Geodesy

This book gives a systematic overview of the fundamental theories, frameworks and methods for measurement and evaluation applying to geodesy, though the contribution of geodetic spatial techniques for positioning and for establishing the gravitational field receives particular emphasis. These methods have led to a change in the setting up of geodetic basic networks that is also of importance in practical terms; for interdisciplinary geodynamics research geodesy can likewise make major contributions with their assistance. The current status of geodesy is illustrated by numerous examples from survey, evaluation and analysis; an extensive literature list makes further study all the easier. The book conveys an extensive overview of the profound changes that geodesy has undergone in the past twenty years. 1 Introduction 1.1 Definition and Classification of Geodesy 1.2 The Problem of Geodesy 1.3 Historical Development of Geodesy 1.3.1 The Spherical Earth Model 1.3.2 The Ellipsoidal Earth Model 1.3.3 Arc Measurements 1.3.4 The Geoid and the Ellipsoid 1.4 Organization of Geodesy, Literature 1.4.1 National Organizations 1.4.2 International Collaboration 1.4.3 Literature 2 The Gravity Field of the Earth 2.1 Components of the Gravity Field 2.1.1 Gravitation, Gravitational Potential 2.1.2 Gravitational Potential of a Spherically Symmetric Earth 2.1.3 Properties of the Gravitational Potential 2.1.4 Centrifugal Acceleration, Centrifugal Potential 2.1.5 Gravity Acceleration, Gravity Potential 2.2 Level Surfaces and Plumb Lines 2.2.1 Definition and Properties of Level Surfaces 2.2.2 Analytical Representation of Level Surfaces 2.2.3 Curvature of the Level Surfaces 2.2.4 Curvature of Plumb Lines 2.2.5 Gravity Gradient 2.3 Spherical Harmonic Expansion of the Gravitational Potential 2.3.1 Expansion of the Reciprocal Distance 2.3.2 Expansion of the Gravitational Potential 2.3.3 The Geometrical Meaning of the Surface Harmonics 2.3.4 Physical Meaning of the Lower Degree Harmonic Coefficients 2.4 Temporal Variations of the Gravity Field 2.4.1 Tidal Acceleration, Tidal Potential 2.4.2 Earth Tides 2.4.3 Other Temporal Variations of the Gravity Field 3 Geodetic Reference Systems 3.1 Global Spatial Cartesian System, Polar Motion 3.2 Coordinate Systems in the Earth’s Gravity Field 3.2.1 Global Astronomic System 3.2.2 Local Astronomic Systems, Computations in the Earth’s Gravity Field 3.2.3 Local Astronomic and Global Cartesian System 3.3 The Geoid as Reference Surface for Heights 3.3.1 Definition of the Geoid 3.3.2 Geopotential Number and Orthometric Height 3.3.3 Mean Sea Level 3.4 Ellipsoidal Reference Systems 3.4.1 Geometric Parameters and Coordinate Systems of the Rotational Ellipsoid 3.4.2 Curvature of the Rotational Ellipsoid 3.4.3 Spatial Ellipsoidal Coordinate System 3.5 The Normal Gravity Field 3.5.1 The Normal Figure of the Earth, Level Ellipsoid 3.5.2 The Normal Gravity Field of the Level Ellipsoid 3.5.3 Series Expansions in the Normal Gravity Field 3.5.4 The Triaxial Ellipsoid 3.5.5 Geodetic Reference Systems 3.5.6 Normal Geographic Coordinates, Normal Heights 4 Methods of Measurement in Geodesy 4.1 Astronomic Measurements 4.1.1 Coordinate Systems of Spherical Astronomy 4.1.2 Variation of Stellar Coordinates, Star Catalogues 4.1.3 Time Systems 4.1.4 Observational Instruments 4.1.5 Methods to Determine Astronomic Positions, Azimuth, and