Gravity and Low-Frequency Geodynamics (eBook)

Front Cover 1
Gravity and Low-Frequency Geodynamics 4
Copyright Page 5
Table of Contents 10
Preface to the Series Physics and Evolution of the Earth's Interior 6
Preface 8
Chapter 1. The Earth's Gravity Field 14
1.1 Introduction 14
1.2 Properties of the gravitational potential 15
1.3 The Green–Gauss identities 22
1.4 The Earth's gravity field and the Stokes formula 24
1.5 Decomposition of the gravitational potential into spherical harmonics 27
1.6 The Earth's inertia tensor 40
1.7 The geoid 43
1.8 Gravimetric reductions, isostasy and gravity anomalies 50
1.9 Molodensky boundary-value problem 55
References 87
Chapter 2. Space Geodesy Methods 91
2.1 Dynamic of satellite motion 91
2.2. Gravity field parameters from changes of orbits 98
2.3 Direct sounding of the geopotential 100
2.4 Geodetic positioning by satellites 101
2.5 New space methods 105
2.6 Very Long Base Interferometry (VLBI) 115
References 120
Chapter 3. The Hydrostatic Figure of the Earth 124
3.1 Introduction 124
3.2 The figure of the Earth deduced from satellite data 127
3.3 The symmetry of equilibrium figures 138
3.4 The Clairaut–Laplace internal field theory 144
3.5 Foundation of the theory of figures 175
3.6 On the hydrostatic flattening of the Earth and some geophysical implications 179
References 193
Chapter 4. The Earth's Rotation 200
4.1 Historical evolution of the problem—Rotation and observations 200
4.2 Principles and fundamental concepts 208
4.3 Deformation of the global Earth 221
4.4 Expression for the inner relations—Constitutive equations 231
4.5 Systems of equations 250
4.6 Tesseral movements, free and forced 257
4.7 Study of precession and nutations 272
4.8 Axial rotation—Rotation and geophysical problems 289
4.9 Numerical Love numbers 302
4.10 Conclusion 304
References 304
Chapter 5. Observational Determinations of the Earth's Rotation 308
Introduction 308
5.1 Historical evolution of observational determination of the Earth's rotation 309
5.2 Methods of observations 311
5.3 Time scales 338
5.4 References coordinate systems 347
5.5 Results of analysis of the Earth's rotation parameters determined observationally 352
References 366
Chapter 6. Free Oscillations of the Earth 375
6.1 Introduction 375
6.2 Free oscillations of a homogeneous liquid sphere 375
6.3 SNREI model 379
6.4 Excitation of free oscillations 388
6.5 Effect of general aspherical perturbation on the free oscillations 393
6.6 Generalized spherical harmonics approach 405
6.7 Oscillations of the Earth's fluid core 408
6.8 Inversion of the free oscillation data 416
References 425
Chapter 7. Earth Tides 429
References 450
Chapter 8. Gravity and Reference Models 451
8.1 Reference ellipsoid 451
8.2 Combined solutions 456
8.3 Geophysical interpretation 462
References 469
Chapter 9. Fundamental Systems of Astronomical and Geodetical Constants 472
9.1 Introduction 472
9.2 The IAU System of Astronomical Constants 477
9.3 Geodetic Reference Systems 478
9.4 MERIT Standards 482
References 488
Index 490