.3.7 Instrumental drift correction... 24 CHAPTER FOUR... 25 MATERIALS AND METHODS... 25 4.1 Introduction... 25 4.2 Instrumentation... 25 4.2.1 Sodin gravity meter... 25 4.2.2 Global positioning system (GPS)... 26 4.3 Gravity Measurements... 28 4.3.1 Station layout... 28

vii 4.3.2 Sources of error in gravity survey... 30 4.3.3 Instrumental drift... 30 4.4 Gravity Data Reduction and Processing... 31 4.4.1 Introduction... 31 4.4.2 Data reduction... 31 4.4.2.1 Drift correction... 31 4.4.2.2 Latitude correction... 33 4.4.2.3 Free air correction... 34 4.4.2.4 Bouguer correction... 34 4.4.2.5 Terrain correction... 35 4.5 Data Processing... 35 4.5.1 Bouguer anomaly map... 35 CHAPTER FIVE... 38 DATA INTERPRETATION... 38 5.1 Introduction... 38 5.2 Theoritical Aspects of Gravity Interpretation... 38 5.2.2 Analytic continuation... 41 5.2.3 Aims and limitations of gravity data interpretation... 42 5.3 Isolation of Gravity Anomalies: Principles... 43 5.4 Qualitative Interpretation... 44 5.4.1 Selection of profiles... 45 5.4.2 Isolation of residual anomalies and description of the profiles... 46 Fig. 5.4(b): Residual gravity anomaly profile BB... 48

viii 5.5 Quantitative Interpretation... 51 5.5.1 Introduction... 51 5.5.2 Empirical determination of depth... 51 5.5.2.1 Half-width method (X 1/2 )... 52 5.5.2.2 Gradient amplitude ratio method... 54 5.5.3 Indirect methods... 56 5.5.3.1 Euler deconvolution: Principles... 56 5.5.3.2 Euler deconvolution along selected profiles... 58 5.5.3.3 Forward numerical modeling: Principles... 63 5.5.3.4 Forward modeling of the data from the selected profiles... 66 5.6 Discussion... 69 CHAPTER SIX... 72 CONCLUSIONS AND RECOMMENDATIONS... 72 6.1 Conclusions... 72 6.2 Recommendations... 73 REFERENCES... 75 APPENDIX 1: Gravity Data Reduction... 78 APPENDIX 2: Residual Gravity for Profiles... 81 APPENDIX 3: Drift Curves... 82

ix LIST OF FIGURES Figure 1.1: Location of Homa Hills geothermal prospect 2 Figure 1.2: Structural map of the Kisumu area 7 Figure 1.3: Geological map of Homa Hills 10 Figure 3.1: Terrain correction 22 Figure 4.1: Station positions 29 Figure 4.2: Drift curve on 15 th April 2011 32 Figure 4.3: Complete Bouger anomaly contour map of Homa Hils 36 Figure 4.4: 3D map of CBA 37 Figure 5.1: Greens equivalent stratum 39 Figure 5.2: Ambiguity in gravity interpretation 40 Figure 5.3: a) CBA profile AA 47 Figure 5.3: b) Residual gravity anomaly profile AA 47 Figure 5.4: a) CBA profile BB 48 Figure 5.4: b) Residual gravity anomaly profile BB 48 Figure 5.5: a) CBA profile CC 49 Figure 5.5: b) Residual gravity anomaly profile CC 49 Figure 5.6: a) CBA profile DD 50 Figure 5.6: b) Residual gravity anomaly profile DD 50 Figure 5.7: Half-width method along profile AA 52 Figure 5.8: Half-width method along profile BB 53 Figure 5.9: Half-width method along profile CC 53 Figure 5.10: Gradient-amplitude ratio method along profile AA 54 Figure 5.11: Gradient-amplitude ratio method along profile BB 55

x Figure 5.12: Gradient-amplitude ratio method along profile CC 55 Figure 5.13: Euler Deconvolution along profile AA 59 Figure 5.14: Euler Deconvolution along profile BB 60 Figure 5.15: Euler Deconvolution along profile CC 61 Figure 5.16: Euler Deconvolution along profile DD 62 Figure 5.17: Observed, calculated anomaly and forward model for 2-D body along profile AA 65 Figure 5.18: Observed, calculated anomaly and forward model for 2-D body along profile BB 66 Figure 5.19: Observed, calculated anomaly and forward model for 2-D body along profile CC 67 Figure 5.20: Observed, calculated anomaly and forward model for 2-D body profile DD 67

xi LIST OF TABLES Table 4.1: Base station readings on 15 th April 2011 43 Table 5.1: Results of depth obtained by empirical methods 56 Table 5.2: Parameters obtained by Euler Deconvolution 62 Table 5.3: Parameters obtained by Foward modelling 68

xii B.C Bouguer Correction ABBREVIATIONS AND ACRONYMS CBA Complete Bouguer Anomaly GPS Global Positioning System GNS Global Navigation Satellite System MT Magnetotellulic TEM Transient Electromagnetic IGSN International Gravity Station Network

