INVESTIGATING THE OPTIMAL INTEGRATION OF AIRBORNE, SHIP-BORNE, SATELLITE AND TERRESTRIAL GRAVITY DATA FOR USE IN GEOID DETERMINATION BY Rachelle Lee Winefield A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science Geophysics School of Geography, Environmental and Earth Science Victoria University of Wellington 2016 “Gravity is a habit that is hard to shake off.” - Terry Pratchett Abstract Each gravity observation technique has different parameters and contributes to different pieces of the gravity spectrum. This means that no one gravity dataset is able to model the Earth’s gravity field completely and the best gravity map is one derived from many sources. Therefore, one of the challenges in gravity field modelling is combining multiple types of heterogeneous gravity datasets. The aim of this study is to determine the optimal method to produce a single gravity map of the Canterbury case study area, for the purposes of use in geoid modelling. This objective is realised through the identification and application of a four-step integration process: purpose, data, combination and assessment. This includes the evaluation of three integration methods: natural neighbour, ordinary kriging and least squares collocation. As geoid modelling requires the combination of gravity datasets collected at various altitudes, it is beneficial to be able to combine the dataset using an integration method which operates in a three- dimensional space. Of the three integration methods assessed, least squares collocation is the only integration method which is able to perform this type of reduction. The resulting product is a Bouguer anomaly map of the Canterbury case study area, which combines satellite altimetry, terrestrial, ship-borne, airborne, and satellite gravimetry using least squares collocation. Preface Page i Acknowledgements I would like to extend my gratitude to my supervisor Prof Euan Smith. I have been amazingly fortunate to have a supervisor with such a positive outlook and the ability to keep things in perspective. I am deeply appreciative for the long discussions that helped me better understand the peculiarities of New Zealand’s gravitational landscape. I am grateful to my co-supervisor, Dr Matt Amos for this support and encouragement. His insightful comments and constructive criticisms at different stages of my research were thought-provoking and continually extended my thinking. I am indebted to my student colleague Jack McCubbine for his support and Matlab training. I am extremely thankful for the support of my employer, Land Information New Zealand, who provided me the opportunity to undertake this research. I would like to acknowledge the National Geodetic Office and the wider Location Information teams for their ongoing encouragement throughout my studies. Finally, I must express my very profound gratitude to my parents for providing me with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis. Thank you. Preface Page ii Table of Contents Abstract .................................................................................................................................................... i Acknowledgements ................................................................................................................................. ii List of Figures ......................................................................................................................................... vi List of Tables .......................................................................................................................................... ix List of Abbreviations ............................................................................................................................... x List of Symbols ...................................................................................................................................... xii 1. INTRODUCTION ............................................................................................................................... 1 1.1. Background ............................................................................................................................. 1 1.2. Motivation ............................................................................................................................... 1 1.3. Significance of Study ............................................................................................................... 3 1.4. Objectives of Study ................................................................................................................. 4 1.5. Outline of Thesis ..................................................................................................................... 4 2. GRAVITY .......................................................................................................................................... 5 2.1. Introduction ............................................................................................................................ 5 2.2. Gravity Instruments ................................................................................................................ 6 2.2.1. Absolute Gravity Meters ................................................................................................. 6 2.2.2. Relative Gravity Meters .................................................................................................. 8 2.2.3. Dynamic Gravity Meters ............................................................................................... 10 2.2.4. Satellite Gravimetry ...................................................................................................... 11 2.3. Data Collection Methods ...................................................................................................... 13 2.3.1. Terrestrial Gravimetry ................................................................................................... 13 2.3.2. Ship-borne Gravimetry .................................................................................................. 15 2.3.3. Airborne Gravimetry ..................................................................................................... 17 2.3.4. Satellite Altimetry ......................................................................................................... 19 2.3.5. Global Geopotential Models ......................................................................................... 21 2.4. Gravity Anomalies and Reductions ....................................................................................... 23 2.4.1. Relative Gravity Observations ....................................................................................... 24 2.4.2. Normal Gravity Model .................................................................................................. 24 2.4.3. Free-Air Model .............................................................................................................. 25 2.4.4. Bouguer Slab Model ...................................................................................................... 25 2.4.5. Terrain Models .............................................................................................................. 27 2.4.6. Complete Bouguer Model ............................................................................................. 32 2.5. Combination Considerations................................................................................................. 33 Preface Page iii 2.5.1. Combination Data Type ................................................................................................ 33 2.5.2. Downward Continuation ............................................................................................... 35 2.6. Summary ............................................................................................................................... 40 3. INTEGRATION ................................................................................................................................ 41 3.1. Introduction .......................................................................................................................... 41 3.2. Step One: Purpose ................................................................................................................ 41 3.3. Step Two: Data ...................................................................................................................... 42 3.4. Step Three: Combination ...................................................................................................... 43 3.4.1. Simple Gridding ............................................................................................................. 43 3.4.2. Kriging ........................................................................................................................... 48 3.4.3. Least Squares ................................................................................................................ 50 3.5. Step Four: Assessment .......................................................................................................... 52 3.6. Summary ............................................................................................................................... 53 4. CASE STUDY: Canterbury,