دانلود کتاب A Student’s Guide to Geophysical Equations

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Contents
Preface
Acknowledgments
1 Mathematical background
1.1 Cartesian and spherical coordinates
1.2 Complex numbers
1.3 Vector relationships
1.3.1 Scalar and vector products
1.3.2 Vector differential operations
1.4 Matrices and tensors
1.4.1 The rotation matrix
1.4.2 Eigenvalues and eigenvectors
1.4.3 Tensor notation
1.4.4 Rotation of coordinate axes
1.4.5 Vector differential operations in tensor notation
1.5 Conservative force, field, and potential
1.6 The divergence theorem (Gauss’s theorem)
1.7 The curl theorem (Stokes’ theorem)
1.8 Poisson’s equation
1.9 Laplace’s equation
1.10 Power series
1.10.1 MacLaurin series
1.10.2 Taylor series
1.10.3 Binomial series
Finite series
Infinite series
1.10.4 Linear approximations
1.11 Leibniz’s rule
1.12 Legendre polynomials
1.13 The Legendre differential equation
1.13.1 Orthogonality of the Legendre polynomials
1.13.2 Normalization of the Legendre polynomials
1.14 Rodrigues’ formula
1.15 Associated Legendre polynomials
1.15.1 Orthogonality of associated Legendre polynomials
1.15.2 Normalization of associated Legendre polynomials
1.16 Spherical harmonic functions
1.16.1 Normalization of spherical harmonic functions
1.16.2 Zonal, sectorial, and tesseral spherical harmonics
1.17 Fourier series, Fourier integrals, and Fourier transforms
1.17.1 Fourier series
1.17.2 Fourier integrals and Fourier transforms
1.17.3 Fourier sine and cosine transforms
Further reading
2 Gravitation
2.1 Gravitational acceleration and potential
2.2 Kepler’s laws of planetary motion
2.2.1 Kepler’s Second Law
2.2.2 Kepler’s First Law
2.2.3 Kepler’s Third Law
2.3 Gravitational acceleration and the potential of a solid sphere
2.3.1 Outside a solid sphere, using Laplace’s equation
2.3.2 Inside a solid sphere, using Poisson’s equation
2.4 Laplace’s equation in spherical polar coordinates
2.4.1 Azimuthal (longitudinal) solution
2.4.2 Polar (latitudinal) solution for rotational symmetry
2.4.3 Radial solution
2.4.4 Solution of Laplace’s equation for rotational symmetry
2.4.5 General solution of Laplace’s equation
2.5 MacCullagh’s formula for the gravitational potential
2.5.1 Gravitational potential of a spheroid
2.5.2 MacCullagh’s formula and the figure of the Earth
Further reading
3 Gravity
3.1 The ellipticity of the Earth’s figure
3.2 The geopotential
3.2.1 Gravitational potential
3.2.2 Centrifugal potential
3.3 The equipotential surface of gravity
3.3.1 Relationship of J2, J4, f, and m
3.3.2 Inferred increase of density with depth in the Earth
3.4 Gravity on the reference spheroid
3.4.1 Polar component of gravity
3.4.2 Radial component of gravity
3.4.3 Variation of reference gravity with geocentric latitude
3.4.4 Clairaut’s formula
3.5 Geocentric and geographic latitude
3.5.1 Normal gravity on the reference ellipsoid
3.6 The geoid
3.6.1 The potential of a geoid undulation
3.6.2 Stokes’ formula for the height of the geoid
3.6.3 Evaluation of the function F(θ)
Further reading
4 The tides
4.1 Origin of the lunar tide-raising forces
4.2 Tidal potential of the Moon
4.2.1 Significance of individual terms in the lunar potential
Potential W0
Potential W1
Potential W2
Potential W3
4.2.2 The lunar tide-raising acceleration
4.2.3 The solar tide-raising acceleration
4.3 Love’s numbers and the tidal deformation
4.3.1 Tidal height
4.3.2 Tidal gravity anomaly
4.3.3 Tidal deflection of the vertical
4.3.4 Satellite-derived values for k, h, and l
4.4 Tidal friction and deceleration of terrestrial and lunar rotations
