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This dissertation has been microfilmed exactly as received 69- 22,089 BADEKAS, John, 1929- ESTABLISHMENT OF AN IDEAL WORLD GEODETIC SYSTEM. The Ohio State University, Ph.D., 1969 Geophysics University Microfilms, Inc., Ann Arbor, Michigan ESTABLISHMENT OF AN IDEAL WORLD GEODETIC SYSTEM DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By John Badekas, Top. -Ing., M. Sc. * * * * * The Ohio State University 1969 Approved by ^ U C L u . / /jjjU d M x ^ A dviser Department of Geodetic Science PLEASE NOTE: Not original copy. Several pages have indistinct print. Filmed as received. UNIVERSITY MICROFILMS To Helen, Dias, Paris, and Ion ( ACKNOWLEDGEMENTS The w riter wishes to express his gratitude and his appreciation to his advisor, Professor Ivan I. Mueller, for his guidance and assistance during the writing of this dissertation. Special thanks go to Professor Richard II. Rapp who made available to the author a computer program for the determination of spherical harmonics from gravity anomalies, as well as various valuable materials from his investigations, some of them prior to their publication. He also helped to clarify several sections with fruitful discussions and as a member of the author's reading committee. Many thanks go to the faculty of the Department of Geodetic Science and especially to the chairman, Professor Urho A. Uotila, who, with consulta­ tions and as a member of the reading committee, contributed several valuable suggestions to this dissertation. Financial support for a Research Associateship, computer programming, and administrative help was received from the U. S. Army Topographic Laboratories and is greatly appreciated. Various aspects connected with this dissertation have been discussed with George Veis of the Smithsonian Astrophysical Observatory Charles A. Whitten of Environmental Science Services Administration Allan J. Pope of Environmental Science Services Administration Richard J. Anderle of the U. S. Naval Weapons Laboratory whose suggestions were found to be very valuable. The work of Lonie Berkebile who gave programming assistance and Charles R. Schwarz who did a thorough editing deserve many thanks. Finally the writer wishes to express his deep appreciation for her considerable help to Mrs. Rene Tesfai for her constructive typing. it VITA April 1, 1929 Born — Klinon, Greece 1952 Topographical Ingenier, National Technical University of A thens 1960-1965 Teaching Assistant, National Technical University of A thens 1966-1967 Research Assistant, Department of Geodetic Science, The Ohio State University, Columbus, Ohio 1967 MSc, The Ohio State University, Columbus, Ohio 1968-1969 Research Associate, Department of Geodetic Science, The Ohio State University, Columbus, Ohio PUBLICATIONS "The Azimuthal Equidistant Projection of Hatt." Technica chronica, No. 5, Athens 1963. "The Horizontal Gradients of Gravity in Southwest Ohio. " The Ohio State University Department of Geodetic Science Report No. 89, September 1967. "Interpolation of Deflections from Horizontal Gravity Gradients." The Ohio State University Department of Geodetic Science Report No. 98, December 1968 (with Ivan I. Mueller). Also published in a short form in Journal of Geophysical Research. Vol. 73, No. 22, November 15, 1968, pp. 6869-6878. "Geodetic Control by Means of Astronomic and Torsion Balance Observations, and the Gravimetric Reduction of Leveling." The Ohio State University Department of Geodetic Science Report No. 99, January 1968 (with Ivan I. Mueller and Edward J. Krakiwsky) FIELDS OF STUDY Higher Geodesy George Veis Geodetic Astronomy Ivan I. Mueller Satellite Geodesy Ivan 1. M ueller Physical Geodesy Ivan I. Mueller Geometric Geodesy Richard H. Rapp Map Projections Richard H. Rapp Adjustment Computations U rho A. U otila iii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS................................................. ii VITA ......................................................................................... iii LIST OF TABLES .............................................................................................................. vi LIST OF FIGURES .............................................................................................................. vii C hapter 1. INTRODUCTION........................................................................................................... 1 2. DEFINITION OF THE WORLD GEODETIC SYSTEM .................................. 5 3. THE ADJUSTMENT SYSTEM .......................................................... .................. 8 3.1 Observations for the World Geodetic System ................................... 8 3.2 Triangulation ................................................................................................... 