Note: Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Acknowledgements -- 1 Introduction -- 1.1 Continuum properties -- 1.1.1 Deformation and strain -- 1.1.2 The stress field -- 1.1.3 Constitutive relations -- 1.2 Earth processes -- 1.3 Elements of Earth structure -- 1.3.1 Mantle -- 1.3.2 Core -- 1.4 The state of the Earth -- Deformation regimes and Earth dynamics -- Lithosphere: -- Asthenosphere: -- Transition zone: -- Lower mantle -- Core-mantle Boundary zone - D": -- Outer core: -- Inner core: -- Part I: CONTINUUM MECHANICS IN GEOPHYSICS -- 2 Description of Deformation -- 2.1 Geometry of deformation -- 2.1.1 Deformation of a vector element -- 2.1.2 Successive deformations -- 2.1.3 Deformation of an element of volume -- 2.1.4 Deformation of an element of area -- 2.1.5 Homogeneous deformation -- 2.2 Strain -- 2.2.1 Stretch -- 2.2.2 Principal fibres and principal stretches -- 2.2.3 The decomposition theorem -- 2.2.4 Pure rotation -- 2.2.5 Tensor measures of strain -- 2.3 Plane deformation -- Shear -- 2.4 Motion -- 2.5 The continuity equation -- Material derivative of a volume integral -- Appendix: Properties of the determinant of the deformation gradient -- 3 The Stress-Field Concept -- 3.1 Traction and stress -- Tensor character of stress -- 3.2 Local equations of linear motion -- 3.2.1 Symmetry of the stress tensor -- 3.2.2 Stress jumps (continuity conditions) -- 3.3 Principal basis for stress -- Stress circle -- 3.4 Virtual work rate principle -- Converse principle -- 3.5 Stress from a Lagrangian viewpoint -- 4 Constitutive Relations -- 4.1 Constitutive relation requirements -- 4.1.1 Simple materials -- 4.1.2 Material symmetry -- 4.1.3 Functional dependence -- 4.2 Energy balance -- Neglect of thermal effects -- 4.3 Elastic materials -- Material symmetry -- 4.4 Isotropic elastic material -- 4.4.1 Effect of rotation. , 4.4.2 Coaxiality of the Cauchy stress tensor and the Eulerian triad -- 4.4.3 Principal stresses -- 4.4.4 Some isotropic work functions -- 4.5 Fluids -- 4.6 Viscoelasticity -- Models of viscoelastic behaviour -- 4.7 Plasticity and flow -- 5 Linearised Elasticity and Viscoelasticity -- 5.1 Linearisation of deformation -- 5.2 The elastic constitutive relation -- 5.2.1 Isotropic response -- 5.2.2 Nature of moduli -- 5.2.3 Interrelations between moduli -- 5.2.4 An example of linearisation -- 5.2.5 Elastic constants -- 5.2.6 The uniqueness theorem -- Kirchhoff's Theorem -- 5.3 Integral representations -- 5.3.1 The reciprocal theorem -- 5.3.2 The representation theorem -- 5.4 Elastic waves -- 5.4.1 Isotropic media -- 5.4.2 Green's tensor for isotropic media -- 5.4.3 Interfaces -- 5.5 Linear viscoelasticity -- Creep and relaxation -- 5.6 Viscoelastic behaviour -- Isotropic linear viscoelasticity -- 5.7 Damping of harmonic oscillations -- 6 Continua under Pressure -- 6.1 Effect of radial stratification -- 6.1.1 Hydrostatic pressure -- 6.1.2 Thermodynamic relations -- 6.2 Finite strain deformation -- 6.3 Expansion of Helmholtz free energy and equations of state -- 6.4 Incremental stress and strain -- 6.4.1 Perturbations in stress -- 6.4.2 Perturbations in boundary conditions -- 6.5 Elasticity under pressure -- Seismic wavespeeds -- 7 Fluid Flow -- 7.1 The Navier-Stokes equation -- 7.1.1 Heat flow -- 7.1.2 The Prandtl number -- 7.2 Non-dimensional quantities -- 7.2.1 The Reynolds number -- 7.2.2 Stokes Flow -- 7.2.3 Compressibility -- 7.3 Rectilinear shear flow -- 7.4 Plane two-dimensional flow -- Viscous flow model of glacial rebound -- 7.5 Thermal convection -- 7.5.1 The Rayleigh and Nusselt numbers -- 7.5.2 The Boussinesq approximation -- 7.5.3 Onset of convection -- 7.5.4 Styles of convection -- 7.6 The effects of rotation -- 7.6.1 Rapid rotation. , 7.6.2 The Rossby and Ekman numbers -- 7.6.3 Geostrophic flow -- 7.6.4 The Taylor-Proudman theorem -- 7.6.5 Ekman layers -- 8 Continuum Equations and Boundary Conditions -- 8.1 Conservation equations -- 8.1.1 Conservation of mass -- 8.1.2 Conservation of momentum -- 8.3 Continuum electrodynamics -- 8.3.1 Maxwell's equations -- 8.3.2 Electromagnetic constitutive equations -- 8.3.3 Electromagnetic continuity conditions -- 8.3.4 Energy equation for the electromagnetic field -- 8.3.5 Electromagnetic disturbances -- 8.3.6 Magnetic fluid dynamics -- 8.4 Diffusion and heat flow -- 8.4.1 Equilibrium heat flow -- 8.4.2 Time-varying problems -- Part II: EARTH DEFORMATION -- 9 From the Atomic Scale to the Continuum -- 9.1 Transport properties and material defects -- 9.1.1 Grains and crystal defects -- 9.1.2 General transport properties -- 9.1.3 Atomic diffusion -- 9.2 Lattice vibrations -- Lattice specific heat -- 9.3 Creep and rheology -- 9.3.1 