xiii ABSTRACT Homa Hills geothermal prospect is located on the Nyanzian rift west of the Kenyan rift system. The manifestation of hot springs and steaming grounds in the area has revealed its geothermal potential. In order to fully asses the potential of this field, the heat source which is one of the main features of a geothermal system had to be properly located based on its perturbation on the gravity field. This enables gravity technique which is a high precision method for measuring density contrast that relates to the subsurface rocks to delineate its effect. The variation of density in a geothermal environment is as a result of magma intruding the crust in form of dykes or other structural conditions of the subsurface rocks. In Homa Hills geothermal field, reconnaissance research was done using Magnetotellurics and Transient electromagnetic by Geothermal Development Company (GDC) in an attempt to locate the heat source and establish the role of structures in the control of fluid dynamics. However, no supportive research using other geophysical methods has been done to compliment the Magnetotellurics and Transient electromagnetic methods in delineating the general extend density and depth of the heat source. In this study, Gravity survey was conducted and the data processed to remove all other effects not related to the subsurface density changes. The Bouguer gravity anomaly was interpreted qualitatively by inspecting the profiles and the grids for variations in the gravitational field and the residual anomaly was separated from the regional gravity field. The anomaly was also interpreted quantitatively by both direct and indirect methods. Direct methods involved the use of the anomalies half-width and gradient-amplitude ratios in estimating the depth of the causative body. Indirect methods involved both Euler Deconvolution and forward modeling where a two-dimensional gravity model along selected profiles was generated by computer software. This was done in order to best fit the observed gravity anomalies in an attempt to estimate depth, density and extend of the prospective heat source. Sharp dyke like structures were delineated at shallow depths of approximately 225, 10, 256, 256 and 512m with a width of 2250, 800, 750, 250 and 1250m respectively by Euler Deconvolution method. These results were found to be consistent with the results from forward modeling which shows the top of these structures at a depth of 192, 33, 206, 850 and 431m with a width of 3321, 604, 166, 394 and 821m respectively. The models obtained are in agreement with the geology of the area and the results of the Magnetotellurics and Transient electromagnetic methods conducted by the Geothermal development company. The hot springs therefore on the Southern part of the study area could be as a result of the heating effect from these shallow, high temperature dykes. As a recommendation these hot springs could be subjected to direct uses.

1 CHAPTER ONE INTRODUCTION 1.1 Background to the Study Homa hills geothermal field is located in the Nyanzian rift west of Kendu, a branch of East African rift valley which occupies most of the Homa peninsula and protrudes into the Kavirondo Gulf. The Kenyan part of East African Rift is oriented in the N-S trending with crustal thickness of 20km in the North and 35km at the centre and forms an active continental extension with a length of about 500km, a width of 60-80km and an average cross-sectional relieve of more than 1000m. It is characterized by intense faulting, seismic activity and abnormally high heat flow (Baker and Wohlenberg, 1971). The northern, central and southern segment of the Kenyan Rift have half graben geometries due to earlier faulting and pronounced subsidence along the western boundary faults. The N80 E trending Nyanza half-graben branches with the main Kenyan rift at Menengai where there is a triple junction and disappears westward under Lake Victoria. The rift floor is generally at 1100 m, the immediate shoulders being at 1600 m. The main arm of the East African Rift valley geothermal prospect have been explored and the potential documented, however the Nyanzian rift (Figure 1.1) has not been explored and its geothermal potential is not well known, hence the need to carry out detailed geothemal exploration surveys in the area. Being a site of an active volcano in tertiary and Pleistocene times, Nyanzian Rift is characterized by rhyolitic, andesitic and basaltic Nyanzian lavas which have been highly folded (Lagat, 2010).

Figure 1.1: Location of Homa Hills geothermal prospect on the Kenyan rift system by Beicip, 1987. 2

3 The presence of thermal flow in form of hot springs at Abundu, Kakdhimu and Kokoth along the shores of Lake Victoria with temperatures in excess of 80 0 C and wide spread Fimbristylis exilis geothermal grass which is also common in other geothermal areas in the main Kenyan Rift, makes it a potential geothermal field which needs to be studied. MT\TEM survey has been conducted by the Geothermal Development Company (GDC) in an attempt to establish the heat source(s), up flow zones, outflow zones and the role of structures in the control of the fluid dynamics and the hydrological controls of the system. The integrated results of the studies indicate the existence of a geothermal resource under in Homa Hills, which is postulated to be associated with shallow magmatic/dyke intrusive along fractures (Lagat, 2010). There is need to compare the research findings using other techniques. In this study, gravity survey of Homa Hills was conducted. Of the physical properties of subsurface rocks which can be measured from the surface, density is influenced by the nature of the structures in the subsurface rocks. Through gravity survey which is based on the fact that a target is limited in space and has a different density from the surrounding geology, it was possible to map gravity variations at Homa Hills, subject the data to both qualitative and quantitative interpretation in an attempt to investigate the cause of high heat flow and presence of hot springs in the area of study. The heat source parameters obtained through modeling and the geological situation is of importance in determining its Geothermal potential.

