Earth's Core: Geophysics of a Planet's Deepest Interior

Front Cover
Earth's Core: Geophysics of a Planet’s Deepest Interior
Copyright
Contents
About the authors
Preface
Chapter 1: Radial structure of Earth's core
1.1. Geophysical evidence
1.1.1. Moment of inertia and gravity
1.1.2. Magnetic field: Spatial spectrum and time variation
1.1.3. Seismology: Body waves and normal modes
1.2. Reference models
1.3. Analysis of the seismic wavefield
1.3.1. Body waves
1.3.2. Free oscillations
1.4. Viscoelastic attenuation
1.5. Scattering
1.6. Anisotropy
1.7. Viscosity
1.8. Summary
Appendix 1.1 Moment of inertia
Appendix 1.2 Elastic equation of motion
Appendix 1.3 Seismic nomenclature
Appendix 1.4 Adams-Williamson equation and the Bullen parameter
Appendix 1.5 Viscoeleastic attenuation parameterization
Appendix 1.6 Birch's law and seismic velocity/density relations
Appendix 1.7 Composite elastic moduli and density
Appendix 1.8 Elastic anisotropy
Appendix 1.9 Equations of state
References
Chapter 2: Chemical and physical state of the core
2.1. Composition of the core
2.1.1. Fe-Ni
2.1.2. Light elements
2.1.3. Solid-liquid phase diagrams
2.2. Temperature in the core
2.2.1. Thermoelastic properties and the adiabatic gradient in the outer core
2.2.2. TICB and TCMB
2.3. Transport properties of the core
2.3.1. Outer core viscosity
2.3.2. Electrical and thermal conductivities
2.4. Thermodynamics of the core
2.4.1. The energy and entropy balance equations
2.4.1.1. Secular cooling
2.4.1.2. Latent heat
2.4.1.3. Radioactive heat
2.4.1.4. Compositional energy
2.4.1.5. Heat of chemical reactions
2.4.2. Geophysical estimates for the energy and entropy balance equations
2.4.2.1. The CMB heat flux, and the heat and entropy conducted up the adiabat
2.4.2.2. The rate of entropy required by Ohmic and viscous dissipation
2.4.2.3. The rate of energy and entropy change due to radiogenic elements in the core
2.4.2.4. The rate of energy and entropy change due to secular cooling, latent heat, heat of chemical reactions, and compo ...