Crystal elasticity -- 9.3.2 Deformation behaviour -- 9.4 Material properties at high temperatures and pressures -- 9.4.1 Shock-wave techniques -- 9.4.2 Pressure concentration by reduction of area -- 9.5 Computational methods -- 9.5.1 Electronic structure calculations -- 9.5.2 Atomistic simulations -- 9.5.3 Simulation of crystal structures -- 9.5.4 Finite temperature -- 9.5.5 Influence of defects -- 10 Geological Deformation -- 10.1 Microfabrics -- 10.1.1 Crystal defects -- 10.1.2 Development of microstructure -- 10.1.3 Formation of crystallographically preferred orientations -- 10.2 Macroscopic structures -- 10.2.1 Multiple phases of deformation -- 10.2.2 Folding and boudinage -- 10.2.3 Fractures and faulting -- 10.2.4 Development of thrust complexes -- 11 Seismology and Earth Structure -- 11.1 Seismic waves -- 11.1.1 Reflection and refraction -- 11.1.2 Attenuation effects -- 11.2 Seismic sources. , 11.3 Building the response of the Earth to a source -- 11.3.1 Displacements as a normal mode sum -- 11.3.2 Free oscillations of the Earth -- 11.4 Probing the Earth -- 11.4.1 Seismic phases -- Branches of core phases -- 11.4.2 Normal mode frequencies -- Observations of modal eigenfrequencies -- 11.4.3 Comparison with observations -- 11.4.4 Imaging three-dimensional structure -- 11.5 Earthquakes and faulting -- 12 Lithospheric Deformation -- 12.1 Definitions of the lithosphere -- 12.2 Thermal and mechanical structure -- 12.2.1 Thermal conduction in the oceanic lithosphere -- 12.2.2 Mechanical deformation -- 12.2.3 Estimates of the elastic thickness of the lithosphere -- 12.2.4 Strength envelopes and failure criteria -- Oceanic lithosphere -- Continental lithosphere -- 12.3 Plate boundaries and force systems -- 12.3.1 Nature of plate boundaries -- 12.3.2 Plate boundary forces -- 12.4 Measures of stress and strain -- 12.4.1 Stress measurements -- 12.4.2 Strain measurements -- 12.5 Glacial rebound -- 12.6 Extension and convergence -- 12.6.1 Extension -- 12.6.2 Convergence -- 13 The Influence of Rheology: Asthenosphere to the Deep Mantle -- 13.1 Lithosphere and asthenosphere -- 13.1.1 Seismic imaging -- 13.1.2 Seismic attenuation -- 13.1.3 Seismic anisotropy -- Surface wave anisotropy -- 13.1.4 Asthenospheric flow -- 13.1.5 The influence of a low-viscosity zone -- 13.2 Subduction zones and their surroundings -- 13.2.1 Configuration of subduction zones -- 13.2.2 Flow around the slab -- 13.2.3 Temperatures in and around the subducting slab -- 13.2.4 Subduction and orogeny -- 13.3 The influence of phase transitions -- Impact of phase transitions on subduction -- 13.4 The deeper mantle -- 13.4.1 Viscosity variations in the mantle and the geoid -- Dynamic compensation -- Spectral representation -- 13.4.2 Material properties -- 13.4.3 The lower boundary layer. , 14 Mantle Convection -- 14.1 Convective forces -- 14.1.1 Boundary layer theory -- 14.1.2 Basic equations -- 14.1.3 Boundary conditions -- 14.1.4 Non-dimensional treatment -- 14.1.5 Computational convection -- 14.2 Convective planform -- 14.3 Thermal structure and heat budget -- 14.3.1 Thermal boundary layers and the geotherm -- Adiabatic gradient -- Heat sources -- Subadiabaticity -- 14.3.2 Plates -- Heat transport -- Influence on mantle flow -- 14.3.3 Hot spots and plumes -- Hot spot swells -- Hot Spot reference frame -- Plume excess temperature and global mantle heat budget -- 14.4 Circulation of the mantle -- 14.4.1 Present-day and past plate motion models -- 14.4.2 Implications of plate motion models for mantle circulation -- 14.4.3 Mantle circulation models -- Heterogeneity pattern -- Adjoint mantle circulation models -- 14.5 Mantle rheology -- 14.5.1 Temperature dependence -- 14.5.2 Strain dependence -- 14.6 Coupled lithosphere-mantle convection models -- 14.7 Thermochemical convection -- 15 The Core and the Earth's Dynamo -- 15.1 The magnetic field at the surface and at the top of the core -- 15.2 Convection and dynamo action -- 15.2.1 Basic equations -- Reference state -- 15.2.2 Boundary conditions -- 15.2.3 Interaction of the flow with the magnetic field -- 15.2.4 Deviations from the reference state -- 15.2.5 Non-dimensional treatment -- Induction equation -- Geostrophy and Taylor Columns -- 15.3 Numerical dynamos -- 15.4 Evolution of the Earth's core -- 15.4.1 Energy balance -- 15.4.2 Thermal and compositional effects -- 15.4.3 Inner core growth in a well-mixed core -- Appendix: Table of Notation -- Stress and Strain -- Solids and Fluids -- Waves -- Thermodynamic Quantities -- Non-dimensional Quantities for Fluids -- Electromagnetic -- Quantum/Atomic -- Deformation -- Seismology -- Core dynamics -- Mathematical -- Bibliography. , Reference Texts.