4 Geothermal energy is the energy that is obtained from the heated rock and fluid that fills the fractures and pores within the earth crust. It originates from radioactive decay deep within the earth and can exist as hot water, steam or hot dry rocks. Geothermal energy can be used directly or indirectly, depending on the temperature of the geothermal resource. Geothermal resources are classified as low temperature(less than 90 C), moderate temperature (90 C-150 C) and high temperature (greater than 150 C). The highest temperatures are generally used for electric power generation and are found in volcanic regions. Geothermal systems are made up of four main components: a heat source, a reservoir, a fluid (the carriers that transfers the heat) and a recharge area. In this study the main focus was the heat source at Homa Hills. The magnetotelluric (MT) survey, in particular, is used extensively for reconnaissance purposes in geothermal exploration, and to a lesser degree in detailed follow up exploration. The MT method offers a vast spectrum of possible applications, despite the fact that it requires sophisticated instrumentation. The main advantage of the MT method is that it can be used to define deeper structures than are attainable using the electric and other electromagnetic techniques. The MT method employs the earth s natural electromagnetic field, which contains a very wide spectrum of frequencies including very low frequencies that are useful in probing to depths of several tens of kilometers. Gravity method has been used elsewhere to map regions with contrasting densities especially within geothermal fields. It can provide valuable information on the shape, size, depth, density and other important characteristics of deep geological structures that

5 could constitute a geothermal system, however, it gives little or no indication as to whether these structures actually contains the hot fluids. Gravitational survey offer significant benefit to the interpretation of MT data and is relatively cheaper than MT. It is well known that the density models obtained through application of gravity method are intrinsically non-unique. 1.2 Location, Physiography and Communication Homa Hills geothermal prospect is located about 50km north of Kendu Bay. The prospect which lies on the Nyanzan Rift covers an area of approximately 150km 2. The study was conducted over the 78km 2 target area. The target area is bounded by geographical location (Easting 664000 to 672000 and Northing 9953000 to 9962700). Figure 1.1 shows the proposed Homa Hills geothermal prospect. The Homa Mountain sticks out sharply from its broad base of gentle slopes and has a flat top with a diameter of approximately 2km across surrounded by a number of steep or gentle secondary hills. The hills has, as a whole, an oval shape approximately 6km in long axis and 5km in short axis. Its top reaches an elevation of about 1571m above sea level or of 610m above the level of Lake Victoria (Saggerson, 1952). The drainage in the area is strongly controlled by structural elements of the region. Surficial drainage radially drains away from raised grounds/topographies following either faults or fissures zones to various directions. Underground drainage systems follow geological structures within the Nyanzian Rift bounded by Kaniamwia fault in the South and Mfangano fault in the North. High percentage of dip sited drainage waters appear to

6 be seeping through Kaniamwia fault from the Winam gulf in the North (Figure 1.2). Homa is situated on the Line of the Kendu Fault. The Samanga fault passes to the south east of the mountain where it has disturbed the phonolite lavas at Homa Bay the north westerly throw of the fault must be small as no prominent features are apparent. The location of the mountain is therefore a weakened zone near the intersection of these two sets of fractures. The Nyanzian rift is closely associated with the formation of the Homa Mountain and the Crater Lake Simbi. The prospect is served by the main tarmac road from Kisumu to Homa Bay and connects to a fairly maintained Kendu Bay Oyugis murram road at Kendu Bay. At about 1km from Kendu Bay junction along Kendu Bay-Homa Bay road, an access road branches to the Homa Hills approximately 30km via Pala. The road encircles the foot of Homa Hills giving accessibility to the mountain from all directions. The communication is fairly good since the area is served by a mobile phone signal transmitter base stations located at Kendu Bay and Obongo shopping centers West of Homa Hills.

Figure 1.2: Structural map of Kisumu area by Saggerson, 1952. 7

8 1.3 Geological and Tectonic setting Homa Mountain is a site of an active volcano in tertiary and Pleistocene times, it dominates the country west of Kendu and occupies most of the Homa peninsula, which protrudes into the Kavirondo gulf and forms the east flank of Homa Bay Mountain. It is composed of a number of massive separate peaks which include Homa, Nyansanja and Apoyo. Homa which is the largest rises to a height of over 5200ft. The depression between the peaks does not however, represent an old volcanic crater nor does the circle circumscribing the peaks bear any relation to the ring structure of Pleistocene to Recent. The mountain is cloaked on its lower slopes by thick mantle of Pleistocene and recent sediments comprising in main upper Pleistocene to recent gravels and soils on the western and southern slopes, Follisiferous lower and middle Pleistocene beds cover the northern slopes. The country rocks to the south of the mountain are composed of rhyolitic, andesitic and basaltic Nyanzian lavas which have been highly folded and form an anticlinorium pitching south-westwards (Figure 1.3). From an examination of the mountain it is apparent that these Nyanzian rocks also extended northwards where the research is to conducted, and are the rocks through which the Homa vent was formed, (Saggerson, 1952). Hermatite and magnetite are also of common occurrence in the Homa area. The Menengai volcano region is a triple junction between the northern Kenyan, central Kenyan and Nyanza rifts, almost at the centre of Kenyan dome. The central Kenyan rift is individualized by a sharp turn in rift direction at the southern end of the northern

9 Kenyan rift valley, at the latitude of Menengai (Figure 1.1). Its N150 E trending segment is set in the middle of the Kenyan dome, with elevations reaching more than 3700 m in the eastern shoulder and more than 3000 m in the western one. Elevations of the rift floor rise from 1050 m in the north, to 2100 m in the middle, and steps down progressively southwards to 600 m at Lake Natron. This bend is an intersection with a large NWstriking basement structure called the Aswa lineament (Baker and Wohlenberg, 1971)

Figure 1.3: Geological map of Homa Hills geothermal prospect by Saggerson, 1952. 10

