Introduction to Theoretical Geophysics

I Introduction.- 1. Mathematical Considerations.- 1.1 Vector Analysis.- 1.2 Curvilinear Coordinates.- 1.3 Vector Relations in Curvilinear Coordinates.- 1.4 Spherical Coordinates.- 1.5 Cylindrical Coordinates.- 1.6 Legendre Polynomials.- 1.7 Laplace's Equation.- 1.8 Fourier Series.- 1.9 Fourier Integrals.- 1.10 Wave Equation.- 1.11 Associated Legendre Polynomials.- 1.12 Bessel Functions.- 1.13 Velocity and Acceleration Referred to Moving Axes.- References.- II Thermodynamics and Hydrodynamics.- 2. Thermodynamics of the Earth.- 2.1 Thermodynamics.- 2.2 Implicit Functions in Thermodynamics.- 2.3 Gravitational Adiabatic Equilibrium.- 2.4 Heat Conduction Equation.- 2.5 Periodic Flow of Heat.- 2.6 Heat Flow.- 2.7 Internal Heat of the Earth.- References.- 3. Hydrodynamics.- 3.1 Kinematic Preliminaries.- 3.2 Conjugate Functions.- 3.3 Equation of Continuity.- 3.4 Equation of Motion.- 3.5 Kelvin's Circulation Theorem.- 3.6 Equation of Motion of a Viscous Fluid.- References.- 4. Physical Oceanography-Circulation.- 4.1 Thermodynamic Circulation.- 4.2 Continuity, Mixing, and Diffusion.- 4.3 Ocean Mixing.- 4.4 Estuary Mixing.- 4.5 Equation of Motion and Circulation Theorem.- 4.6 Pressure Gradient and Geostrophic Effects.- 4.7 Inertia Effects.- 4.8 Equation of Motion with Internal Friction.- 4.9 Friction and Geostrophic Effects.- 4.10 Friction, Geostrophic, and Pressure Gradient Effects.- 4.11 Wind-Driven Ocean Circulation.- References.- 5. Physical Oceanography-Waves and Tides.- 5.1 Tidal Waves.- 5.2 Driven Tidal Waves.- 5.3 Seiches.- 5.4 Geostrophic Effects on Tidal Waves.- 5.5 Internal Tidal Waves.- 5.6 Surface Waves.- 5.7 Permanent Waves.- 5.8 Waves Due to a Local Disturbance.- 5.9 Equilibrium Theory of the Tides.- 5.10 Dynamical Theory of the Tides.- References.- III Seismology, Gravity, and Magnetism.- 6. Seismology-Ray Theory.- 6.1 Dynamics.- 6.2 Bodily Elastic Waves.- 6.3 Reflection and Refraction of Elastic Waves.- 6.4 Development of Solution in Terms of Rays.- 6.5 Ray Characteristics for a Flat Earth.- 6.6 Ray Characteristics for a Spherically Stratified Earth.- References.- 7. Seismology-Wave Theory.- 7.1 Normal Modes.- 7.2 Dispersion.- 7.3 Dispersive Normal Modes.- 7.4 Rayleigh Waves.- 7.5 Love Waves.- References.- 8. Gravity.- 8.1 Fundamental Relations.- 8.2 Gauss' Law and Green's Equivalent Layer.- 8.3 Gravitational Potential and Attraction for an Ellipsoidal Earth.- 8.4 Geocentric and Geographic Latitude.- 8.5 Deviations of the Geoid from a Reference Ellipsoid.- 8.6 Deflection of the Vertical.- 8.7 Gravity Corrections and Gravity Anomalies.- 8.8 Internal Mass Distribution of the Earth.- References.- 9. Geomagnetism.- 9.1 Electromagnetism.- 9.2 Earth's Main Magnetic Field.- 9.3 Electromagnet Theory.- 9.4 Internal and Atmospheric Dynamos.- 9.5 Electromagnetic Induction in the Earth.- References.- IV Dynamics of the Earth.- 10. Earth Motion, Rotation, and Deformation.- 10.1 Motion under an Inverse Square Force of Attraction.- 10.2 Precession of the Equinoxes.- 10.3 Gyroscopic Compass.- 10.4 Eulerian Free Motion.- 10.5 Marine Tides.- 10.6 Earth Tides.- 10.7 Chandler Wobble.- 10.8 Tidal Friction.- 10.9 Free Oscillations of the Earth.- References.- 11. Earth Crustal and Mantle Deformation.- 11.1 Introduction.- 11.2 Loading of an Elastic Crust.- 11.3 Loading of a Floating Lithosphere.- 11.4 Postglacial Uplift.- 11.5 Thermal Contraction of the Earth.- 11.6 Thermal Convection Currents in the Mantle.- References.