Sciences of Geodesy - I (eBook)

Preface 4
Contents 15
Contributors 22
1 Absolute and Relative Gravimetry 24
1.1 Introduction 24
1.2 Characteristics of Absolute Gravimetry 25
1.2.1 General Aspects 25
1.2.2 Objectives of Geo-scientific and State-geodetic Surveys 26
1.3 Measurements with Free-Fall Absolute Gravimeters 28
1.3.1 Principles of FG5 Gravimeters 29
1.3.2 Observation Equation 30
1.3.3 Operational Procedures with FG5-220 32
1.3.4 Accuracy and Instrumental Offset 35
1.4 Relative Gravimetry 41
1.4.1 Principles of Spring Gravimeters 42
1.4.2 Observation Equation 44
1.4.3 Regional and Local Surveys with Scintrex SC-4492 45
1.4.4 Microgravimetric Measurements 49
1.4.5 Instrumental Drift 51
1.5 Reduction of Non-tectonic Gravity Variations 53
1.5.1 Earth's Body and Ocean Tides 54
1.5.2 Polar Motion 57
1.5.3 Atmospheric Mass Movements 60
1.5.4 Groundwater Variations 61
1.6 Gravity Changes: Examples 61
1.6.1 Hydrology: Groundwater Variations in Hannover 62
1.6.2 Tectonics: Isostatic Land Uplift in Fennoscandia 63
References 66
2 Adaptively Robust Kalman Filters with Applications in Navigation 72
2.1 Introduction 73
2.2 The Principle of Adaptively Robust Kalman Filtering 76
2.3 Properties of the Adaptive Kalman Filter 79
2.3.1 Difference of State Estimate 79
2.3.2 The Expectation of the State Estimate of the Adaptive Filter 80
2.3.3 Posterior Precision Evaluation 81
2.4 Three Kinds of Learning Statistics 83
2.4.1 Learning Statistic Constructed by State Discrepancy 83
2.4.2 Learning Statistic Constructed by Predicted Residual Vector 84
2.4.3 Learning Statistic Constructed by the Ratio of Variance Components 85
2.4.4 Learning Statistic Constructed by Velocity 86
2.5 Four Kinds of Adaptive Factors 86
2.5.1 Adaptive Factor by Three-Segment Function 86
2.5.2 Adaptive Factor by Two-Segment Function 87
2.5.3 Adaptive Factor by Exponential Function 87
2.5.4 Adaptive Factor by Zero and One 88
2.5.5 Actual Computation and Analysis 89
2.6 Comparison of Two Fading Filters and Adaptively Robust Filter 91
2.6.1 Principles of Two Kinds of Fading Filters 92
2.6.2 Comparison of Fading Filter and Adaptive Filter 94
2.6.3 Actual Computation and Analysis 95
2.7 Comparison of Sage Adaptive Filter and Adaptively Robust Filter 97
2.7.1 IAE Windowing Method 97
2.7.2 RAE Windowing Method 98
2.7.3 The Problems of the Windowing Estimation for Covariance Matrix of Kinematic Model 99
2.8 Some Application Examples 100
References 103
3 Airborne Gravity Field Determination 106
3.1 Introduction 106
3.2 Principles of Airborne Gravimetry 108
3.3 Filtering of Airborne Gravity 112
3.4 Some Results of Large-Scale Government Airborne Surveys 114
3.5 Downward Continuation of Airborne Gravimetry 116
3.6 Use of Airborne Gravimetry for Geoid Determination 119
3.6.1 Case Story of Mongolian Geoid 120
3.7 Conclusions and Outlook 124
References 126
4 Analytic Orbit Theory 128
4.1 Introduction 128
4.2 Perturbed Equation of Satellite Motion 130
4.2.1 Lagrangian Perturbed Equation of Satellite Motion 131
4.2.2 Gaussian Perturbed Equation of Satellite Motion 133
4.2.3 Keplerian Motion 135
4.3 Singularity-Free and Simplified Equations 135
4.3.1 Problem of Singularity of the Solutions 136
4.3.2 Disturbed Equations in the Case of Circular Orbit 137
4.3.3 Disturbed Equations in the Case of Equatorial Orbit 138
4.3.4 Disturbed Equations in the Case of Circular and Equatorial Orbit 138
4.3.5 Singularity-Free Disturbed Equations of Motion 139
4.3.6 Simplified Singularity-Free Disturbed Equations of Motion 140
