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Author Smylie, D. E., author.

Title Earth dynamics : deformations and oscillations of the rotating Earth / D.E. Smylie
Published Cambridge : Cambridge University Press, 2013


Description 1 online resource (xii, 543 pages)
Contents EARTH DYNAMICS Deformations and Oscillations of the Rotating Earth; Contents; Preface and acknowledgments; The book website; 1 Introduction and theoretical background; 1.1 Scalar, vector and tensor analysis; 1.1.1 Scalars; 1.1.2 Vectors; 1.1.3 Vectors and co-ordinate transformations; 1.1.4 Tensors; 1.1.5 Metric tensors and elements of arc, surface and volume; 1.1.6 The cross product and differential operators; 1.1.7 Orthogonal co-ordinates; 1.1.8 Pseudo-tensors; 1.1.9 Cartesian tensors; 1.2 Separation of vector fields; 1.3 Vector spherical harmonics
1.4 Elasticity theory1.4.1 Analysis of stress; 1.4.2 Conditions of equilibrium; 1.4.3 Analysis of deformation; 1.4.4 Hooke's law and the Navier equation; 1.4.5 Solutions of the Navier equation; 1.4.6 Kelvin's problem; 1.4.7 The Papkovich-Neuber solution; 1.4.8 The Galerkin vector; 1.4.9 The Boussinesq problem; 1.4.10 Cerruti's problem; 1.4.11 The Mindlin problems; 1.5 Linear algebraic systems; 1.6 Interpolation and approximation; 1.6.1 Natural splines; 1.6.2 Local Hermite splines; 1.6.3 Even or odd local basis functions; 2 Time sequence and spectral analysis; 2.1 Time domain analysis
2.1.1 Classification of time sequences2.1.2 Convolution and the z-transform; 2.1.3 Expected value, auto- and crosscorrelation; 2.1.4 White noise and Wold decomposition; 2.1.5 Properties of wavelets; 2.2 Linear optimum Wiener filters; 2.2.1 Prediction and prediction error filters; 2.2.2 Predictive deconvolution; 2.2.3 The Levinson algorithm; 2.3 Frequency domain analysis; 2.3.1 The discrete Fourier transform; 2.3.2 The DFT and the z-transform; 2.3.3 The fast Fourier transform; 2.3.4 Generalisation of the FFT; 2.3.5 The DFT for unequally spaced samples; 2.3.6 Singular value decomposition
2.4 Fourier series and transforms2.4.1 Convolution theorems; 2.4.2 The effect of finite record length; 2.4.3 The effects of discrete sampling; 2.5 Power spectral density estimation; 2.5.1 Autocorrelation and spectral density; 2.5.2 Multiple discrete segment estimate; 2.5.3 Overlapping segment analysis; 2.5.4 The product spectrum; 2.6 Maximum entropy spectral analysis; 2.6.1 Information and entropy; 2.6.2 The maximum entropy spectrum; 2.6.3 The Burg algorithm; 3 Earth deformations; 3.1 Equilibrium equations; 3.2 The reciprocal theorem of Betti; 3.3 Radial equations: spheroidal and torsional
3.4 Dynamical equations3.5 Solutions near the geocentre; 3.6 Numerical integration of the radial equations; 3.7 Fundamental, regular solutions in the inner core; 4 Earth's rotation: observations and theory; 4.1 Reference frames; 4.2 Polar motion and wobble; 4.2.1 The VLBI pole path; 4.2.2 Spectral analysis of the VLBI pole path; 4.2.3 Interpolation of the VLBI pole path; 4.2.4 Maximum entropy spectral analysis of the VLBI pole path; 4.3 The dynamics of polar motion and wobble; 4.3.1 Response of the Earth to changes in the centrifugal force; 4.3.2 Free and forced polar motion and dissipation; 4.3.3 Relating theory to observations
Summary A rigorous overview of the solid Earth's dynamical behaviour, explaining the theory with methodology and online freeware for numerical implementation
Bibliography Includes bibliographical references and index
Notes English
Print version record
Subject Geodynamics.
SCIENCE -- Geophysics.
SCIENCE -- Earth Sciences -- Geography.
SCIENCE -- Earth Sciences -- Geology.
Planets -- Rotation
Earth (Planet) -- Rotation.
Earth (Planet)
Form Electronic book
LC no. 2012040769
ISBN 9781107308381