Geodesy

Geodesy

by Wolfgang Torge

Hardcover(2. ed. Reprint 2015)

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Product Details

ISBN-13: 9783111174549
Publisher: De Gruyter
Publication date: 04/01/1991
Edition description: 2. ed. Reprint 2015
Pages: 274
Product dimensions: 6.10(w) x 9.06(h) x 0.03(d)
Age Range: 18 Years

About the Author

Prof. Dr.-Ing. Wolfgang Torge, Institut für Erdmessung, Universität Hannover, Hannover, Germany.

Table of Contents

Preface to the Fourth Edition v

1 Introduction 1

1.1 Definition of geodesy 1

1.2 The objective of geodesy 2

1.3 Historical development of geodesy 4

1.3.1 The spherical Earth model 4

1.3.2 The ellipsoidal Earth model 7

1.3.3 The geoid, arc measurements and national geodestic surveys 9

1.3.4 Three-dimensional geodsey 11

1.3.5 Four-dimensional geodesy 12

1.4 Organization of geodesy, literature 12

1.4.1 National organizations 12

1.4.2 International collaboration 13

1.4.3 Literature 15

2 Reference Systems and Reference Frames 17

2.1 Basic units and constants 17

2.2 Time systems 19

2.2.1 Atomic time, dynamical time systems 20

2.2.2 Sidereal and Universal Time 21

2.3 Reference coordinate systems: fundamentals 24

2.3.1 Celestial Reference System 25

2.3.2 Precession, nutation 27

2.3.3 Terrestrial Reference System 28

2.3.4 Polar motion, Earth rotation 30

2.4 International reference systems and reference frames 34

2.4.1 International Celestial Reference frames 34

2.4.2 International Terrestrial Reference System and Frame 39

2.4.3 Transformation between celestial and terrestrial reference systems, Earth orientation parameters 42

2.4.4 International Earth Rotation and Reference Systems Service 45

2.5 Local level systems 46

3 The Gravity Field of the Earth 53

3.1 Fundamentals of gravity field theory 53

3.1.1 Gravitation, gravitational potential 53

3.1.2 Gravitation of a spherically symmetric Earth 55

3.1.3 Properties of the gravitational potential 57

3.1.4 Centrifugal acceleration, centrifugal potential 60

3.1.5 Gravity accelleration, gravity potential 61

3.2 Geometry of the gravity field 62

3.2.1 Level surfaces and plumb lines 63

3.2.2 Local gravity field representation 64

3.2.3 Natural coordinates 67

3.3 Spherical harmonic expansion of the gravitational potential 69

3.3.1 Expansion of the reciprocal distance 69

3.3.2 Expansion of the gravitational potential 71

3.3.3 Geometrical interpretation of the surface spherical harmonics 73

3.3.4 Physical interpretation of the spherical harmonic coefficients 74

3.4 The geoid 76

3.4.1 Definition 76

3.4.2 Mean sea level 78

3.4.3 The geoid as height reference surface 81

3.5 Temporal gravity variations 84

3.5.1 Gravitational constant, Earth rotation 85

3.5.2 Tidal acceleration, tidal potential 85

3.5.3 Non-tidal temporal gravity variations 89

4 The Geodetic Earth Model 91

4.1 The rotational ellipsoid 91

4.1.1 Parameters and coordinate systems 91

4.1.2 Curvature 94

4.1.3 Spatial geodetic coordinates 96

4.2 The normal gravity field 99

4.2.1 The level ellipsoid, level spheroids 99

4.2.2 The normal gravity field of the level ellipsoid 101

4.2.3 Geometry of the normal gravity field 105

4.3 Geodetic reference systems, optimum Earth model 108

5 Methods of Measurement 113

5.1 Atmospheric refraction 113

5.1.1 Fundamentals 114

5.1.2 Tropospheric refraction 117

5.1.3 Ionospheric refraction 121

5.2 Satellite observations 123

