Wolfgang Torge Muller
Geodesy th
4 Edition
DE GRUYTER
Contents
Preface to the Fourth Edition. 1 Introduction Definition of geodesy The objective of geodesy Historical development of geodesy The spherical Earth model 1.3.2 The ellipsoidal Earth model 1.3.3 The geoid, arc measurements and national geodetic surveys Three-dimensional geodesy 1.3.5 Four-dimensional geodesy Organization of geodesy, literature National organizations 1.4.2 International collaboration 1.4.3 Literature
1 1 2 4 4 7 9 12 12 12
2 Reference Systems and Reference Frames 2.1 Basic units and constants 2.2 Time systems 2.2.1 Atomic time, dynamical time systems 2.2.2 Sidereal and Universal Time 2.3 Reference coordinate systems: fundamentals 2.3.1 Celestial Reference System 2.3.2 Precession, nutation 2.3.3 Terrestrial Reference System 2.3.4 Polar motion, Earth rotation 2.4 International reference systems and reference frames 2.4.1 International Celestial Reference System and Frame 2.4.2 International Terrestrial Reference System and Frame 2.4.3 Transformation between celestial and terrestrial reference systems, Earth orientation parameters 2.4.4 International Earth Rotation and Reference Systems Service 2.5 Local level systems
42 45 46
3 The Gravity Field of the Earth 3.1 Fundamentals of gravity field theory Gravitation, gravitational potential Gravitation of a spherically symmetric Earth Properties of the gravitational potential Centrifugal acceleration, centrifugal potential Gravity acceleration, gravity potential
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20 21 24 25 27 28 30 34 34 39
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Contents 3.2 Geometry of the gravity field 3.2.1 Level surfaces and plumb lines 3.2.2 Local gravity field representation 3.2.3 Natural coordinates 3.3 Spherical harmonic expansion of the gravitational potential 3.3.1 Expansion of the reciprocal distance 3.3.2 Expansion of the gravitational potential 3.3.3 Geometrical interpretation of the surface spherical harmonics 3.3.4 Physical interpretation of the spherical harmonic coefficients 3.4 The geoid 3.4.1 Definition 3.4.2 Mean sea level 3.4.3 The geoid as height reference surface 3.5 Temporal gravity variations 3.5.1 Gravitational constant, Earth rotation 3.5.2 Tidal acceleration, tidal potential 3.5.3 Non-tidal temporal gravity variations The Geodetic Earth Model 4.1 The rotational ellipsoid 4.1.1 Parameters and coordinate systems 4.1.2 Curvature Spatial geodetic coordinates 4.2 The normal gravity field 4.2.1 The level ellipsoid, level spheroids 4.2.2 The normal gravity field of the level ellipsoid 4.2.3 Geometry of the normal gravity field 4.3 Geodetic reference systems, optimum Earth model Methods of Measurement 5.1 Atmospheric refraction 5.1.1 Fundamentals 5.1.2 Tropospheric refraction 5.1.3 Ionospheric refraction 5.2 Satellite observations 5.2.1 Undisturbed satellite motion 5.2.2 Perturbed satellite motion 5.2.3 Artificial Earth satellites 5.2.4 Direction, range and range rate (Doppler, DORIS) measurements 5.2.5 Global Navigation Satellite Systems GNSS (GPS, GLONASS, Galileo and others) 5.2.6 Laser distance measurements 5.2.7 Satellite 5.2.8 Satellite-to-satellite tracking, satellite gravity gradiometry
62 63 64 67 69 69 71 73 74 76 76 78 81 84 85 85 89 91 91 91 94 96 99 99 101 105 108
114 121 123 124 126 128
135 150
Contents 5.3 Geodetic astronomy 5.3.1 Optical observation instruments 5.3.2 Astronomic positioning and azimuth determination 5.3.3 Reductions 5.3.4 Very Long Baseline 5.4 Gravimetry 5.4.1 Absolute gravity measurements 5.4.2 Relative gravity measurements 5.4.3 Gravity reference systems and gravity standard 5.4.4 Gravity measurements on moving platforms 5.4.5 Gravity gradiometry 5.4.6 Continuous gravity measurements 5.5 Terrestrial geodetic measurements 5.5.1 Horizontal and vertical angle measurements 5.5.2 Distance measurements, total stations 5.5.3 Inertial surveying, underwater acoustic positioning 5.5.4 Leveling 5.5.5 Tilt and strain measurements 6 Methods of Positioning and Gravity Field Modeling 6.1 Residual gravity field Disturbing potential, height anomaly, geoid height Gravity disturbance, gravity anomaly, deflection of the vertical Statistical description of the gravity field, interpolation 6.2 Three-dimensional positioning 6.2.1 Observation equations 6.2.2 Geodetic datum 6.3 Horizontal positioning 6.3.1 Ellipsoidal trigonometry 6.3.2 Reductions to ellipsoid 6.3.3 Computations on the ellipsoid 6.4 Height determination 6.4.1 Heights from geometric leveling 6.4.2 Trigonometrical heights 6.4.3 Heights from GNSS (GPS) 6.5 Fundamentals of gravity field modeling 6.5.1 The geodetic boundary-value problem 6.5.2 Gravitation of topography, digital elevation models 6.5.3 Gravity' reductions to the geoid 6.5.4 Orientation and scale of gravity field models 6.6 Global gravity field modeling 6.6.1 Spherical harmonic expansion 6.6.2 gravity field models 6.6.3 Combined (high resolution) gravity field models
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175 183 190 199 203 204 206
219 223 224 224 226 229 233 234 240 245 245 247 249 252 253 255 256 258 258 262 264 269 271 271 275 278
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Contents 6.7 Local gravity field modeling 6.7.1 Gravimetric geoid heights and deflections of the vertical: integral formulas 6.7.2 Gravimetric height anomalies and surface deflections of the vertical 6.7.3 The external gravity field 6.7.4 Astrogeodetic geoid and quasigeoid determination 6.8 Least-squares collocation
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7 Geodetic and Gravimetric Networks 7.1 Horizontal control networks 7.2 Vertical control networks 7.3 Three-dimensional networks 7.4 Gravity networks
305 305
8 Structure and Dynamics of the Earth 8.1 The geophysical Earth model 8.2 The upper layers of the Earth 8.2.1 Structure of the Earth's crust and upper mantle 8.2.2 Isostasy 8.2.3 Plate tectonics 8.2.4 Interpretation of the gravity field 8.3 Geodesy and recent 8.3.1 Geophysical processes and effects on geodetic products 8.3.2 Changes in Earth rotation 8.3.3 Sea level variations 8.3.4 Crustal deformations 8.3.5 Gravity field variations wi th time 8.3.6 Earth tides and tidal loading
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References
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