11 1.4 Statement of Research Problem Hydroelectric source of energy has been widely used as the main source of energy in Kenya. The amount of power it supplies completely depends on the level of water in the dams which in turn depends on the amount of rainfall. However, due to fluctuations in the dam level as a result of seasonality of the water supply, Kenya has been faced with a challenge of electric power shortage. This has lead to low productivity in the industries and jua kali sector, hence low economic growth of the country. The government has therefore taken an initiative in exploring alternative sources of energy. Geothermal energy which is one of the cheapest and most stable sources of energy is expected to play a larger role as an alternative source of energy for electricity generation. Gravity survey as a method of geothermal exploration was used to outline the expected heat source and other structural conditions (i.e. fault systems) below the surface and in turn helped in identifying zones of fracturing and faulting which are related to the geothermal environment in Homa Hills. 1.5 Thesis Objectives 1.5.1 Main Objective To utilize gravity data to locate significant geothermal heat source responsible for the presence of hot springs in Homa Hills. 1.5.2 Specific Objectives i) To conduct gravity survey of Homa Hills. ii) To carry out qualitative interpretation in an attempt to locate the depth and size of the heat source in Homa Hills.

12 iii) To develop a conceptualised model of the geothermal system in Homa Hills so as to establish the characteristics such as the shape, density, depth and width of the causative body. 1.6 Rationale of the Study The major problem confronting geothermal companies is how to effectively, economically and efficiently predict the optimal site location for drill holes in order to provide the best chance of intersecting productive geothermal fluid channels and reservoirs deep beneath the subsurface. Gravity survey is important in detecting the heat source and fault systems below the surface which was used to analyze and understand ground hot water channels. It is well known that heat sources in the subsurface leads to increase in density and is mapped by the gravity survey as gravity highs and low resistivity for the case of MT survey. Unlike the main arm of East African rift valley geothermal prospects which have been explored and the potential documented, Nyanzian rift has not been explored and its geothermal potential not yet well known, hence the need to conduct a detailed geothermal exploration survey in the area. In this study gravity technique was used to validate the MT/TEM result.

13 CHAPTER TWO LITERATURE REVIEW 2.1 High Temperature Geothermal System The occurrence of hot springs in Homa Hills signifies the presence of a hydrothermal system in the area. These manifestations have been used for a long time as indicators of the existence of geothermal systems associated with shallow magma chambers (Omenda et al., 1991). The high temperature intrusive acts as a heat source when it caps geothermal fluids due to up-doming, aiding steam production. These exploitable resources are however, limited to certain geological environments that are conductive or development of geothermal systems. Essential features of a geothermal system include; i. Intense heat source at relatively shallow levels of the earth crust ii. Favorable geological /structural settings like presence of permeable formations or fracture/fault systems, to allow transmission and storage of geothermal fluid and iii. Sufficient recharge-water supply to enable heat transfer. The size of geothermal systems and reservoir characteristics vary greatly but are mainly controlled by secondary permeability used by tectonics and geological setting (Omenda et al., 1991). Like the geothermal system of Sibayak Indonesia which is mainly controlled by volcanic activities along with regional tectonic activities and characterized by volcanic rock formations (Atmoja et al., 2000), Homa Hills geothermal system is located in the tectonically active Rift Valley associated with regions of quaternary volcanism. In Hungary, the geothermal system comprises multilayered Pannonia sediments; lower impermeable Pannonia sediments and upper porous and permeable Pannonia, creating a good environment for a geothermal reservoir (Bobok et al., 1998). Significant strike slip

14 movements along the basement rocks have caused high secondary porosity and along some tectonic lines, high pressure geothermal conditions were generated in Hungary geothermal system (Arpasi et al., 2000). The high heat flow in the Homa Hills is expected to be controlled by the structural patterns and faulting of the Kendu side of the Nyanzian rift system, influenced by the grain in the Precambrian rocks. The main driving force could have been convection currents separating the crustal plates and hence is a zone of asthenosphere upwelling. Hence high heat flow in the rift valley (Omenda et al., 1991). The steam produced from the reservoir can be trapped for geothermal power generation. In the exploration for an optimal site to drill the holes, a number of techniques are used. In this study Gravity technique will be considered. 2.2 MT/TEM Results of Homa Hills Geophysical techniques employed during the survey in Homa Hills included, transient electromagnetic (TEM) and magnetotellurics (MT). Joint TEM and MT imaging were employed to study the subsurface for the existence of electrically conductive zones that form the geothermal reservoirs. In a geothermal system, the magnetotellurics (MT) survey which employs the earth s natural electromagnetic field has been used extensively for reconnaissance purposes. The main advantage of the MT method is that it can be used to define deeper structures than are attainable by other resistivity methods (Malin et al, 2004). Integrated results of the MT/TEM studies indicate the existence of a geothermal resource under Homa Hills. The heat source is postulated to be associated with shallow