Time 4.2 Gravity Measurements 4.2.1 Absolute Gravity Measurements 4.2.2 Relative Gravity Measurements 4.2.3 Gravity Measurements on the Ocean and in the Air 4.2.4 Gravity Reference Systems 4.2.5 Determination of the Gravity Gradient 4.2.6 The Measurement of Earth Tides 4.3 Terrestrial Geodetic Measurements 4.3.1 Atmospheric Refraction 4.3.2 Horizontal Angle Measurements 4.3.3 Distance Measurements 4.3.4 Zenith Angle Measurements, Trigonometrically Determined Heights 4.3.5 Leveling 4.4 Satellite Observations 4.4.1 The Unperturbed Motion of a Satellite 4.4.2 The Perturbed Motion of the Satellite 4.4.3 Artificial Earth Satellites, Time Measuring Systems 4.4.4 Direction Measurements, Early Distance Measurements 4.4.5 Laser Distance Measurements 4.4.6 Doppler Frequency Shift Measurements 4.4.7 Global Positioning System 4.4.8 Very Long Baseline Interferometry 4.4.9 Satellite Altimetry 5 Methods of Evaluation, Global Geodesy 5.1 Astrogeodetic Methods 5.1.1 Deflection of the Vertical, Geoid Undulation, Height Anomaly 5.1.2 Three-Dimensional Computations, Geodetic Datum 5.1.3 Geometric-astronomic Leveling 5.1.4 Positional Systems 5.1.5 Height Systems 5.1.6 Astrogeodetic Determination of the Geoid and Quasigeoid 5.1.7 Orientation of Astrogeodetic Systems, Best Fitting Ellipsoids 5.2 Gravimetric Methods 5.2.1 Geodetic Boundary-Value Problem, Disturbing Potential, Gravity Anomaly 5.2.2 Linearization of the Geodetic Boundary-Value Problem 5.2.3 Solution of the Geodetic Boundary-Value Problem for the Geoid 5.2.4 Gravity Reductions, Cogeoid 5.2.5 Solution of the Geodetic Boundary-Value Problem for the Surface of the Earth 5.2.6 Physical Surface of the Earth and External Gravity Field 5.2.7 Prediction of Gravity Anomalies 5.2.8 Potential, Mass and Position of the Gravimetric Reference Ellipsoid 5.3 Methods of Satellite Geodesy 5.3.1 Observation Equations 5.3.2 Geometric Method 5.3.3 Dynamic Method, Harmonic Coefficients 5.3.4 Orbital Method, Absolute and Relative Positioning 5.3.5 Analysis of Satellite Altimetry 5.4 Combined Methods of Evaluation 5.4.1 Astrogravimetric Leveling 5.4.2 Remove — Restore Methods in Gravity Field Determination 5.4.3 Least Squares Collocation 5.4.4 Earth Models (Gravity Field and Geocentric Coordinates) 5.4.5 Centering and Strengthening Astrogeodetic Systems 5.4.6 Optimal Earth Parameters 5.5 Structure and Dynamics of the Earth’s Body 5.5.1 The Radial Structure of the Earth 5.5.2 The Earth as a Body in Equilibrium 5.5.3 Interpretation of the Gravity Field, the Crust of the Earth, and the Upper Mantle 5.5.4 Isostasy 5.5.5 Geodesy and Geodynamics 5.6 Lunar and Planetary Geodesy 5.6.1 Lunar Geodesy (Selenodesy) 5.6.2 Planetary Geodesy 6 Geodetic Networks 6.1 Horizontal Control Networks 6.1.1 Design, Monumentation, Observations 6.1.2 Computations 6.1.3 Geodesics on the Rotational Ellipsoid 6.1.4 Solution of Ellipsoidal Triangles 6.1.5 Direct and Inverse Geodetic Problems 6.1.6 National Networks: Examples 6.1.7 Network Unification and Large-Scale Control 6.2 Vertical Control Networks 6.2.1 Design, Monumentation, Observations 6.2.2 Computations 6.2.3 National Networks: Examples 6.2.4 Network Unification and Large-Scale Control 6.3 Gravity Networks 6.3.1 Design, Monumentation, Observations, and Computations 6.3.2 National Networks: Examples References Index

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