Geodesy: Treatise on Geophysics

Cover......Page 1
Editor-in-Chief......Page 2
Volume Editors......Page 3
Preface......Page 4
Coordinate Systems......Page 7
Ground-Based Positioning Systems......Page 10
Gravimeters......Page 14
Error Sources, Signals, and Noise......Page 15
References......Page 16
Glossary......Page 17
Historical Notes......Page 18
Preliminary Definitions and Concepts......Page 20
Newton’s Law of Gravitation......Page 21
Green’s Identities......Page 24
Uniqueness Theorems......Page 26
Solutions by Integral Equation......Page 27
Spherical Harmonics and Green’s Functions......Page 28
Inverse Stokes and Hotine Integrals......Page 31
Vening-Meinesz Integral and Its Inverse......Page 32
Concluding Remarks......Page 33
Low-Degree Harmonics as Density Moments......Page 34
Normal Ellipsoidal Field......Page 36
Methods of Determination......Page 38
Measurement Systems and Techniques......Page 39
Models......Page 43
The Geoid and Heights......Page 44
References......Page 47
Definition of Absolute and Relative Gravity and Their Practical Uses......Page 49
Precision......Page 51
Repeatability......Page 54
Accuracy......Page 55
Gravity Meters......Page 56
Absolute Gravity Meters......Page 57
Pendulum absolute gravimeters......Page 58
The free-fall chamber......Page 59
The distance and time measurement: Trajectory determination......Page 61
Commercial absolute gravity meters......Page 64
The L&R zero-length spring suspension......Page 65
The superconducting gravity meter......Page 68
Gravimeter Applications......Page 69
References......Page 70
3.04 Gravimetric Methods - Superconducting Gravity Meters......Page 71
Early years at UCSD......Page 72
Early commercial model TT instruments (1981-94)......Page 73
The Compact SG (1994-2002)......Page 74
Superconducting components......Page 75
Tilt compensation system......Page 77
Development of the Dual-Sphere Design......Page 78
Instrumental noise and precision......Page 79
Ultralong hold time dewar......Page 80
Data acquisition system and remote control......Page 81
Operation and maintenance......Page 82
Site stability......Page 83
Second data sampled from an SG......Page 84
Minute data from the GGP database (ICET)......Page 85
Treatment of gaps in gravity data......Page 87
Automatic procedures......Page 88
Processing for different purposes......Page 89
Tide-generating potential......Page 91
Elastic response of the Earth......Page 92
Ocean tides and loading......Page 93
Atmospheric Pressure Effects......Page 94
Frequency-dependent admittance......Page 95
Green’s functions and nonlocal pressure corrections......Page 96
3-D atmospheric corrections......Page 97
Basics......Page 98
Calibration using AGs......Page 99
Calibration using a moving platform......Page 100
The step response method......Page 101
Hydrology......Page 102
The Global Geodynamics Project......Page 103
Seismic and Subseismic Signals......Page 106
Atmospheric Loading......Page 109
Resonance effects in diurnal tides......Page 110
Nonlinear tides......Page 111
Nontidal Ocean Circulation......Page 112
Hydrology......Page 113
Earth Rotation......Page 114
Tectonic Effects......Page 115
Ground/Satellite Gravity Field Comparison......Page 116
Future Possibilities......Page 118
Conclusions......Page 119
Acknowledgments......Page 120
References......Page 121
Relevant Websites......Page 128
nomenclature......Page 129
Glossary......Page 130
Measuring Range......Page 134
Ionosphere Path Delay......Page 135
Wet Troposphere Path Delay......Page 136
Sea State Bias......Page 138
Orbit and Ground Track......Page 141
Aliasing......Page 144
Precise Orbit Determination......Page 146
Calibration at Single Site,\rInstrumented Platforms......Page 148
Cal/Val from Comparison to Tide Gauges......Page 150
The TOPEX/Poseidon - Jason-1 Calibration Phase......Page 152
Mean Sea Surface, Gravity,\rand Bathymetry......Page 153
Tides......Page 156
Sea Level Change......Page 158
Laser Altimetry......Page 161
Wide Swath Altimeter......Page 162
References......Page 163
Relevant Website......Page 167
Introduction......Page 168
An Overview......Page 169
The Tidal Forces......Page 170
The Tidal Potential......Page 171
Computing the Tides: Direct Computation......Page 172
Computing the Tides (I): Harmonic Decompositions......Page 173
The Pole Tide......Page 177
Radiational Tides......Page 178
Some combinations of Love numbers (I): gravity and tilt......Page 179
Combinations of Love numbers (II): displacement and strain tides......Page 180
Response of a Rotating Earth......Page 181
NDFW resonance......Page 182
Coupling to other modes......Page 184
Anelastic effects......Page 185
Computing Loads I: Spherical Harmonic Sums......Page 186
Computing Loads II: Integration Using Green Functions......Page 188
Tidal Analysis and Prediction......Page 190
Predicting tides......Page 193
Earth-Tide Instrumentation......Page 194
Local Distortion of the Tides......Page 195
References......Page 196
Jdot2: A Review of Early GIA Research......Page 201
New Approaches to Long-Wavelength Gravity Trends......Page 204
A Problem with the Jdot2 Constraint?......Page 205
Geoid Height Change: The Influence of Rotational Feedback......Page 206
The Influence of Lateral Variations in Mantle Viscosity......Page 210
Summary......Page 212
References......Page 213
Introduction......Page 216
Nonuniqueness......Page 217
Time-Variable Gravity......Page 218
Changes in the Earth’s Oblateness......Page 219
Gravity Solutions......Page 221
Using the Harmonic Solutions to Solve for Mass......Page 222
Love Numbers......Page 223
Spatial Averaging......Page 224
Smoothing......Page 225
Estimating Errors and Accounting for Leakage......Page 227