15 magmatic/dyke intrusives along fractures. Estimated subsurface temperatures from gas geothermometers range from 160-235 C, which are ideal production of electricity using binary fluids and for direct use utilization. The resource area is approximately 11 km 2 which translates to 165 MWe using the world s average of 15 MWe per km 2. It is recommended that 2 exploratory wells be drilled within the anomaly to confirm the nature and potential of the resource at the prospect (Lagat, 2010). For a detailed follow up exploration, gravity technique was used to validate the MT results. 2.3 Gravity Technique in a Geothermal Field Local gravity anomalies in geothermal fields are generally associated with metamorphism or increase in density of the sediment. This is due to deposition of minerals from the rising plumes of thermal water (Combs, 1971). Rex, (1970) reported that every known geothermal field in the imperial valley, California, is associated with a measurable residual gravity anomaly varying from 2 to 22 mgal. These anomalies are believed to have originated from the combination of (i) intrusive bodies which may have been the original source of the geothermal anomaly and (ii) precipitation of minerals out of the thermal water at shallow depth (Biehler and Combs, 1972). In New Zealand geothermal areas the observed positive residual gravity anomalies are considered to be caused by rhyolitic domes and hydrothermal alteration of reservoir rocks (Thanassoulas and Lazou, 1993). On the other hand, a large gravity anomaly has been observed over the Mt. Hannah area, at the Geysers. This has been due to presence of hot silicic magma beneath this area. With the presence of geological and geophysical manifestations in Homa Hills,

16 gravity survey was useful in providing information which would be important in identifying localized subareas where geothermal related processes may have taken place. In Hungary, the gravity survey was done along the MT survey lines to assist in detecting faults system below the surface. Fault system information was used to analyze and to understand groundwater channels and water flow directions. At the same time, gravity data was used to interpret the subsurface and to aid in locating prospective heat sources (Strack et al., 2005). Homa Hills gravity survey was done to compliment the MT/TEM in order to reduce intrinsic ambiguity of either dataset and to produce a better lateral resolution in an attempt to locate the features which are often associated with localized heat source. This may be detected by gravity measurements as gravity high (Arpasi et al., 2000). A similar study was done in Cerro Prieto Geothermal field located within the San Andrews Tectonic system. This survey was done to observe differences in gravity due to changes in the well field, perhaps as a result of removal of fluid, densification of the permeable rocks and the formation of gaseous phases due to pressure reductions (Fytikas et al., 2005). Slight ground subsidence originating from extraction of fluid has been observed to be located over gravity maximum. Similar gravity maxima are located near large fault and basement structure and are associated with observed thermal anomalies (Davenport et al., 1984). The study was meant to help in getting a clear picture of the Homa Hills geothermal system during interpretation.

17 Gravity data has also been used together with resistivity data in modelling the structure and possible source of heat for the geothermal systems in Olkaria Kenya. Geologically Olkaria, located within the Rift Valley just like the Homa Hills is associated with quaternary volcanic centres (Omenda et al., 1991). Interpretation of the gravity data within the Greater Olkaria area shows that a dense body occurs at the southern part of Olkaria between the Ol Njorowa gorge and the Suswa lineament (mapped as gravity high). Such gravity highs are also expected in Homa Hills geothermal field. The Olkaria west, Olkaria East and Olkaria Northeast fields occurs within gravity lows. The gravity survey of the shallow crust beneath Olkaria indicated a volcanic zone of layers that is down-faulted in the Olkaria West area (Ndombi, 1981). Dense dike material of rhyolitic composition occurs along the Ololbutot fault separating the Western and Eastern Sectors of Greater Olkaria geothermal area. This system of dikes is thought to be a significant hydrological barrier between Olkaria West and Olkaria East and Olkaria Northeast fields. Gravity survey and magnetic survey has also been conducted in the area surrounding Lake Magadi Kenya to investigate presence of any geological bodies related to high heat flow in the area. Local gravity highs were mapped often associated with a heat source in a geothermal environment. (Githiri et al., 2005).

18 CHAPTER THREE THEORY OF GRAVITY METHOD 3.1 Introduction Gravity method is a geophysical technique that measures differences in the earth s gravitational field at specific locations. It depends on the fact that different earth materials have different bulk densities (mass) that produce variations in the measured gravitational field. These variations can then be interpreted by a variety of analytical and computer methods to determine the depth, geometry and density that causes the gravity field variations. 3.2 Principles of Gravity Method 3.2.1 Gravitational force and gravitational potential Gravity survey method is based on Newton s Law of Gravitation, which states that the force of attraction F between two masses m 1 and m 2, whose dimensions are small with respect to the distance r between them, is given by,...3.1 where G is the gravitational constant(6.67x10-11 m 3 kg -1 s -2 ). For a small mass m on the surface of a spherical, non-rotating, homogeneous Earth of mass M and radius R, the gravitational attraction it experiences is given by 3.2 The term is known as gravitational acceleration (gravity). On such an Earth, gravity would be constant (Keary and Brooks, 1991). However, the Earths oblate

19 ellipsoidal shape, rotation, irregular surface relief and internal mass distribution cause gravity to vary over its surface. The gravitational potential (V) due to the field is given as 3.3 The acceleration of any point mass towards the centre of the earth is the derivative of the potential V. The acceleration is as if the whole mass of the earth were concentrated into a point mass at the centre (Telford et al., 1976) 3.2.2 Relative measurement of the gravity In applied geophysics, the absolute gravity value is not of immediate interest. The main concern is the relative gravity measurements. It involves determining gravity difference between different locations on the earth s surface. These measurements are carried out using a gravimeter which measures small variations in the vertical component of gravity. Before the measurement is taken the gravimeter has to be leveled. That means that the line between center of mass and axis is horizontal. The corresponding scale value is read. The gravity difference is within some limits proportional to the scale value. 3.3 Gravity Reductions 3.3.1 Need for correction The observed gravity readings obtained from the gravity survey will be reflecting the gravitational field due to all masses in the earth and the effect of the earth s rotation. Several corrections have to be applied to the field gravity readings. To interpret gravity