4.3.7 Singularity-Free Gaussian Equations of Motion 140
4.4 Solutions of Extraterrestrial Disturbances 141
4.4.1 Key Notes to the Problems 141
4.4.2 Solutions of Disturbance of Solar Radiation Pressure 142
Three Approximations 142
Discretisation and Solution 143
Properties of the Solution 144
4.4.2.1 Solutions via Gaussian Perturbed Equations 144
Gaussian Perturbed Equations 144
Characters of Gaussian Perturbed Equations 146
Solutions of Gaussian Perturbed Equations 147
Properties of the Solution 149
4.4.3 Solutions of Disturbance of Atmospheric Drag 149
4.4.3.1 Solutions via Gaussian Perturbed Equations 150
Air Drag Force Vector for Gaussian Perturbed Equations 150
Gaussian Perturbed Equations and the Solutions 151
4.4.4 Solutions of Disturbance of the Sun 152
Potential Function of the Sun 152
Disturbed Equation of Motion and the Solutions 153
4.4.5 Solutions of Disturbance of the Moon 157
Discretisation and Solution 158
4.4.6 Solutions of Disturbance of Planets 159
4.4.7 Summary 159
4.5 Solutions of Geopotential Perturbations 159
Principle of the Derivations 160
4.6 Principle of Numerical Orbit Determination 164
Limitations of the Numerical Orbit Determination 166
4.7 Principle of Analytic Orbit Determination 167
Real-Time Ability of Analytic Orbit Determination 169
Properties of Analytic Orbit Determination 169
Initial Time Selection 169
Using General Models for Second-Order Geopotential Disturbances 169
4.8 Summary and Discussions 170
Summary 170
Discussions 170
Simplified Singularity-Free Equations of Motion 170
Analytic Solution vs. Numeric Solution 171
Potential Functions of the Sun, Moon and Planets 171
Confusion of Non-conservative Force with Conservative Effect 171
Long-Term Effects in Extraterrestrial Disturbances 172
Long-Term and Long Periodic Effects in Short Periodic Disturbances 172
Further Studies 172
References 172
5 Deformation and Tectonics: Contribution of GPS Measurements to Plate Tectonics -- Overview and Recent Developments 178
5.1 Introduction 178
5.2 Plate Tectonic Models 181
5.3 Mapping Issues 185
5.4 Geophysical Corrections for the GPS-Derived Station Positions 190
5.5 Time-Series Analysis 192
5.6 GPS and Geodynamics An Example 197
5.7 Further Developments 202
References 203
6 Earth Rotation 208
6.1 Reference Systems 209
6.2 Polar Motion 214
6.3 Variations of Length-of-Day and UT 218
6.4 Physical Model of Earth Rotation 221
6.4.1 Balance of Angular Momentum in the Earth System 221
6.4.1.1 Angular Momentum Approach 224
6.4.1.2 Torque Approach 225
6.4.2 Solid Earth Deformations 226
6.4.2.1 Rotational Deformations 227
6.4.2.2 Deformations Due to Surface Loads 231
6.4.3 Solution of the Euler--Liouville Equation 235
6.4.3.1 Linear Analytical Approach 236
6.4.3.2 Non-linear Numerical Approach 238
6.5 Relation Between Modelled and Observed Variations of Earth Rotation 241
References 244
7 Equivalence of GPS Algorithms and Its Inference 251
7.1 Introduction 252
7.2 Equivalence of Undifferenced and Differencing Algorithms 253
7.2.1 Introduction 254
7.2.2 Formation of Equivalent Observation Equations 254
7.2.3 Equivalent Equations of Single Differences 256
7.2.4 Equivalent Equations of Double Differences 259
7.2.5 Equivalent Equations of Triple Differences 261
7.2.6 Method of Dealing with the Reference Parameters 262
7.2.7 Summary of the Unified Equivalent Algorithm 263
7.3 Equivalence of the Uncombined and Combining Algorithms 264
7.3.1 Uncombined GPS Data Processing Algorithms 264
7.3.1.1 Original GPS Observation Equations 264
7.3.1.2 Solutions of Uncombined Observation Equations 265
