Masters thesis of geospatial sciences development of a precise gravimetric geoid model for argentina

Development of a Precise Gravimetric Geoid Model for Argentina A thesis submitted in fulfilment of the requirements for the degree of Master of Science in Geospatial Sciences Diego Alejandro Pinon B Surv Eng School of Mathematical and Geospatial Sciences College of Science Engineering and Health RMIT University March 2016 Declaration I certify that except where due acknowledgement has been made, the work is that of the author alone; the work has not been submitted previously, in whole or in part, to qualify for any other academic award; the content of the thesis is the result of work which has been carried out since the official commencement date of the approved research program; any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics procedures and guidelines have been followed Diego Alejandro Pinon March 2016 ABSTRACT The main aims of physical geodesy are to study the shape of the Earth, its gravity field and the geoid which is an equipotential surface closest to the mean sea level Precise geoid determination has been an important research topic in geodesy and geophysics in the past two decades Scientists and government agencies all around the world have made great efforts on the development of highaccuracy geoid models These geoid models are developed not only for scientific applications, but also for other purposes such as serving for a reference surface for mapping, sea level monitoring and natural resources exploitation and management A geoid model is required to define a national height or vertical datum Precise geoid models have experienced an unprecedented demand due to the rapid development of GPS/GNSS technologies Geoid models allow transforming ellipsoidal heights, which are relatively easily determined from GPS/GNSS observations, into physical heights, which are associated to the Earth’s gravity field, without the need for expensive and time-consuming spirit-levelling Physical heights are used for mapping, engineering and civil engineering infrastructure since they indicate the flow direction of fluids, due to the fact that fluids are attracted by the gravity of the Earth rather than geometric height differences Moreover, vertical datums have been historically based on a local mean sea level surface determined by averaging tide gauge readings over a certain period of time However, due to the sea surface topography effect, which is mainly caused by the sea dynamics and other meteorological processes, observations from different tide gauges not commonly coincide Therefore, when vertical datums are separated by oceans or other bodies of water, direct methods such as spirit levelling and gravity measurements are not applicable In this case, geoid models can be used for unifying two or more vertical datums together This research aims to develop a new and optimal precise geoid for Argentina using all available measurements from the most state of the art technologies and the latest global geopotential models (GGMs), along with detailed digital terrain models (DTMs) The remove-compute-restore technique and the combination of an optimal GGM with 658,111 land and marine gravity observations were used for the new model determination Several GGMs (e.g EGM2008, GOCO05S and EIGEN-6C4) were evaluated to investigate the best GGM that fits Argentinian regional gravity field Terrain corrections were calculated using a combination of the SRTM_v4.1 and SRTM30_Plus v10 DTMs for Page i Abstract all gravity observations For the regions that lacked gravity observations, the DTU13 world gravity model was utilised for filling-in the gravity voids The residual gravity anomalies were gridded by the Kriging method and the resultant grid was applied in the Stokes’ integral using the spherical multiband FFT approach and the deterministic kernel modification proposed by Wong and Gore in 1969 The accuracy of the new geoid was assessed by comparing its geoidal undulations over 1,904 benchmarks, which have both orthometric and ellipsoidal heights Results showed that an accuracy of better than 10 centimetres has been achieved Abstract Page ii ACKNOWLEDGEMENTS This acknowledgement list should be quite long It is probably more convenient to divide it into three: those who are experts in Geodesy or Geophysics, those who learned something about my research throughout my Masters and those who not have a clue about what I have accomplished during these last two and a half years From the first group, I would like to thank my supervisors, Prof Kefei Zhang and Dr Suqin Wu, for their continuous support, encouragement, motivation and direction I would like to express my profound gratitude to Sergio Cimbaro, President of the Instituto Geográfico Nacional (IGN), who not only provided most of the datasets (or helped me to obtain them) and bent over backwards to assist me with all of my requests, but has been a constant source of support and motivation over many years I seriously enjoyed sharing all my research questions, concerns and outcomes with the IGN staff (in particular with Demián, Ezequiel, Hernán, Gonzalo, Agustín, Tomás and Juan Carlos) I grew through my conversations with them all Finally, I would like to acknowledge Prof C.C Tscherning (R.I.P 1942 – 2014) for providing the GRAVSOFT software, his patience towards my silly questions and his selfless assistance Regarding those who now understand the basics of the geoid model, I would like to thank my beloved Hayley for all her support during this quest She probably learned about Geodesy as much as I did, or even more From the last group of