20 data, all known gravitational effects not related to the subsurface density changes will be removed. Each reading has to be corrected for elevation, the influence of tides, latitude and, if significant local topography exists, a topographic correction. To execute the corrections, a gravity reading is first considered on the surface of a flat ground surface (geoid). Corrections are then applied to account for deviations from this condition. 3.3.2 Latitude correction Gravity varies with latitude because of the non-spherical shape of the earth, with the polar radius smaller than the equatorial radius. In addition, the angular velocity of a point on the earth s surface decreases from a maximum at the equator to zero at the poles. The centrifugal acceleration generated by this rotation has a negative radial component that consequently causes gravity to decrease from pole to equator. The Gravity Formula 1967 equation, m/s 2,.3.4 where Ф is measured in radians will be subtracted from the measured value to isolate the latitude effect. This equation may be used to derive a formula for the change in g z as one move from North to South a long a line of latitude. For a change in distance ds the approximate expression is mgal/km 3.5 It must be subtracted or added to the measured gravity difference accordingly as the station is on higher or lower latitude than the base station. The correction is linear to distances in North-South direction of order 1-2km (about 0.5-1 minute of latitude) on

21 either side of the base. If the measurement extends beyond this distance a new base station must be selected. 3.3.3 Free air correction As one moves a way from the centre of the Earth, gravity decreases. The rate of decrease can be deduced by assuming spherical earth,..... 3.6 Therefore.. 3.7 The change in gravity due to elevation change is ( g in mgal and h in m). If the site is above the reference point, Free Air correction is added to the observed gravity value. If the site is below the reference point, Free Air correction is subtracted from the observed gravity value (Mariita, 2007). Thus the Free Air Gravity Anomaly can be obtained by,. 3.8 3.3.4 Bouguer correction This correction takes care of attraction of a slab of rock present between the observation point and the datum (geoid) which is measured by the gravimeter. It removes the effect by approximating the rock layer beneath the observation point to be infinite horizontal

22 slab with thickness equal to the elevation of the observation point above the datum. To the first order, the difference in gravity between two points A and B can be approximated by an infinite slab of uniform density and thickness between the two points. The gravitational attraction of this layer is g, where h is the thickness and ρ is the density of the material. The Bouger correction (C B ) is obtained by C B =0.1119 hmgal (ρ=2670kg/m 3 ). This value must be subtracted (Mariita, 2007). 3.3.5 Terrain correction Consider three points as in the Figure 3.1 below. S 2 S S 1 Figure 3.1: Terrain consisting of both valley and a hill. Gravity at S 1 is lower than at S because the adjacent hill to S 1 exerts an attraction upwards whose net effect is to reduce gravity. Similarly, gravity at S 2 is less than at S because the valley has removed an attracting mass from below the level of S 2. Therefore a hill or a valley at vicinity of a station reduces gravity. Therefore a factor has to be added to compensate the reduction in gravity due to terrain. Terrain corrections are performed with the help of computers. The procedure is as follows,-(i) Start with a good topographic map (contour interval less than 10m) a round the station and extend beyond

23 the survey area. (ii) With the station as the centre, concentric compartment are placed on the topo map. (iii) For each compartment, estimate the average elevation n with respect to the elevation of the station. The terrain gravity due to this compartment with bounding radius r 1 and r 2 and angle Ф is. 3.9 Note that n appears as a square, this is because, the corrections for extra mass deficit bellow the station having the same sign. Also the correction is small if. (iv) Sum up the contributions from all compartments to give the total Terrain correction (Hammer, 1939). No provision for relief within 2m from the station as any 1m relief can be large ( 0.04mgal) correction. In areas of steep and erratic slopes, terrain corrections are usually not very accurate. So it is better to have the gravity stations located away from sharp relief. 3.3.6 Tidal correction Due to the periodic variation of the gravitational effects of the sun and moon associated with their orbital motions, the gravity measured at a fixed location varies with time. The gravitational effect of the moon (larger than the sun) causes the shape of the solid earth to vary with time. Hence the resulting bulges in the surface have diurnal periodicity which is predictable to first order at any point on the earth. The tidal variations can be on the order of ±0.1mgal and so to use the full sensitivity of the gravimeter these variations must be removed. In some small scale surveys it may be reasonable to assume that the tidal variations are linear with time during the intervals between the times that a base or

24 reference station is reoccupied. In this case the tidal variations are included and treated in the same manner as the slow drift in gravimeter readings caused by inherent strain in the sensing element. 3.3.7 Instrumental drift correction The value of the gravity meter reading at a fixed position also varies as a result of small changes in the physical constants of the gravimeter components. This effect is referred to as the instrumental drift effect. Ideally, we would want to take gravity measurements at all the sites in the survey area at the same time. But since only one gravimeter was used, this was not possible, so there is need to correct for instrumental drift. This is done by, (i) establishing a base station. (ii) Visiting the base station several times during the survey and make a gravity measurement. Variations in the observed gravity tell you how the values are changing due to instrumental drift. (iii) Assuming a linear variation between consecutive base station measurements. (iv) Applying the observed variation to the observed gravity at other stations to get the value of gravity that would have been recorded at each station if all measurements were taken at the same time. Time at which the measurements are taken must be recorded.

