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Waves and rays in seismology : answers to unasked questions / Michael A. Slawinski

Author
Slawinski, M. A. (Michael A.), 1961-
Published
Singapore : World Scientific, [2018]
Copyright Date
©2018
Edition
Second edition.
Physical Description
xxxiii, 543 pages : illustrations ; 24 cm

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Contents
Machine generated contents note: Preliminary remarks -- 1.1.Purpose and methodology: Historical sketch -- 1.2.Classification -- Closing remarks -- 1.3.Exercises -- Preliminary remarks -- 2.1.On axiomatic formulation -- 2.2.Kinematic descriptions -- 2.2.1.Spacetime -- 2.2.2.Motion -- 2.2.3.Coordinates -- 2.3.Field equations -- 2.3.1.Balance equations -- 2.3.2.Balance of mass: Continuity equation -- 2.3.3.Balance of momentum: Equation of motion -- Closing remarks -- 2.4.Exercises -- Preliminary remarks -- 3.1.Hookean solids -- 3.2.Material symmetry -- 3.2.1.On symmetries -- 3.2.2.On tensor rotations -- 3.2.3.Finite and infinitesimal elasticities -- 3.2.3.1.Deformation gradient -- 3.2.3.2.Elasticity tensor -- 3.2.3.3.Prestressed linearly elastic materials -- 3.2.3.4.Material symmetry: Finite elasticity -- 3.2.3.5.Material symmetry: Relation between finite and infinitesimal elasticities -- 3.2.4.Symmetry classes -- 3.2.4.1.Material-symmetry conditions -- 3.2.4.2.Hooke's law in R3 and R6 -- 3.2.4.3.Index symmetries -- 3.2.4.4.Kelvin notation -- 3.2.4.5.Monoclinic tensor -- 3.2.4.6.On tensorial properties of monoclinic tensor -- 3.2.4.7.Orthotropic tensor -- 3.2.4.8.Tetragonal tensor -- 3.2.4.9.On tensorial properties of tetragonal tensor -- 3.2.4.10.Transversely isotropic tensor -- 3.2.4.11.Trigonal tensor -- 3.2.4.12.Cubic tensor -- 3.2.4.13.Isotropic tensor -- 3.2.4.14.On isotropic parameters -- 3.2.4.15.Relations among elasticity parameters -- 3.2.4.16.Diclinic solids -- 3.2.4.17.Hexagonal solids -- Closing remarks -- 3.3.Exercises -- Preliminary remarks -- 4.1.Effective symmetries -- 4.1.1.On accuracy -- 4.1.2.Fixed orientation of coordinate system -- 4.1.2.1.Introduction -- 4.1.2.2.Monoclinic tensor -- 4.1.2.3.Orthotropic tensor -- 4.1.2.4.Tetragonal tensor -- 4.1.2.5.Transversely isotropic tensor -- 4.1.2.6.Trigonal tensor -- 4.1.2.7.Cubic tensor -- 4.1.2.8.Isotropic tensor -- 4.1.3.Optimal orientation of coordinate system -- 4.2.Equivalent media -- 4.2.1.Introduction -- 4.2.2.Equivalence parameters for isotropic layers -- 4.2.2.1.Formulae -- 4.2.2.2.Justification -- 4.2.2.3.Interpretation -- 4.2.2.4.Possible issues with Backus averaging -- 4.2.3.Equivalence parameters for TI layers -- 4.3.Relation between effective and equivalent formulations -- 4.3.1.Introduction -- 4.3.2.Analytical formulation -- 4.3.2.1.Anisotropic layers, monoclinic medium -- 4.3.2.2.Monoclinic layers, orthotropic medium -- 4.3.2.3.Orthotropic layers, tetragonal medium -- 4.3.2.4.Transversely isotropic layers -- 4.3.2.5.Combining rotational averages -- 4.3.3.Discussion -- Closing remarks -- 4.4.Exercises -- Preliminary remarks -- 5.1.Wave equations -- 5.1.1.Assumptions and formulation -- 5.1.2.Particular case: Isotropy and homogeneity -- 5.1.3.Particular case: Inhomogeneous string -- 5.1.4.Particular case: String with friction -- 5.2.Solutions of wave equation -- 5.2.1.Introduction -- 5.2.2.Product solution -- 5.2.3.d'Alembert solution -- 5.2.3.1.d'Alembert's approach -- 5.2.3.2.Euler's approach -- 5.2.3.3.Spherical-symmetry approach -- 5.2.4.Fourier-transform solution -- 5.2.5.Green's-function solution -- 5.3.On approximations -- Closing remarks -- 5.4.Exercises -- Preliminary remarks -- 6.1.Introduction -- 6.2.Surface waves: Homogeneous elastic halfspace -- 6.3.Guided waves: Homogeneous layer above halfspace -- 6.3.1.Elastic layer above rigid halfspace -- 6.3.2.Elastic layer above elastic halfspace -- 6.3.3.Love wave as superposition of SH waves -- 6.3.4.On Rayleigh and Love waves in Earth's crust -- 6.4.Existence of surface and guided waves -- 6.4.1.Introduction -- 6.4.2.Elasticity parameters and mass densities -- 6.4.3.On Love waves in homogeneous halfspace -- 6.4.4.On P waves in homogeneous halfspace -- 6.5.Interface waves: Homogeneous halfspaces -- 6.5.1.Introduction -- 6.5.2.Elastic and liquid halfspaces -- 6.5.3.Liquid halfspaces -- 6.6.Existence of interface waves -- 6.6.1.Introduction -- 6.6.2.Elasticity parameters and mass densities -- 6.6.3.On SH waves as interface waves -- Closing remarks -- 6.7.Exercises -- Preliminary remarks -- 7.1.Historical comments -- 7.2.Fermat's principle -- 7.2.1.Isotropic layered medium -- 7.2.2.Isotropic continuously inhomogeneous medium -- 7.2.3.Global optimization and causality -- 7.2.4.Stationarity versus minimization -- 7.2.5.Mathematical justification -- 7.2.5.1.Fermat's principle -- 7.2.5.2.Head waves -- 7.2.6.Physical interpretation -- 7.2.6.1.Macroscopic interpretation -- 7.2.6.2.Microscopic interpretation -- 7.2.6.3.Phase consideration -- 7.2.7.On teleology of Fermat's principle -- 7.3.Hamilton's principle -- 7.3.1.Action -- 7.3.2.Wave equation -- 7.3.3.Mathematical justification -- 7.3.4.Physical interpretation -- 7.4.Conserved quantities -- 7.4.1.Introduction -- 7.4.2.Ray parameter -- 7.4.2.1.Isotropy -- 7.4.2.2.Anisotropy -- 7.4.3.Hamiltonian and Lagrangian -- 7.4.3.1.Ray theory -- 7.4.3.2.Classical mechanics -- Closing remarks -- 7.5.Exercises -- Preliminary remarks -- 8.1.Gravitation -- 8.1.1.Body forces -- 8.1.2.Wave speeds -- 8.2.On weak gravitational waves -- 8.3.Temperature -- 8.3.1.Propagation and diffusion -- 8.3.2.Isothermal and adiabatic formulations -- 8.3.2.1.Lame parameters -- 8.3.2.2.Bulk moduli -- Closing remarks -- 8.4.Exercises -- Preliminary remarks -- 9.1.Hypotheticodeductive formulation -- 9.1.1.Hypotheses -- 9.1.2.Deductive argumentation -- 9.2.Theory versus data -- 9.2.1.Introduction -- 9.2.2.Theory-ladenness of data -- 9.2.3.Underdetermination of theory by data -- 9.3.Bayesian inference -- 9.4.Predictions versus explanations -- 9.4.1.Introduction -- 9.4.2.Covering-law model -- 9.4.3.Inference to best explanation -- 9.5.Realistic approach versus instrumental approach -- 9.6.Coherence theory of justification -- Closing remarks -- 9.7.Exercises -- Preliminary remarks -- A.1.Displacement-vector field -- A.2.Deformation-gradient tensor -- A.3.Compatibility of deformation gradient -- A.4.Cauchy-Green strain tensors -- A.4.1.Right Cauchy-Green strain tensor -- A.4.2.Left Cauchy-Green strain tensor -- A.4.3.Relations between right and left tensors -- A.5.Green-Lagrange and Almansi strain tensors -- A.6.Deformation of volume element -- A.7.Deformation of oriented surface element -- A.8.Stretch ratio -- A.9.Stretch and rotation tensors -- A.9.1.Polar decomposition -- A.9.2.Right Stretch Tensor -- A.9.3.Left Stretch Tensor -- A.9.4.Relations between right and left Stretch Tensors -- A.9.5.Local and global rotations -- A.10.Infinitesimal strain and rotation tensors -- A.11.Objective tensors -- A.12.On terminology -- Closing remarks -- Preliminary remarks -- B.1.Cauchy stress tensor -- B.2.Piola-Kirchhoff stress tensors -- B.2.1.First Piola-Kirchhoff stress tensor -- B.2.2.Second Piola-Kirchhoff stress tensor -- B.3.Stress tensors for infinitesimal strains -- B.4.Objective stress tensors -- Closing remarks -- Preliminary remarks -- B.1.First law of thermodynamics -- B.2.Second law of thermodynamics -- B.3.Heat conduction -- B.4.Thermodynamic processes and potentials -- B.4.1.Processes -- B.4.2.Helmholtz free energy as potential -- B.4.3.Internal energy as potential -- B.4.4.Gibbs free energy as potential -- B.4.5.Enthalpy as potential -- B.5.Stress tensors in terms of potentials -- B.6.Isothermal infinitesimal strains -- B.6.1.Introduction -- B.6.2.Single spatial dimension -- B.6.3.Three spatial dimensions -- Closing remarks -- Preliminary remarks -- D.1.Strain-energy function -- D.2.Hyperelastic materials -- D.2.1.Introduction -- D.2.2.Finite strains -- D.2.3.Infinitesimal strains -- D.3.Material symmetry -- D.3.1.Rotation invariance -- D.3.2.Isotropy -- D.3.3.Infinitesimal strain -- Closing remarks -- Preliminary remarks -- E.1.Contravariant transformations -- E.2.Covariant transformations -- E.3.Mixed transformations -- Closing remarks -- Preliminary remarks -- F.1.Metric tensor -- F.2.Christoffel symbol -- F.3.Covariant derivative -- Closing remarks -- G.1.Mathematical relations and operations -- G.2.Physical quantities -- G.2.1.Greek letters -- G.2.2.Roman letters.
Subject(s)
ISBN
9789813239876
9813239875
Bibliography Note
Includes bibliographical references (pages 499-510) and index.
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