4.4.1 Angular momentum of the Earth–Moon system
4.4.2 Slowing of terrestrial and lunar rotations
4.4.3 Development of the Earth–Moon separation
Further reading
5 Earth’s rotation
5.1 Motion in a rotating coordinate system
5.1.1 Velocity
5.1.2 Acceleration
5.2 The Coriolis and Eötvös effects
5.2.1 Vertical component: the Eötvös effect
5.2.2 Horizontal component: the Coriolis effect
5.3 Precession and forced nutation of Earth’s rotation axis
5.3.1 Effects of the torque due to the Sun’s attraction
5.3.2 Comparison of vectors in the coordinate systems of Earth and Sun
5.3.3 Computation of the Sun’s torque on the Earth
5.3.4 Equations of solar-induced precession and nutation
5.3.5 Simplification of the equations of motion
5.3.6 Precession and nutation induced by the Sun
5.3.7 Precession and nutation induced by the Moon
5.3.8 Nutation due to precession of the Moon’s orbit
5.4 The free, Eulerian nutation of a rigid Earth
5.5 The Chandler wobble
5.5.2 Computation of the products of inertia
5.5.3 Comparison of the wobble potential with MacCullagh’s formula
5.5.4 Period of the Chandler wobble
5.5.5 Calculation of Love’s number k from the period of the Chandler wobble
Further reading
6 Earth’s heat
6.1 Energy and entropy
6.2 Thermodynamic potentials and Maxwell’s relations
6.2.1 Thermodynamic potentials
6.3 The melting-temperature gradient in the core
6.4 The adiabatic temperature gradient in the core
6.5 The Grüneisen parameter
6.5.1 Temperature and density in the Earth
6.6 Heat flow
6.6.1 The heat-flow equation
6.6.2 The thermal-conduction equation
6.6.3 Penetration of solar heat in the Earth
6.6.4 Cooling of a semi-infinite half-space
6.6.5 Cooling of oceanic lithosphere
Further reading
7 Geomagnetism
7.1 The dipole magnetic field and potential
7.2 Potential of the geomagnetic field
7.2.1 The fields of internal and external origin
7.2.2 Determination of the Gauss coefficients
7.3 The Earth’s dipole magnetic field
7.3.1 The geocentric axial dipole
7.3.2 The geocentric inclined dipole
7.3.3 Axial dipole with axial offset
7.3.4 Axial dipole with equatorial offset
7.3.5 Best-fitting eccentric inclined dipole
7.4 Secular variation
7.5 Power spectrum of the internal field
7.5.1 Estimation of the source depth of the main field
7.6 The origin of the internal field
7.6.1 Electromagnetic model
7.6.2 The magnetohydrodynamic model
7.6.3 The frozen-flux theorem
Further reading
8 Foundations of seismology
8.1 Elastic deformation
8.2 Stress
8.2.1 Symmetry of the stress tensor
8.2.2 Equation of motion
8.3 Strain
8.3.1 Normal strain
8.3.2 Shear strain
8.4 Perfectly elastic stress–strain relationships
Young’s modulus
Shear modulus (or rigidity modulus)
Bulk modulus (or incompressibility)
8.4.1 The Lamé constants
8.5 The seismic wave equation
8.5.1 Primary waves (P-waves)
8.5.2 Secondary waves (S-waves)
8.5.3 Displacement potentials
P-waves
S-waves
8.6 Solutions of the wave equation
8.6.1 One-dimensional solution for plane P-waves
8.6.2 One-dimensional solution for plane S-waves
8.7 Three-dimensional propagation of plane P- and S-waves
8.7.1 P-wave propagation
8.7.2 S-wave propagation
Further reading
Appendix A. Magnetic poles, the dipole field, and current loops
A1. The concept of magnetic poles and Gauss’s law
A2. The magnetic dipole
A3. The Lorentz force
A4. Torque on a current loop in a magnetic field
Appendix B Maxwell’s equations of electromagnetism
1. Coulomb’s law
1.1. The effect of bound charges
2. Ampère’s law
2.1. The effect of displacement currents
3. Gauss’s law for magnetism
3.1. The magnetic field inside a magnetizable material
4. Faraday’s law
References
Index