25 CHAPTER FOUR MATERIALS AND METHODS 4.1 Introduction Gravity survey just like any other geophysical survey, involves the use of measuring instruments for parameters under investigation. This includes the relative gravity measurements and position co-ordinates of the measurement point. In this survey relative gravity measurements are taken using Worden gravity meter model Prospector 410 while the position co-ordinates were measured using a hand held GPS model Garmin 45. Absolute base station was identified at Kisumu Railway station with known absolute value of gravity, the relative gravity value at this station was obtained at the beginning of this survey. The reading at the absolute base station was later used to obtain absolute gravity values at other stations in the study area. While in the field, other base stations were established and periodically engaged during each day for the instrumental drift correction. 4.2 Instrumentation 4.2.1 Sodin gravity meter Gravity survey is made possible by the use of accurate and portable gravimeter which is based on spring balance-principles. These torsion balance gravimeters however suffer from all the disadvantages associated with mechanical systems. Sensitivity is enhanced by the use of multiple-spring ecstatic system which is more vulnerable than single springs to breakage or simple tangling. Gravity meters also require calibration and even then measure only differences in gravity field between two points rather than absolute field

26 values. Survey must therefore be based on networks of readings ultimately linking back to one or more points of known (or arbitrary assigned) absolute gravity. In calculating field differences, allowance have to be made not only for the instrumental drift but also for background variations (known as tidal effects) caused by the changing positions of the sun and the moon which is usually small (generally less than 1g.u.). The Worden gravimeter is in essence a very sensitive balance which pivots a small mass on a tortion fibre against the torque provided by stretching a calibrated quartz spring. The meter reads changes in gravity, with an impressive sensitivity of about 0.01mgal. It is temperature compensating. Greater care must be taken in handling, operating and transporting the gravity meter. At all times the meter has to be carried upright and during transport securely placed in an upright position. Tilting the gravimeter more than 30 degrees off the vertical position, will expose the quartz system to severe stresses, which may cause loss of accuracy and permanent damage to the meter. 4.2.2 Global positioning system (GPS) This is a space-based global navigation satellite system (GNSS) that provides reliable location and time information. It is maintained by the United States government and is accessible by anyone with a GPS receiver. GPS consists of three major segments; these are space segment, a control segment and a user segment. Space segment is composed of the orbiting GPS satellite. Control segment is composed of (i) a master control station. (ii) an alternate master control station. (iii) four dedicated ground antennas and (iv) six dedicated monitor stations. User segment is composed of an antenna, turned to the

27 frequencies transmitted by the satellites, receiver processors, and a highly stable clock (often a crystal oscillator). They may also include a display for providing location and speed information to the user. A receiver is often described by its number of channels; this signifies how many satellites it can monitor simultaneously. GPS uses principles of general relativity to correct the satellite atomic clocks. A GPS receiver calculates its position by precisely timing the signals sent by GPS satellites high above the earth. Each satellite continually transmits messages that include: - the time the message was transmitted, precise orbital information and general system health and rough orbits of all GPS satellites. The receiver uses the messages it receives to determine the transit time of each message and computes the distance to each satellite. These distances along with the satellite locations are used with the possible aid of trilateration, depending on the algorithm is used, to compute the position of the receiver. This position is then displayed, perhaps with a moving map display or latitude and longitude: elevation information may be included. Many GPS units show derived information such as direction and speed, calculated from position changes. A GPS receiver must be locked on to the signal of at least three satellites to calculate a 2D position (Latitude and Longitude) and track movement. With four or more satellites in view, the receiver can determine the user s 3D position (Latitude, Longitude and Altitude). Once the user s position has been determined, the GPS unit can calculate other information, such as speed, bearing, track, trip distance, distance to destination, sunrise

28 and sunset time and more. Sources of GPS signal errors are (i) Ionosphere and troposphere delays-the satellite signals delays as it passes through the atmosphere. The GPS system uses a built in model to correct the delay. (ii) Signal multipath-this occurs when the GPS signal is reflected off objects such as tall buildings. This increases the travel time of the signal. (iii) Receiver clock errors-a receivers built in clock is not as accurate as the atomic clocks onboard the GPS satellites. (iv) The Number of satellites visible-the more satellites a GPS receiver can see the better the accuracy. (v) Orbital errors-this is as a result of inaccuracy of the satellites reported location. (vi) Satellite geometry/shading. 4.3 Gravity Measurements 4.3.1 Station layout The gravity data was collected in the month of April 2011 from 87 gravity stations established over an area of 78km 2 in Homa Hills geothermal prospect at a spacing of 500m. These stations were located along 16 profiles at about 500m spacing arranged in a grid system. Due to inaccessibility of some parts of the study area, especially on the western side which is occupied by the hills, the profiles were discontinued and therefore not strictly followed. A short station separation distance was preferred to minimize the chances of missing the body under investigation which could be of a relatively short wavelength. The positioning of stations was measured using a GPS while the gravity measurements were conducted using a Worden gravimeter as mentioned earlier. Figure 4.1 shows the distribution of gravity stations with Easting and Northing in metres.

29 9962000 9961000 9960000 9959000 NORTHING 9958000 9957000 9956000 9955000 9954000 664000 665000 666000 667000 668000 669000 670000 671000 672000 EASTING Figure 4.1: Gravity Station positions in Homa Hills during data collection using GPS.