5.2.1 Undisturbed satellite motion 124

5.2.2 Perturbed satellite motion 126

5.2.3 Artificial Earth satellites 128

5.2.4 Direction, range and range rate (Doppler, DORIS) measurements 131

5.2.5 Global Navigation Satellite Systems GNSS (GPS, GIONASS, Galileo and others) 135

5.2.6 Laser distance measurements 150

5.2.7 Satellite altimetry 154

5.2.8 Satellite-to-satellite tracking, satellite gravity gradiometry 158

5.3 Geodetic astronomy 162

5.3.1 Optical observation instruments 163

5.3.2 Astronomic positioning and azimuth determination 166

5.3.3 Reductions 168

5.3.4 Very Long Baseline Interferometry 170

5.4 Gravimetry 175

5.4.1 Absolute gravity measurements 175

5.4.2 Relative gravity measurements 183

5.4.3 Gravity reference systems and gravity standard 189

5.4.4 Gravity measurements on moving platforms 190

5.4.5 Gravity gradiometry 197

5.4.6 Continuous gravity measurements 199

5.5 Terrestrial geodetic measurements 203

5.5.1 Horizontal and vertical angle measurements 204

5.5.2 Distance measurements, total stations 206

5.5.3 Inertial surveying, underwater acoustic positioning 212

5.5.4 Leveling 215

5.5.5 Tilt and strain measurements 219

6 Methods of Positioning and Gravity Field Modeling 223

6.1 Residual gravity field 224

6.1.1 Disturbing potential, height anomaly, geoid height 224

6.1.2 Gravity disturbance, gravity anomaly, deflection of the vertical 226

6.1.3 Statistical description of the gravity field, interpolation 229

6.2 Three-dimensional positioning 233

6.2.1 Observation equations 234

6.2.2 Geodetic datum 240

6.3 Horizontal positioning 245

6.3.1 Ellipsoidal trigonometry 245

6.3.2 Reductions to the ellipsoid 247

6.3.3 Computations on the ellipsoid 249

6.4 Height determination 252

6.4.1 Heights from geometric leveling 253

6.4.2 Trigonometrical heights 255

6.4.3 Heights from GNSS (GPS) 256

6.5 Fundamentals of gravity field modeling 258

6.5.1 The geodetic boundary-value problem 258

6.5.2 Gravitation of topography, digital elevation models 262

6.5.3 Gravity reductions to the geoid 264

6.5.4 Orientation and scale of gravity field models 269

6.6 Global gravity field modeling 271

6.6.1 Spherical harmonic expansion 271

6.6.2 "Satellite-only" gravity field models 275

6.6.3 Combined (high resolution) gravity field models 278

6.7 Local gravity field modeling 283

6.7.1 Gravimetric geoid heights and deflections of the vertical: integral formulas 283

6.7.2 Gravimetric height anomalies and surface deflections of the vertical 290

6.7.3 The external gravity field 293

6.7.4 Astrogeodetic geoid and quasigeoid determination 296

6.8 Least-squares collocation 301

7 Geodetic and Gravimetric Networks 305

7.1 Horizontal control networks 305

7.2 Vertical control networks 316

7.3 Three-dimensional networks 321

7.4 Gravity networks 330

8 Structure and Dynamics of the Earth 333

8.1 The geophysical Earth model 333

8.2 The upper layers of the Earth 337

8.2.1 Structure of the Earth's crust and upper mantle 337

8.2.2 Isostasy 338

8.2.3 Plate tectonics 342

8.2.4 Interpretation of the gravity field 344

8.3 Geodesy and recent geodynamics 349

8.3.1 Geophysical processes and effects on geodetic products 350

8.3.2 Changes in Earth rotation 353

8.3.3 Sea level variations 355

8.3.4 Crustal deformations 359

8.3.5 Gravity field variations with time 367

8.3.6 Earth tides and tidal loading 375

References 383

Index 421

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