Deformations of an Elastic Earth (eBook)

Front Cover 1
Deformations of an Elastic Earth 4
Copyright Page 5
Contents 8
Preface 12
Chapter I. Concepts of Physical Geodesy 18
1.00 Introduction 18
1.01 Differential Geometry of a Surface of Revolution 19
1.02 Some Properties of the Ellipse. Definition of Ellipsoidal Coordinates 24
1.03 Potential of the Ellipsoid Expressed in Terms of Ellipsoidal Coordinates 28
1.04 Normal Gravity 31
1.05 Some Series Expansions and the Gravity Formula 34
1.06 Potential of the Ellipsoid Expressed by Means of Spherical Harmonics 36
1.07 Stokes Formula for Geoidal Heights 38
1.08 Deflection of the Vertical and the Formula of Vening-Meinesz 43
1.09 Computational Techniques 47
1.10 Determination of the Geoid by Astrogeodetic Methods: Helmert Formula and Shift in Geodetic Datum 52
Chapter II. Hydrostatic Equilibrium and Earth Density Models 58
2.00 Introduction 58
2.01 Equilibrium Configuration of a Rotating Body of Arbitrary Density 59
2.02 Clairaut Equation Expressed up to Third-Order Terms 64
2.03 Exterior Potential and Moments of Inertia 69
2.04 Density Distortion Generated by Rotation 71
2.05 Considerations on Earth Density Models 75
2.06 Introduction to Numerical Methods 93
2.07 Numerical Solution of the Clairaut Equation for Various Earth Models 95
2.08 Determination of the Exterior Potential by Methods of Celestial Mechanics 100
Chapter III. Elastic Deformations of a Rotating Earth Caused by Surface Loads 108
3.00 Introduction 108
3.01 Linearized Navier–Stokes Equations 109
3.02 Analytic Preliminaries 114
3.03 Spheroidal Deformations 119
3.04 Regularity Conditions for the Solutions at the Center When µ . 0 and n . 0 124
3.05 Fundamental Equations of Motion for Some Limiting Cases 127
3.06 Boundary Conditions. Love and Load Numbers. Toroidal Deformations 130
Chapter IV. Solution of the Linearized Navier–Stokes Equations 136
4.00 Introduction 136
4.01 Boussinesq Theory for an Elastic Flat Plate 137
4.02 Asymptotic Behavior of the Load Numbers 142
4.03 Poisson Sum of Certain Legendre Series. Evaluation of the Stokes Series 146
4.04 Computation of the Spheroidal Deformations of the Earth 150
4.05 Dynamics of the Liquid Core 153
4.06 Numerical Results 165
Chapter V. Precessional and Nutational Motions of a Rigid Earth 174
5.00 Introduction 174
5.01 Motion of a Rigid Earth about Its Center of Gravity 175
5.02 Precession and Nutation of the Rotational Axis 178
5.03 Eulerian Motion and Lunisolar Perturbations 182
5.04 Development of the Disturbing Function. Motion of the Ecliptic and Equinox of Date 187
5.05 Solution of the Poisson Equations in Terms of the Lunar and Solar Theories 194
5.06 Dynamics of a System of Two Rigid Bodies of Comparable Size 199
Chapter VI. Ocean Tides 207
6.00 Introduction 207
6.01 Laplace Tidal Equations 207
6.02 Darwin’s Power Series Solutions 210
6.03 Hough’s Solutions in Spherical Harmonics 214
6.04 Potential of the Tide-Generating Forces 219
6.05 Some Considerations on the Lunar Orbit 222
6.06 Classification of Tides 226
6.07 Evaluation of the Global Ocean Tides as a Boundary-Value Problem 229
6.08 Computational Techniques 231
References 234
Index 238
Internationl Geophysics Series 244