30 4.3.2 Sources of error in gravity survey Apart from the ambiguity in the interpretation of the gravity data, the survey procedure is still subject to a number of uncertainties ranging from the GPS signal errors mentioned under 3.4 to operational errors. The operational sources of error include the fluctuation in the reading in a GPS as a result of the change in the height at which the GPS is held during the survey. This height also adds up to the altitude. The depth to which the gravimeter stand sinks into the ground could also be a source of error; it is not always possible to maintain this depth since it depends on the nature of the ground where the reading is to be taken. In this study, based on the expected wavelength of the anomaly under investigation these errors are of minimal effect unlike in microgravity survey in which these slight errors might seriously affect the result and differential GPS is therefore highly recommended. To further minimize the error due to position of the GPS in this study, the GPS was held close to the ground to reduce the lateral displacement in altitude. 4.3.3 Instrumental drift To monitor the instrumental drift and to allow the absolute value of gravity to be determined at each observation point, readings were taken at a base station before, during and after the survey. The measurement drifts of the gravimeter were therefore linearly extrapolated (with respect to time) from the differences of readings made at the same base station. The dial reading was first taken at an IGSN station in Kisumu Railway station where the absolute value of gravity is 977607.97mgal (Khan and Swain, 1977).

31 The dial reading of the gravimeter was recorded as 268.40g.u. This information was used to calculate the absolute value of gravity at different stations. 4.4 Gravity Data Reduction and Processing 4.4.1 Introduction Before the data obtained from gravity survey is interpreted it is necessary to correct for all variations in the earths gravitational field which do not result from the differences of density in the underlying rocks. Microsoft excel was used to make a spreadsheet of the gravity data and correct for instrumental drift, latitude, elevation and terrain (Appendix 1). 4.4.2 Data reduction 4.4.2.1 Drift correction It was done by having a base station which was preoccupied periodically in the day. For example during day four of the data collection the base station readings were as in table 4.1 below Table 4.1: Base station readings on 15th April 2011 Time Dial reading 9.14am 286.00 11.45am 290.75 1.36pm 292.65 4.18pm 290.95

GAVIMETER READINGR 32 A drift curve was then plotted as in figure 4.2 below and readings made in other stations assumed to have a linear drift as fitted base readings. Using the drift rate each reading is corrected to what it would have read if there were no drift. B 293 292 291 290 289 288 287 286 285 9.14am 11.45am 1.36pm 4.18pm TIME Figure 4.2: Drift curve on 15 th April 2011 The dial reading at station 44 which was taken at 11.00am was found to be 123.10 (Appendix 1). 4.1 The drift free dial reading data is then converted to gal units (g.u) by multiplying it with the conversion factor of the gravimeter which was 1.0008 for this study. The reading is

33 further converted to milligals (1mgal=10g.u). The absolute value of gravity is then calculated with the help of the International Gravity Station (IGSN) details. For this study, Kisumu railway station with absolute gravity value of 977607.67mgal (Khan and Swain, 1977) and relative gravimeter reading of 268.40g.u was used. For example, at station 1, after correcting for both instrumental and tidal drifts, the dial reading is 504.62g.u. The difference in the relative gravity between station 1 and the railway station is: This means that the gravity at station 1 is 23.622mgal larger than that of Kisumu railway station. Since the absolute gravity at the railway station is known, the absolute gravity at station 1 is: This process was applied to all other stations in order to obtain absolute gravity (Appendix 1). Other drift curves are shown in Appendix 3. 4.4.2.2 Latitude correction The expected (Theoretical) value of gravity at given latitude is calculated with respect to Gravity Formula 1967..4.2 Where Ф is measured in radians will be subtracted from the measured value to isolate the latitude effect.

34 This correction was done for all the stations as shown in Appendix 1. 4.4.2.3 Free air correction This is to correct for decrease in gravity with height above the sea level. For example, station 20 which at an altitude of 1208m. in metres 4.4 The free air correction for each station is added to the absolute gravity at that station (Appendix 1).....4.5 4.4.2.4 Bouguer correction This is done to correct for the attraction of a slab of rock present between the observation point and the datum.. 4.6 Where ρ is the average crustal density and h is the height above the datum. For example, station 10 which is at an altitude of 1146m, This factor is subtracted from the free air anomaly for each station; the results are shown in appendix 1.

35 4.4.2.5 Terrain correction With the station as the centre, concentric compartments were overlaid on a topographic sheet, for each compartment the average elevation was computed (Hammer, 1938) and the gravity contribution obtained by the use of a computer programme. These contributions are summed for all the zones from zone E to zone K for this particular study (Appendix 1). Once the terrain and Bouger slab corrections are made, the anomaly is called complete Bouger anomaly. 4.5 Data Processing 4.5.1 Bouguer anomaly map Once the complete Bouguer anomaly gravity values are obtained, a Bouguer anomaly contour map was drawn as in figure 4.3 below by the use of sufer8 Golden software. The map was drawn based on a contour interval of one milligal, Easting and Northing are in metres. In homogeneity in density is quite evident in the nature of the distribution of gravity contour lines.

36 Figure 4.3: Complete Bouger contour map of Homa Hills drawn using Surfer8 Golden Software.

37 Figure 4.4: 3D map of the Complete Bouguer gravity anomaly drawn using Surfer8 Golden software. The perturbation of the gravity field by the subsurface density variations can further be illustrated by the use of 3D map as in figure 4.4 above. The amplitude of perturbation increases with the increase in density of the subsurface materials.