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Airborne Gravimetry for Geoid Determination

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Airborne Gravimetry for Geoid Determination University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies Legacy Theses 2000 Airborne gravimetry for geoid determination Li, Ye Cai Li, Y. C. (2000). Airborne gravimetry for geoid determination (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/10791 http://hdl.handle.net/1880/40021 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca THE UNlVERSITY OF CALGARY Airborne Gravimetry for Geoid Determination by Yecai Li A DISSERTATION SUBMITTED TO TJd5 FACULTY OF GRADUATE STUDIES IN PARTIAL, FULFILLMENT OF THE REQUIREA4ENTS FOR DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA JULY, 2000 0 Yecai Li 2000 National Library Bibliotheque nationale m*l of Canada du Canada Acquisitions and Acquisitions et Bibliographic Services services bibliographiques 395 Wellington Street 395, rue Wellington Ottawa ON K1A ON4 Ottawa ON K1 A ON4 Canada Canada Your fiIn Vorre reference Our M Notre refdnmce The author has granted a non- L'auteur a accorde une licence non exclusive licence allowing the exclusive pennettant a la National Librq of Canada to Bibliotheque nationale du Canada de reproduce, loan, distribute or sell reproduire, przter, distribuer ou copies of this thesis in microform, vendre des copies de cette these sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format electronique. The author retains ownership of the L'auteur conserve la propried du copyright in this thesis. Neither the droit d'auteur qui protege cette these. thesis nor substantial extracts &om it Ni la these ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent Stre imprimes reproduced without the author's ou autrement reproduits sans son permission. autorisation. Abstract In this dissertation, the potential contribution of an airborne gravity system consisting of a strapdown inertial navigation system and differential global positioning system is investigated. Specifically, its contribution to geoid determination in terms of wavelength resolution and achievable accuracy is studied fiom a numerical and operational point of view. Gravity values in various areas with typical topographic features were used for the spectral analysis of the requirements of geoid determination on gravity data. Results indicate that a cm-geoid can be achieved if the minimum wavelength resolved on the ground is about 14 Ian in flat areas and 5 km in mountainous areas. The achievable accuracy and resolution of airborne gravimetry in geoid determination is studied through an assessment of MSand GPS errors in the spectral range of interest. The results show that the total GPSKNS induced geoid error is less than 1 cm for wavelengths between 5 lan and 100 km and less than 10 cm for wavelengths between 5 krn and 500 km. To verify these results, an airborne test was flown over a very rugged area. Airborne gravity disturbances were collected above a 100 km x 100 krn area and were downward continued to the ground level. The downward continued gravity disturbances agree with ground gravity data at the level of 3.8 mGal (la)and 2.5 rnGa.1 (la) for a wavelength resolution of 10 km and 20 km,respectively. In the test area, the local airborne geoid agrees with the reference solution at the level of 1-2 cm (1 o).The regional geoid computed fiom the downward continued gravity disturbances and 30' x 30' mean gravity anomalies in the outer area agrees with the reference geoid computed fiom ground gravity data on a 5' x 5' grid at the 5 cm level (1 c). The same level of agreement exists between the reference geoid and a GPSAevelling- derived geoid when fitting out the systematic trend. Thus, airborne gravimetry is capable of geoid determination at the 2 cm level for wavelengths between 10 krn and 100 km and at the 5 cm level for wavelengths above 10 km when the systematic trend is removed. Acknowledgments I wish to express my deepest gratitude to my supervisor, Dr. Klaus-Peter Schwarz, for his help, support and guidance throughout the course of my Ph.D. program. His encouragement was essential for the completion of this dissertation. Many thanks also go to Dr. Michael Sideris and Dr. Michael Chapman for their help and suggestions on various aspects. Dr. Doug Phillips at IT of the university is appreciated for help running the downward continuation program under the MACI-based DEC Alpha workstation. I want to extend my appreciation to Professor Zelin Guan (Oct. 30, 193 1 -- Nov. 10, 1999) for his teaching of my frrst course in physical geodesy, supervision of my f~stM. Sc. program, and the continuous encouragement and friendship during the eight years I worked with him at Wuhan Technical University of Surveying and Mapping, China. Special thanks go to my fellow student Mr. Gengsheng Zhang for the discussions we have had on inertial navigation systems, Mr. Alex Bruton for his help and friendship, and Dr. Craig Glemie for providing the processed airborne gravity data. Financial support for this research partly came fiom research grants of the supervisor, and partly fiom the Graduate Research Scholarship of the University of Calgary (1994, 1995, 1996, 1997), Province of Alberta Graduate Fellowship (1995, 1997): Ralph Steinhauer Awards of Distinction (1 996), Izaak Walton Killam Memorial Scholarships (1996), and Helmut Moritz Graduate Scholarship (I996). Research on Chapter 4 was initially sponsored by a contract between Sander Geophysics Ltd and the University of Calgary. This is sincerely appreciated. Finally, I would like to appreciate my wife Sheny Jin for her understanding and support, and our children Richard and Jessica for missing their father on numerous weekends and evenings. Table of Contents .. Approval Page .................................................................................................................. ...11 Abstract ........................................................................................................................... 111 Acknowledgments ...................... .... .......................................................................... iv Table of Contents ........................................................................................................... v List of Tables .................................................................................................................. vii... List of Figures ......................... .. ................................................................................. vrli Notation ................... .., .... ................................................................................................. xi Chapter 1 Introduction ................................................................................................... 1 1.1 Background ........................................................................................................... 1 1-2 Airborne Gravity Measurements ............................................................................ 3 1.3 Dissertation Outline ............................................................................................. 8 Chapter 2 Requirements for Geoid Determination ...... .. ........... .. ......*................... 11 2-1 Geoid Determination with the Stokes Integral ........................................................ 11 2.1.1 The Stokes integral ................. ,. ...... ........................................................ 11 2.1.2 Modification of the Stokes kernel function .................................................... 16 2.2 Geoid Deterrnination with the Hotine Integral ................................... .... 20 2.2.1 The Hotine integral .................................................................................... 20 2.2.2 Modification of the Hotine kernel function ................................................... 23 2.3 Height Anomaly Determination with the Mo lodensky Integral Series .................... 24 2.3.1 The Molodensky integral series ................................................................. 24 2-3-2 Relation between the Molodensky and the Stokes solution ................... ..... 26 2.4 Requirements for Wavelength Resolution .............................................................. 27 2.5 Requirement for an Optimal Integral Radius .......................................................... 32 2.6 Summary of Results ................................................................................................ 35 Chapter 3 Airborne Gravity Systems and Their Potential Contribution .................... 36 3.1 System Principle .................................................................................................... 36 3 -2 Effect of INS Errors on Airborne Gravirnetry ........................................................ 43 3 -3 Effect of GPS Errors on Airborne Gravirnetry ...................................................... 49 3 -4Effect of Combined INS/GPS Errors on Airborne Gravimetry ....................... ........ 55 3 -5 Effect of Other Critical Factors on Airborne Gravimetry ........................................ 56 3 -6Possible Geoid Resolution
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