7.3.2 Combining Algorithms of GPS Data Processing 266
7.3.2.1 General Combinations 268
7.3.3 Secondary GPS Data Processing Algorithms 268
7.3.3.1 In the Case of More Satellites in View 268
7.3.3.2 GPS Data Processing Using Secondary ''Observations'' 270
7.3.3.3 Precision Analysis 271
7.3.4 Summary of the Combining Algorithms 271
7.4 Parameterisation of the GPS Observation Model 271
7.4.1 Evidence of the Parameterisation Problem of the Undifferenced Observation Model 272
7.4.1.1 Evidence from Undifferenced and Differencing Algorithms 272
7.4.1.2 Evidence from Uncombined and Combining Algorithms 273
7.4.1.3 Evidence from Practice 273
7.4.2 A Method of Uncorrelated Bias Parameterisation 273
7.4.3 Geometry-Free Illustration 279
7.4.4 Correlation Analysis in the Case of Phase--Code Combinations 280
7.4.5 Conclusions and Comments on Parameterisation 281
7.5 Equivalence of the GPS Data Processing Algorithms 282
7.5.1 Equivalence Theorem of GPS Data Processing Algorithms 282
7.5.2 Optimal Baseline Network Forming and Data Condition 285
7.5.3 Algorithms Using Secondary GPS Observables 286
7.5.4 Non-equivalent Algorithms 288
7.6 Inferences of Equivalence Principle 288
7.6.1 Diagonalisation Algorithm 288
7.6.2 Separability of the Observation Equation 290
7.6.3 Optimal Ambiguity Search Criteria 291
7.7 Summary 293
References 293
8 Marine Geodesy 296
8.1 Introduction 296
8.2 Bathymetry and Hydrography 297
8.2.1 Scope of Work 297
8.2.1.1 Echo Soundings of Oceans and Coastal Waters 298
8.2.1.2 Seafloor Maps 299
8.2.1.3 Scientific Investigations 299
8.2.1.4 Boundary Demarcation and Determination 300
8.2.2 Hydroacoustic Measurements 302
8.2.2.1 Basic Principles 302
8.2.2.2 Singlebeam Echo Sounders 304
8.2.2.3 Multibeam Echo Sounders 305
8.2.2.4 Side-Scan Sonar 306
8.2.2.5 Sub-bottom Profilers 307
8.3 Precise Navigation 309
8.3.1 Maps of Coastal Waters and Approach Channels 309
8.3.2 ENC and ECDIS 309
8.3.3 Ship's Attitude 310
8.3.4 Hydrodynamics of Ships 312
8.3.4.1 Basics of Squat 313
8.3.4.2 SHIPS Method 314
8.3.4.3 Squat and Trim 318
8.4 Conclusion 319
References 319
9 Satellite Laser Ranging 321
9.1 Background 321
9.1.1 Introduction 322
9.1.2 Basic Principles 323
9.2 Range Model 326
9.2.1 Atmospheric Delay Correction 328
9.2.2 Centre-of-Mass Correction 331
9.2.3 SLR Station Range and Time Bias 333
9.2.4 Relativistic Range Correction 336
9.3 Force and Orbital Model 337
9.3.1 Introduction 337
9.3.2 Orbital Modelling 338
9.3.3 Force Model 338
9.3.3.1 Gravitational Perturbations 339
9.3.3.2 Temporal Changes of the Gravity Field 342
9.3.3.3 Three-Body Perturbing Acceleration 343
9.3.3.4 General Relativity Contribution to the Perturbing Force 343
9.3.3.5 Atmospheric Drag 344
9.3.3.6 Solar Radiation Pressure 344
9.3.3.7 Earth Radiation Pressure 345
9.3.3.8 Other Forces 346
9.3.3.9 Empirical Forces 346
9.4 Calculated Range 346
9.5 SLR System and Logistics 348
9.5.1 System Configuration 349
9.5.1.1 Laser Assembly 349
9.5.1.2 Tracking and Mount Control 351
9.5.1.3 Data Measurement 352
9.5.1.4 Timing 353
9.5.1.5 Controller 354
9.5.1.6 Processor 354
9.5.1.7 Safety 354
9.6 Network and International Collaboration 354
9.6.1 Tracking Network 355
9.6.2 International Laser Ranging Service 355
9.7 Summary 356
References 356
10 Superconducting Gravimetry 359
10.1 Introduction 360
10.2 Description of the Instrument 363
10.2.1 Gravity Sensing Unit 364
10.2.2 Tilt Compensation System 366
10.2.3 Dewar and Compressor 366
10.2.4 Gravimeter Electronic Package 367
10.2.5 SG Performance 367
10.3 Site Selection and Observatory Design 368
