Geodesy (eBook)

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Wolfgang Torge and Jürgen Müller, University of Hannover, Germany.

Preface to the Fourth Edition 5
1 Introduction 11
1.1 Definition of geodesy 11
1.2 The objective of geodesy 12
1.3 Historical development of geodesy 14
1.3.1 The spherical Earth model 14
1.3.2 The ellipsoidal Earth model 17
1.3.3 The geoid, arc measurements and national geodetic surveys 19
1.3.4 Three-dimensional geodesy 21
1.3.5 Four-dimensional geodesy 22
1.4 Organization of geodesy, literature 22
1.4.1 National organizations 22
1.4.2 International collaboration 23
1.4.3 Literature 25
2 Reference Systems and Reference Frames 27
2.1 Basic units and constants 27
2.2 Time systems 29
2.2.1 Atomic time, dynamical time systems 30
2.2.2 Sidereal and Universal Time 31
2.3 Reference coordinate systems: fundamentals 34
2.3.1 Celestial Reference System 35
2.3.2 Precession, nutation 37
2.3.3 Terrestrial Reference System 38
2.3.4 Polar motion, Earth rotation 40
2.4 International reference systems and reference frames 44
2.4.1 International Celestial Reference System and Frame 44
2.4.2 International Terrestrial Reference System and Frame 49
2.4.3 Transformation between celestial and terrestrial reference systems, Earth orientation parameters 52
2.4.4 International Earth Rotation and Reference Systems Service 55
2.5 Local level systems 56
3 The Gravity Field of the Earth 63
3.1 Fundamentals of gravity field theory 63
3.1.1 Gravitation, gravitational potential 63
3.1.2 Gravitation of a spherically symmetric Earth 65
3.1.3 Properties of the gravitational potential 67
3.1.4 Centrifugal acceleration, centrifugal potential 70
3.1.5 Gravity acceleration, gravity potential 71
3.2 Geometry of the gravity field 72
3.2.1 Level surfaces and plumb lines 73
3.2.2 Local gravity field representation 74
3.2.3 Natural coordinates 77
3.3 Spherical harmonic expansion of the gravitational potential 79
3.3.1 Expansion of the reciprocal distance 79
3.3.2 Expansion of the gravitational potential 81
3.3.3 Geometrical interpretation of the surface spherical harmonics 83
3.3.4 Physical interpretation of the spherical harmonic coefficients 84
3.4 The geoid 86
3.4.1 Definition 86
3.4.2 Mean sea level 88
3.4.3 The geoid as height reference surface 91
3.5 Temporal gravity variations 94
3.5.1 Gravitational constant, Earth rotation 95
3.5.2 Tidal acceleration, tidal potential 95
3.5.3 Non-tidal temporal gravity variations 99
4 The Geodetic Earth Model 101
4.1 The rotational ellipsoid 101
4.1.1 Parameters and coordinate systems 101
4.1.2 Curvature 104
4.1.3 Spatial geodetic coordinates 106
4.2 The normal gravity field 109
4.2.1 The level ellipsoid, level spheroids 109
4.2.2 The normal gravity field of the level ellipsoid 111
4.2.3 Geometry of the normal gravity field 115
4.3 Geodetic reference systems, optimum Earth model 118
5 Methods of Measurement 123
5.1 Atmospheric refraction 123
5.1.1 Fundamentals 124
5.1.2 Tropospheric refraction 127
5.1.3 Ionospheric refraction 131
5.2 Satellite observations 133
5.2.1 Undisturbed satellite motion 134
5.2.2 Perturbed satellite motion 136
5.2.3 Artificial Earth satellites 138
5.2.4 Direction, range and range rate (Doppler, DORIS) measurements 141
5.2.5 Global Navigation Satellite Systems GNSS (GPS, GLONASS, Galileo and others) 145
5.2.6 Laser distance measurements 160
5.2.7 Satellite altimetry 164
5.2.8 Satellite-to-satellite tracking, satellite gravity gradiometry 168
5.3 Geodetic astronomy 172
5.3.1 Optical observation instruments 173
5.3.2 Astronomic positioning and azimuth determination 176
5.3.3 Reductions 178