people who never understood what I was doing in my Masters, I want to acknowledge all my Argentinean friends, for helping me to remember that there is another life beyond Geodesy, and my new Aussie friends, for providing me a rest after a long research day Finally, I would like to thank my Australian family, for encouraging me and being positive always, and my parents, Luis and Carolina, for being my raw model of effort, persistence and integrity Page iii Acknowledgements TABLE OF CONTENTS Abstract i Acknowledgements iii Table of Contents iv List of Figures viii List of Tables xiii List of Abbreviations xv Introduction 1.1 Background 1.2 History of the Argentinean Geoid 1.2.1 Argentinean Geoid 1998 1.2.2 Argentinean Geoid 2005 (ARG05) 1.2.3 Argentinean Geoid 2006 (GAR) 1.3 Aim and Objectives 1.4 Significance 1.5 Structure of the Thesis 10 Gravity Field, Vertical Datum and Height System 12 2.1 Gravity Field of the Earth 12 2.1.1 Gravitational Potential 12 2.1.2 Centrifugal Potential 15 2.1.3 Gravity Potential 16 2.1.4 Potential Expressed in Terms of Spherical Harmonics 16 2.1.5 Normal Potential 17 2.1.6 Gravity 18 2.1.7 Normal Gravity 19 2.2 Height System 19 2.2.1 Ellipsoidal Height 20 2.2.2 Levelling Height 23 2.2.3 Geopotential Number 25 2.2.4 Orthometric Height 27 2.2.5 Normal Height 30 2.3 Vertical Datum 31 Table of Contents Page iv 2.3.1 Local Vertical Datum (LVD) 33 2.3.2 Global Vertical Datum (GVD) 34 2.3.3 Earth Tides 36 2.4 Argentinean Vertical Datum, Height System and Gravity System 39 2.4.1 History of the Argentinean Vertical Datum and Height System 39 2.4.2 History of the Argentinean Gravity System 42 2.5 Summary 48 Geoid Determination 49 3.1 Theory of Geoid Determination 49 3.1.1 Disturbing Potential 49 3.1.2 Geodetic Boundary Value Problem (GBVP) 50 3.1.3 Computation of Gravity Anomalies Outside the Earth 52 3.1.4 Stokes’ Formula 53 3.2 Global Geopotential Models (GGMs) 55 3.2.1 Earth Gravitational Model 2008 (EGM2008) 57 3.2.2 European Improved Gravity Model of the Earth by New Techniques (EIGEN-6C4) 58 3.2.3 GO_CONS_GCF_2_DIR_R5 59 3.2.4 Gravity Observation Combination (GOCO05S) 59 3.3 Terrain Reduction 60 3.3.1 Terrain Correction 61 3.3.2 Isostatic Reduction 62 3.3.3 Helmert’s Second Condensation Method 63 3.3.4 Residual Terrain Model (RTM) 65 3.3.5 Hammer Chart 66 3.3.6 Rectangular Prism Integration 67 3.3.7 Terrain Correction by Fast Fourier Transformation (FFT) 68 3.4 Digital Terrain Models (DTMs) 69 3.4.1 SRTM v4.1 70 3.4.2 SRTM30_Plus v10 71 3.5 Remove-Compute-Restore (RCR) Technique 72 3.5.1 Stokes’ Integral by FFT 73 3.5.2 Modification to Stokes’ Kernel 75 3.6 Summary 76 Data Preparation and Pre-processing 78 Page v Table of Contents 4.1 Introduction 78 4.2 Compilation of a DTM 79 4.3 Terrain Gravity Data and Gravity Reductions 80 4.3.1 Normal Gravity 83 4.3.2 Atmospheric Correction 84 4.3.3 Free-Air Correction 85 4.3.4 Refined Bouguer Correction 85 4.3.5 Free-Air Anomaly 86 4.3.6 Refined Bouguer Anomaly 87 4.4 Marine Gravity Data and Gravity Reductions 87 4.4.1 Free-Air Anomaly 88 4.4.2 Refined Bouguer Anomaly 89 4.4.3 Eötvös Correction 90 4.5 Validation of Gravity Anomalies 91 4.5.1 GGM Method 91 4.5.2 Satellite Altimetry Method 92 4.5.3 Least Square Collocation (LSC) Method 94 4.6 GPS-levelling data 96 4.7 Selection of an Optimal GGM 99 4.8 Gridding the Argentinean Gravity Field 104 4.8.1 Gridding Methods 104 4.8.2 World Gravimetric Grids 112 4.8.3 Residual Anomaly Grid 116 4.8.4 Computation Scheme for Residual Anomaly Grid 121 4.9 Summary 122 Numerical Results 123 5.1 Introduction 123 5.2 Geoid Determination 123 5.2.1 Stokes’ Integral 123 5.2.2 Contribution of the GGM 125 5.2.3 Indirect Topographic Effect 126 5.2.4 Geoid Model Determination 127 5.3 Geoid Fitting 129 5.4 Modelling Procedure Scheme 135 Table of Contents Page vi 5.5 Validation of the New Geoid Model 135 5.6 Improvement Made by the New Geoid Model 137 5.7 Summary 139 Conclusions and Recommendations 141 6.1 Summary 141 6.2 Conclusions and Major Findings 141 6.3 Recommendations 144 References 146 Page vii Table of Contents D'Onofrio, E, Fiore, M, Mayer, F, Perdomo, R & Ramos, R 1999, 'La referencia vertical', Contribuciones a la Geodesia en la Argentina de fines del siglo XX Universidad Nacional de Rosario, pp 99-127 De Witte, L 1967, 'Truncation errors in the Stokes and Vening Meinesz formulae for 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1, pp 81-91 Zhang, K 1997, 'An evaluation of FFT geoid determination techniques and their application to height determination using GPS in Australia', Curtin University of Technology References Page 162 Zhang, K 1998, Altimetric gravity anomalies, their assessment and combination with local gravity field, 98(4), Finnish Geodetic Institute Zhang, K 1999, 'On the determination of a new Australian geoid', Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, vol 24, no 1, pp 61-6 Zhang, K & Featherstone, W 1995, 'The statistical fit of high degree geopotential models to the gravity field of Australia', Geomatics Research Australasia, pp 1-18 Page 163 References ... undulations values from USA, Canada, Europe, Australia, Japan and Brazil (International Centre for Global Earth Models 2015) 103 Table 4.8: Number of gravity anomalies used for evaluating... a new precise and high resolution geoid model that agrees with the national vertical datum, and that the national mapping, geological and cadastres agencies can adopt as the new vertical reference... will be adopted as the official Argentinean geoid model A large number of public agencies, universities and private companies are eager to access to an official precise high resolution geoid model