10.4 Calibration of the Gravity Sensor 371
10.4.1 Calibration Factor 371
10.4.2 Phase Shift 374
10.5 Noise Characteristics 375
10.5.1 Noise Magnitude 375
10.5.2 Noise Caused by Misaligned Instrumental Tilt 377
10.6 Modelling of the Principal Constituents of the Gravity Signal 378
10.6.1 Theoretical Earth Tides and Tidal Acceleration 380
10.6.2 Gravity Variations Induced by the Atmosphere 384
10.6.2.1 Empirical Methods 385
10.6.2.2 Physical Models 388
10.6.3 Hydrology-Induced Gravity Variation 392
10.6.3.1 Bouguer Plate Model 393
10.6.3.2 Precipitation Model 393
10.6.3.3 Single Admittance Model 394
10.6.3.4 Global Hydrological Models 395
10.6.4 Ocean Tide Loading Gravity Effect 398
10.6.4.1 Ocean Tide Loading Correction of the Tidal Parameters 399
10.6.5 Polar Motion 401
10.6.6 Instrumental Drift 403
10.7 Analysis of Surface Gravity Effects 403
10.7.1 Pre-processing 404
10.7.2 Earth Tides 405
10.7.2.1 Program ANALYZE 406
10.7.2.2 Program BAYTYP-G 407
10.7.2.3 Program VAV 409
10.7.2.4 Analysis Results 409
10.7.3 Nearly Diurnal-Free Wobble 411
10.7.4 Polar Motion 413
10.7.5 Free Oscillation of the Earth 413
10.7.6 Translational Oscillations of the Inner Core (Slichter Triplet) 415
10.7.7 Co-seismic Gravity Change 416
10.7.8 Gravity Residuals 418
10.8 Combination of Ground (SG) and Space Techniques 419
10.8.1 Combination of SG and GPS Measurements 420
10.8.2 Comparison of SG, GRACE and Hydrological Models-Derived Gravity Variations 420
10.8.2.1 Preparing of the Data Sets 421
10.8.2.2 Comparing Results 424
10.9 Future Applications 425
References 426
11 Synthetic Aperture Radar Interferometry 434
11.1 Introduction 434
11.2 Synthetic Aperture Radar Imaging 435
11.2.1 Radar Transmitted and Received Signal 437
11.2.2 Impulse Response of SAR 439
11.2.3 Pulse Compression (Focus) and Doppler Frequency 440
11.2.3.1 Range Compression 440
11.2.3.2 Azimuth Compression 441
11.2.4 Spotlight Mode 442
11.2.5 ScanSAR Mode 445
11.3 SAR Interferometry 446
11.3.1 Principle of SAR Interferometry 448
11.3.2 Phase Unwrapping 451
11.3.2.1 Least-Squares Method 452
11.3.2.2 Branch Cuts Method 454
11.3.2.3 Minimizing Cost Flow Method 455
11.3.3 Image Registration 457
11.3.4 Coherence of SAR Images 458
11.4 Differential SAR Interferometry 459
11.4.1 Principle of D-INSAR 459
11.4.2 Persistent Scatterer SAR Interferometry 460
11.4.2.1 Selection of Master Image 461
11.4.2.2 Generation of Differential Interferograms 461
11.4.2.3 Modelling of Differential Interferometric Phase 461
11.4.2.4 Preliminary Estimation of Persistent Scatterer Candidates (PSCs) 462
11.4.2.5 Estimation of Linear Deformation 463
11.4.3 Example: Coseismic Deformation Measurement of Bam Earthquake 464
11.4.3.1 Radar Data 464
11.4.3.2 Baseline Estimation 464
11.4.3.3 Interferogram and Elevation Model 466
11.4.3.4 Differential Interferometry and Surface Deformation 466
11.4.3.5 Determination of the Location and Shape of the Ruptured Fault 468
11.4.3.6 Estimation of the Theoretical Model for the Earthquake Source 470
11.4.4 Example: Subsidence Monitoring in Tianjin Region 471
11.5 SAR Interferometry with Corner Reflectors (CR-INSAR) 472
11.5.1 Orientation of the Corner Reflectors 474
11.5.2 Interpolation Kernel Design and Co-registration 474
11.5.3 Phase Pattern of Flat Terrain 475
11.5.4 Elevation-Phase-Relation Matrix Ch and Phase Unwrapping 477
11.5.5 Differential Interferogram Modelling 478
11.5.6 CR-INSAR Example: Landslide Monitoring in Three Gorges Area 480
11.6 High-Resolution TerraSAR-X 487
References 492
Index 494