5.3.4 Very Long Baseline Interferometry 180
5.4 Gravimetry 185
5.4.1 Absolute gravity measurements 185
5.4.2 Relative gravity measurements 193
5.4.3 Gravity reference systems and gravity standard 199
5.4.4 Gravity measurements on moving platforms 200
5.4.5 Gravity gradiometry 207
5.4.6 Continuous gravity measurements 209
5.5 Terrestrial geodetic measurements 213
5.5.1 Horizontal and vertical angle measurements 214
5.5.2 Distance measurements, total stations 216
5.5.3 Inertial surveying, underwater acoustic positioning 222
5.5.4 Leveling 225
5.5.5 Tilt and strain measurements 229
6 Methods of Positioning and Gravity Field Modeling 233
6.1 Residual gravity field 234
6.1.1 Disturbing potential, height anomaly, geoid height 234
6.1.2 Gravity disturbance, gravity anomaly, deflection of the vertical 236
6.1.3 Statistical description of the gravity field, interpolation 239
6.2 Three-dimensional positioning 243
6.2.1 Observation equations 244
6.2.2 Geodetic datum 250
6.3 Horizontal positioning 255
6.3.1 Ellipsoidal trigonometry 255
6.3.2 Reductions to the ellipsoid 257
6.3.3 Computations on the ellipsoid 259
6.4 Height determination 262
6.4.1 Heights from geometric leveling 263
6.4.2 Trigonometrical heights 265
6.4.3 Heights from GNSS (GPS) 266
6.5 Fundamentals of gravity field modeling 268
6.5.1 The geodetic boundary-value problem 268
6.5.2 Gravitation of topography, digital elevation models 272
6.5.3 Gravity reductions to the geoid 274
6.5.4 Orientation and scale of gravity field models 279
6.6 Global gravity field modeling 281
6.6.1 Spherical harmonic expansion 281
6.6.2 “Satellite-only” gravity field models 285
6.6.3 Combined (high resolution) gravity field models 288
6.7 Local gravity field modeling 293
6.7.1 Gravimetric geoid heights and deflections of the vertical: integral formulas 293
6.7.2 Gravimetric height anomalies and surface deflections of the vertical 300
6.7.3 The external gravity field 303
6.7.4 Astrogeodetic geoid and quasigeoid determination 306
6.8 Least-squares collocation 311
7 Geodetic and Gravimetric Networks 315
7.1 Horizontal control networks 315
7.2 Vertical control networks 326
7.3 Three-dimensional networks 331
7.4 Gravity networks 340
8 Structure and Dynamics of the Earth 343
8.1 The geophysical Earth model 343
8.2 The upper layers of the Earth 347
8.2.1 Structure of the Earth’s crust and upper mantle 347
8.2.2 Isostasy 348
8.2.3 Plate tectonics 352
8.2.4 Interpretation of the gravity field 354
8.3 Geodesy and recent geodynamics 359
8.3.1 Geophysical processes and effects on geodetic products 360
8.3.2 Changes in Earth rotation 363
8.3.3 Sea level variations 365
8.3.4 Crustal deformations 369
8.3.5 Gravity field variations with time 377
8.3.6 Earth tides and tidal loading 385
References 393
Index 431

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"The book is thoroughly revised and extended with the important results achieved in the years since the last edition (2001). The section on Satellite Observations has been extended with descriptions of the current missions like GRACE and GOCE. Geodynamics is well treated in an extended chapter on “Structure and Dynamics of the Earth”. The book contains an extensive bibliography with 500 references added since the edition of 2001.[..] But what is extremely important is the index, which makes the book useful as a handbook for everyone. The book also includes many fine figures and illustrations, now also in color. [..] It is a wonderful book with so much important information covering all of modern geodesy."
Carl Christian Tscherning in: Journal of Geodesy, 86, p.786(2012)