Geodesy

ForewordForeword to the Second EditionPart I. Introduction 1. History of Geodesy 1.1. Historical Beginnings of Geodesy 1.2. Scientific Beginnings of Geodesy 1.3. Geodesy in the Service of Mapping 1.4. Geodesy of the Modern Era 2. Geodesy and Other Disciplines 2.1. Applications of Geodesy 2.2. Symbiotic Relation Between Geodesy and some Other Sciences 2.3. Theoretical Basis of Geodesy 3. Mathematics and Geodesy 3.1. Algebra 3.2. Analysis 3.3. Geometry 3.4. Statistics 4. Structure of Geodesy 4.1. Functions of Geodesy 4.2. Geodetic Theory 4.3. Geodetic Practice 4.4. Geodetic Profession ReferencesPart II. The Earth 5. Earth and its Motions 5.1. Earth's Annual Motion 5.2. Earth's Spin, Precession, and Nutation 5.3. Earth's Free Nutation 5.4. Observed Polar Motion and Spin Velocity Variations 6. Earth and its Gravity Field 6.1. Gravity Field 6.2. Gravity Anomaly 6.3. Gravity Potential 6.4. Geoid and Deflections of the Vertical 7. Earth and its Size and Shape 7.1. Actual Shape of the Earth 7.2. Geoid as a Figure of the Earth 7.3. Biaxial Ellipsoid as a Figure of the Earth 7.4. Other Mathematical Figures of the Earth 8. Earth and its Deformations in Time 8.1. Tidal Phenomena 8.2. Crustal Loading Deformations 8.3. Tectonic Deformations 8.4. Man-Made and Other Deformations 9. Earth and its Atmosphere 9.1. Some Physical Properties of the Atmosphere 9.2. Wave Propagation Through the Atmosphere and Water 9.3. Temporal Variations of the Atmosphere 9.4. Gravitational Field of the Atmosphere ReferencesPart III. Methodology 10. Elements of Geodetic Methodology 10.1. General Procedure 10.2. Formulation of the Mathematical Model 10.3. Observables and their Properties 10.4. Vector of Observables 11. Classes of Mathematical Models 11.1. Classification of Models 11.2. Models with a Unique Solution 11.3. Models with an Underdetermined Solution 11.4. Models with an Overdetermined Solution 12. Least-Squares Solution of Overdetermined Models 12.1. Formulation of the Least-Squares Problem 12.2. Solution of the Least-Squares Problem 12.3. Covariance Matrices of the Results 13. Assessment of Results 13.1. Hubert Space and Statistics 13.2. Statistical Testing 13.3. Assessment of Observations of One Observable 13.4. Simultaneous Assessment of Observations and Mathematical Models 13.5. Assessment of the Determined Parameters 14. Formulation and Solving of Problems 14.1. Optimal Accuracy Design 14.2. Analysis of Trend 14.3. Adjustment of Observations 14.4. Problems with a Priori Knowledge About the Parameters 14.5. Problems with Constraints and Singularities 14.6. Step-by-Step Procedures in Dynamic and Static Problems ReferencesPart IV. Positioning 15. Point Positioning 15.1. Fundamentals of Geodetic Astronomy 15.2. Astronomical Positioning 15.3. Satellite Positioning 15.4. Transformations of Terrestrial Positions 16. Relative Positioning 16.1. Relative Three-Dimensional Positioning 16.2. Relative Horizontal Positioning on Reference Ellipsoid 16.3. Relative Horizontal Positioning on Conformal Map 16.4. Relative Vertical Positioning 17. Three-Dimensional Networks 17.1. Three-Dimensional Networks Using Terrestrial Observations 17.2. Photogrammetrical Networks 17.3. Three-Dimensional Networks Using Extraterrestrial Observations 17.4. Assessment and Merger of Three-Dimensional Networks 18. Horizontal Networks 18.1. Horizontal Datum 18.2. Mathematical Models and their Solution 18.3. Assessment, Expansion, and Merger of Horizontal Networks 18.4. Marine Positioning 19. Height Networks 19.1. Vertical Datum 19.2. Mathematical Models for Leveling 19.3. Assessment and Design of Height Networks 19.4. Other Heighting Concepts ReferencesPart V. Earth's Gravity Field 20. Global Treatment of the Gravity Field 20.1. Fundamental Equations for Gravity Potential 20.2. Eigenfunction Development of Gravitational Potential 20.3. Model Gravity Field 20.4. Disturbing Potential 21. Local Treatment of the Gravity Field 21.1. Conversion of Disturbing Potential into Other Field Parameters 21.2. Vertical Gradient of Gravity 21.3. Curvature of the Plumb Line 21.4. Topographical and Isostatic Effects 22. Determination of the Gravity Field from Gravity Observations 22.1. Stokes's Concept 22.2. Molodenskij's Concept 22.3. Gravimetry 22.4. Evaluation of the Surface Integrals 23. Determination of the Gravity Field from Observations to Satellites 23.1. Satellites and the Gravitational Field 23.2. Prediction of Orbits 23.3. Analysis of Orbital Perturbations 23.4. Evaluation of Gravity Field Parameters 24. Determination of the Gravity Field from Deflections and from Heterogeneous Data 24.1. Geometrical Solution for the Geoid 24.2. Transformation of Gravity Field Parameters 24.3. Densification and Refinement of Deflections of the Vertical 24.4. Solutions for the Geoid from Heterogeneous Data ReferencesPart VI. Temporal Variations 25. Corrections for Temporal Variations 25.1. Elastic Response to Tidal Stress 25.2. Tidal Corrections 25.3. Corrections Due to Sea Tide Effects 25.4. Corrections Due to Polar Motion Deformations, and Other Causes 26. Detection of Vertical Movements 26.1. Sources of Information on Vertical Movements 26.2. Interdependence of Temporal Variations of Gravity and Heights 26.3. Vertical Displacement Profiles 26.4. Areal Modeling of Vertical Movements 27. Detection of Horizontal Movements 27.1. Sources of Information on Horizontal Movements 27.2. Comparison of Horizontal Positions 27.3. Direct Evaluation of Horizontal Displacements 27.4. Strain, Shear, and Other Models ReferencesAuthor IndexSubject Index