Preface and acknowledgments .................................... xi
The book website www.cambridge.org/smylie .................... xiii
1 Introduction and theoretical background ...................... 1
1.1 Scalar, vector and tensor analysis ...................... 1
1.2 Separation of vector fields ............................ 25
1.3 Vector spherical harmonics ............................. 27
1.4 Elasticity theory ...................................... 33
1.5 Linear algebraic systems ............................... 74
1.6 Interpolation and approximation ........................ 79
2 Time sequence and spectral analysis ......................... 93
2.1 Time domain analysis ................................... 94
2.2 Linear optimum Wiener filters ......................... 105
2.3 Frequency domain analysis ............................. 119
2.4 Fourier series and transforms ......................... 154
2.5 Power spectral density estimation ..................... 171
2.6 Maximum entropy spectral analysis ..................... 198
3 Earth deformations ......................................... 212
3.1 Equilibrium equations ................................. 212
3.2 The reciprocal theorem of Betti ....................... 215
3.3 Radial equations: spheroidal and torsional ............ 217
3.4 Dynamical equations ................................... 223
3.5 Solutions near the geocentre .......................... 231
3.6 Numerical integration of the radial equations ......... 245
3.7 Fundamental, regular solutions in the inner core ...... 256
4 Earth's rotation: observations and theory .................. 273
4.1 Reference frames ...................................... 273
4.2 Polar motion and wobble ............................... 274
4.3 The dynamics of polar motion and wobble ............... 294
4.4 Nutation and motion of the celestial pole ............. 307
5 Earth's figure and gravitation ............................. 323
5.1 Historical development ................................ 323
5.2 External gravity and figure ........................... 325
5.3 Equilibrium theory of the internal figure ............. 341
5.4 Gravity coupling ...................................... 371
6 Rotating fluids and the outer core ......................... 386
6.1 The inertial wave equation ............................ 386
6.2 Dynamics of the fluid outer core ...................... 398
6.3 Scaling of the core equations ......................... 407
6.4 Compressibility and density stratification ............ 412
7 The subseismic equation and boundary conditions ............ 420
7.1 The subseismic wave equation .......................... 420
7.2 Deformation of the shell and inner core ............... 423
8 Variational methods and core modes ......................... 445
8.1 A subseismic variational principle .................... 445
8.2 Representation of the functional ...................... 450
8.3 Finite element support functions ...................... 453
8.4 Boundary conditions and constraints ................... 456
8.5 Numerical implementation and results .................. 459
8.6 Rotational splitting and viscosity .................... 467
8.7 A viscosity profile for the outer core ................ 478
9 Static deformations and dislocation theory ................. 482
9.1 The elasticity theory of dislocations ................. 482
9.2 The theory for realistic Earth models ................. 497
9.3 Changes in the inertia tensor and the secular polar
shift ................................................. 509
Appendix A Elementary results from vector analysis ........... 514
A.l Vector identities ..................................... 514
A.2 Vector calculus identities ............................ 514
A.3 Integral theorems ..................................... 516
Appendix В Properties of Legendre functions .................. 517
B.1 Recurrence relations .................................. 518
В.2 Evaluation of Legendre functions ...................... 519
Appendix С Numerical Earth models ............................ 522
C.1 The Earth models ...................................... 522
References .................................................... 531
Fortran index ................................................. 536
Subject index ................................................. 537
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