12 3.21 Mathematical Model for Terrestrial Triangulation 12 3. 22 Weighting of the Geodetic Coordinates .................................. 27 3. 3 Gravity Observations .................................................................................. 31 3. 31 Modeling the Gravity Anomalies .............................................. 31 3.32 Various Gravity Estimates for the Unsurveyed Areas. 42 3.33 Weighting of Gravity Anom alies ................................................. 43 3.4 Astrogeodetic Undulations ........................................................................ 44 3.41 Modeling the Astrogeodetic Undulations .................................. 44 3.42 Weighting of the Astrogeodetic Undulations ............................ 55 3.5 Geometric Use of Satellite Observations ............................................. 58 3.51 Geometric Models for Satellite Observations ...................... 58 3.52 Weighting of Geometric Satellite O bservations ................... 63 3. 6 Dynamic Satellite Solution ......................................................................... 63 3.61 Dynamic Use of Satellite Observations ................................... 63 3.62 Smithsonian Astrophysical Observatory Dynamic S o lu tio n .................................................................................................. 64 3. 621 Computation of O rbits ..................................................... 65 3. 622 Determination of Zonal Harmonic Coefficients . 76 3. 623 Determination of the Tesseral Harmonics and Station Coordinates ............................................................. 77 3.63 Naval Weapons Laboratory Dynamic Solution ....................... 79 3.64 Jet Propulation Laboratory Solution .......................................... 84 3.65 Combination of Satellite D ynam ics .......................................... 88 iv 3.7 Some Additional Constraints ......................................................................... 91 3. 8 Combination of Normal Equations ................................................................ 94 4. ERROR ESTIMATES FOR THE PRESENT DETERMINATION OF THE COMPONENTS OF THE WORLD GEODETIC SYSTEM........................... 98 4.1 Accuracy of the Present Determination of Geocentric Coordi­ nates and Shifts, Rotations, and Scale of D atum s ............................ 98 4. 2 Accuracy of Present Determination of Spherical Harmonic Coefficients of the P otential ...................................................................... 117 4.21 Determination of Harmonic Coefficients from Satellites . 117 4. 22 Determination of Harmonic Coefficients from Terrestrial Gravity Anomalies .................................................... 130 4.23 Determination of Harmonic Coefficients from Astro­ geodetic Undulations .................. 136 4. 24 Determination of Harmonic Coefficients from a Combi­ nation of Satellite, Terrestrial, and Astrogeodetic Data . 147 4. 3 Accuracy of a Determination of the Components of the Mean Earth Ellipsoid ................................. 152 5. SUMMARY AND CONCLUSIONS ............................................................. 155 REFERENCES......................................................................................................................... 158 v LIST OF TABLES Page T a b le 3.3-1 Block Size from an Expansion to Degree n ................................... 38 3.8-1 Type of Observation and Parameters Involved ................................ 94 4.1-1 Coordinates of NWL Stations Referred to an Ellipsoid of a = 6378166m, l/f = 298. 3 ...................................................................... 103 4.1-2 Geocentric Coordinates of the Points Used ....................................... 104 4.1-3 Geodetic Coordinates on the North American Datum ..................... 105 4.1-4 Geodetic Cartesian Coordinates of the Points Used ........................ 107 4.1-5 North American Datum Shifts, and Shifts, Rotations and Scale Corrections from SAO Stations ................................................... 109 4.1 - 5a Correlation Matrices of Datum Transformation Parameters from SAO S ta tio n s ......................................................................................... 110 4.1-6 North American Datum Shifts, and Shifts, Rotations, and Scale Correction from NWL Stations .................................................... 113 4 .1 - 6 a Correlation Matrices of Datum Transformation Parameters from NWL Stations ......................................................................................... 114 4.1-7 Adjusted Geocentric Coordinates .......................................................... 116 4.2-1 Even Zonal Harmonics
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