Comparing with land surface models......Page 230
Anthropogenic effects and sea-level contributions......Page 231
Cryosphere......Page 232
Solid Earth......Page 234
Oceanography......Page 235
References......Page 237
nomenclature......Page 241
Instantaneous Rotation Vector......Page 245
Celestial Intermediate Pole......Page 250
Earth Rotation Measurement Techniques......Page 254
Optical Astrometric......Page 255
Global navigation satellite system......Page 256
Satellite and lunar laser ranging......Page 257
Doppler orbitography and radio positioning integrated by satellite......Page 258
Intertechnique Combinations......Page 259
UT1 and LOD Variations......Page 260
Secular trend, tidal dissipation,\rand glacial isostatic adjustment......Page 261
Decadal variations and core-mantle interactions......Page 263
Tidal variations and solid Earth, oceanic,\rand atmospheric tides......Page 266
Seasonal variations......Page 269
Interannual variations and the ENSO......Page 270
Intraseasonal variations and the Madden-Julian oscillation......Page 272
True polar wander and GIA......Page 273
Decadal variations, the Markowitz wobble,\r and core-mantle interactions......Page 277
Tidal wobbles and oceanic and atmospheric tides......Page 278
Chandler wobble and its excitation......Page 280
Seasonal wobbles......Page 282
Nonseasonal wobbles......Page 284
References......Page 285
3.10 Earth Rotation Variations......Page 297
nomenclature......Page 298
Manifestations of Variations in Earth Rotation and Orientation......Page 303
Forced Motions......Page 304
Gravitational Perturbations and Displacement Fields......Page 306
Role of Deformations in Earth Rotation......Page 307
Precision of Observations: Challenge to Theory......Page 308
Precession......Page 309
The CIP and CIO......Page 310
Equation of Motion in a Celestial Frame......Page 311
Euler’s equations for a rigid body......Page 312
Potential, Acceleration,\r Torque......Page 313
Torque Components in Terrestrial Frame......Page 314
Expansion of the Potential: Tidal Spectrum......Page 315
Degree 2 Potential and Torque: Spectra......Page 316
Equatorial Components of Torque......Page 317
Terms of General Degree and Order in the Torque......Page 318
The Torque in the Simple Model......Page 319
Nutation and Precession in the Model......Page 320
The Spectrum and the Fundamental Arguments of Nutation......Page 321
Resolution of Elliptical Motions into Pairs of Circular Motions......Page 322
Kinematical Relations between the Nutation of the Figure Axis and the Wobble......Page 324
Kinematic Relations in the Frequency Domain......Page 325
Transfer Function......Page 326
Relations Connecting the Nutations of Different Axes: Oppolzer Terms......Page 327
Rigid Earth Nutation......Page 328
Hamiltonian Approach......Page 329
Torque Approach......Page 330
Rigorous Treatment of the General Case......Page 331
Deformable wholly solid Earth......Page 332
Equations of motion......Page 333
Wobble normal modes......Page 334
Coupling of the Core and the Mantle at the CMB......Page 335
Inclusion of Solid Inner Core......Page 336
Confronting Theory with Observations......Page 337
Poisson equation......Page 340
GSH expansions: Radial functions......Page 341
Motion equation......Page 342
Solutions of the radial equations......Page 344
Atmospheric Tides and Nontidal Effects from Surficial Fluids......Page 345
Nonrotating Origin......Page 346
Transformation between ICRF and ITRF......Page 347
Rotational Normal Mode Definitions......Page 348
Generalized Spherical Harmonics......Page 349
References......Page 350
Introduction......Page 352
The Limitations of Classical Surveying Methods......Page 353
The Impact of Space Geodesy......Page 354
LLR Development......Page 355
SLR Development......Page 356
VLBI Development......Page 357
GPS Development......Page 358
Comparing GPS with VLBI and SLR......Page 360
The Future of GNSS......Page 361
International GNSS Service......Page 362
Basic Principles......Page 364
GPS System Design and Consequences......Page 366
Introducing High-Precision GPS......Page 368
GPS Observable Modeling......Page 369
Data Processing Software......Page 373
Introduction......Page 375
Estimation of Station Velocity......Page 376
Plate-Tectonic Rotations......Page 378
Plate-Boundary Strain Accumulation......Page 380
The Earthquake Cycle......Page 383
Surface Mass Loading......Page 385
References......Page 387
Relevant Websites......Page 391
Motivation......Page 392
History and Overview......Page 394
Scope......Page 397
InSAR......Page 398
The Interferogram......Page 400
Interferometric Baseline and Height Reconstruction......Page 402
Differential Interferometry......Page 404
Correlation......Page 406
ScanSAR or Wide Swath Interferometry......Page 409
Permanent Scatterers and Time-Series Analysis......Page 410
Speckle Tracking and Pixel Tracking......Page 413
A Best-Practices Guide to Using InSAR and Related Observations......Page 414
Interferometric Baseline Errors......Page 415
Propagation Delays......Page 416
Stacking Single-Component Images......Page 419
InSAR Time Series......Page 421
Vector Displacements......Page 422
The Luxury of Sampling - Rationale and Approach......Page 424
Decorrelation as Signal......Page 425
The Link between Science and Mission Design......Page 426
Radar Imaging......Page 429
Matched filtering......Page 430
Radar signal return from a 3-D surface......Page 432
Azimuth signal and aperture synthesis......Page 433
Range-Doppler images......Page 436
Other Doppler considerations......Page 437
The sampled azimuth spectrum and range migration......Page 439
Speckle......Page 440
Doppler and the Interferometric Baseline......Page 443
References......Page 444