2.4.3. Age of the inner core
2.4.4. Power for the geodynamo
2.4.5. Stably stratified layers in the outer core
2.5. Inner core mineralogy
2.5.1. Review of crystallography
2.5.2. Stable phase of Fe and its alloys under inner core conditions
2.5.3. Elastic properties of Fe under inner core conditions
2.5.4. Shear modulus of Fe
2.6. Summary
Appendix 2.1 Construction of phase diagrams and the partition coefficient
Appendix 2.2 Thermodynamic relations and the Gruneisen parameter
Appendix 2.3 The free electron Fermi gas, phonons, and the Debye model
Appendix 2.4 Miller indices and pole figures
References
Further reading
Chapter 3: Geodynamo and geomagnetic basics
3.1. Preliminaries
3.1.1. What is a planetary magnetic field?
3.1.2. What is a planetary dynamo?
3.1.3. Rationale for the self-sustaining dynamo mechanism
3.1.4. Dynamo ingredients
3.1.5. What we learn from the geodynamo
3.2. The geomagnetic field in the core
3.2.1. The geomagnetic field as a probe of the geodynamo
3.2.2. The geomagnetic field in spherical harmonics
3.2.3. The core field
3.2.4. Secular variation of the core field
3.2.5. Historical dipole moment variations
3.2.6. Geomagnetic jerks
3.2.7. The secular variation time scale
3.2.8. Dipole variations on millennium times scales
3.2.9. Dipole variations on 100kyr time scales
3.2.10. The geomagnetic polarity reversal record
3.2.11. Long-time average core field structure
3.2.12. Geomagnetic intensity in the deep past
3.3. The geodynamo process
3.3.1. How to make a self-sustaining fluid dynamo
3.3.2. The magnetic Reynolds number in the core
3.3.3. Magnetic induction in the core
3.3.4. Poloidal and toroidal magnetic field components
3.3.5. Toroidal-poloidal magnetic feedback
3.3.5.1. Toroidal magnetic field generation in a shear flow
3.3.5.2. Poloidal magnetic field generation by helical flow
3.3.6. A simple kinematic dynamo
3.3.7. The VKS dynamo experiment
3.3.8. Dynamo energy pathways
3.3.9. Ohmic dissipation in the core
3.4. Geomagnetic images of the core flow
3.4.1. Frozen flux tracing: Methods, assumptions, and limitations
3.4.2. Velocity constraints
3.4.3. Core flow images
3.4.4. Length-of-day variations
3.4.5. Polar vortices
3.4.6. Remarks on frozen flux
3.5. Summary
Appendix
Appendix 3.1. Schmidt Legendre polynomials for geomagnetism
Appendix 3.2. Magnetohydrodynamic induction and magnetic energy equations
References
Further readings and resources
Chapter 4: Outer core dynamics
4.1. The outer core environment
4.2. Dimensionless parameters
4.2.1. Characteristic time scales
4.2.2. Control versus response parameters
4.3. Thermochemical transport and buoyancy
4.3.1. Light element and heat transport in the outer core
4.3.2. Codensity
4.3.3. Thermochemical buoyancy flux
4.4. Steady laminar flows
4.4.1. Geostrophic flow
4.4.2. Thin-layer geostrophy
4.4.3. Magnetostrophic flow
4.4.4. Magnetic wind
4.4.5. Thermal wind
4.4.6. Reynolds stress
4.4.7. Ekman boundary layers
4.5. Waves in the outer core
4.5.1. Alfvén waves
4.5.2. Torsional oscillations
4.5.3. Inertial waves
4.5.4. Internal gravity waves
4.5.5. Rossby waves
4.5.6. Magnetic Rossby waves
4.5.7. MAC waves
4.6. Outer core convection
4.6.1. Onset of outer core convection
4.6.2. Fully developed convection in the outer core
4.6.3. Mantle heterogeneity effects on outer core convection
4.7. Numerical dynamos
4.7.1. A low magnetic Reynolds number dynamo
4.7.2. A high magnetic Reynolds number dynamo
4.7.3. Crustal filtering effects
4.7.4. Scaling laws for outer core convection and the geodynamo
4.7.4.1. Power-law scaling
Diffusion-free velocity scaling
Diffusion-free magnetic field scaling
Diffusive magnetic field scaling
4.7.4.2. Scaling law applications
4.7.5. Effects of mantle heterogeneity and E layer stratification
4.7.6. Effects of heterogeneous inner core growth
4.7.7. Dynamo model reversals
4.7.7.1. Simple and complex reversals
4.7.7.2. Reversal onset
4.7.7.3. Reversal frequency
4.8. Summary
Appendix
Appendix 4.1. Accelerations in Earth's rotating coordinates
Appendix 4.2. Equations of motion
Appendix 4.3. Nondimensional equations
Appendix 4.3.1. Temperature scaling
Appendix 4.3.2. Codensity scaling
Appendix 4.4. Lorentz force and Maxwell stress
Appendix 4.5. Convective dynamos
Appendix 4.6. Global kinetic energy balance
References
Further readings and resources
Chapter 5: Boundary regions
5.1. D (lowermost mantle region)
5.1.1. Travel-time tomography
5.1.2. Slabs and plumes
5.1.3. The post-perovskite phase transition
5.1.4. Ultralow velocity zones and LLVPs
5.1.5. Constraints from scattering
5.1.6. Constraints from elastic anisotropy
5.2. CMB topography
5.3. E region (uppermost outer core)
5.3.1. Seismic velocity anomalies
5.3.2. Constraints from chemistry and MAC waves
5.3.3. Alternative theories for the formation of E
5.4. F region
5.4.1. Seismic velocity anomalies
5.4.2. Theories for formation and stability
5.5. ICB topography
5.6. Summary
References
Chapter 6: Inner core explored with seismology
6.1. Elastic anisotropy
6.1.1. Differential travel times
6.1.2. Depth dependence
6.2. Attenuation and scattering
6.2.1. Frequency dependence and parameter trade-offs
6.2.2. Depth dependence
6.2.3. Lateral variations in scattering
6.2.4. Anisotropy of the heterogeneity spectrum
6.3. Hemispherical differences
6.3.1. Observations
6.3.2. Theories
6.4. Differential rotation
6.4.1. Observations
6.4.2. Theories
6.5. Shear modulus, density, and viscosity
6.5.1. Shear modulus from seismology
6.5.2. Transition defining the ICB
6.5.3. Predictions from mineral physics
6.5.4. Viscosity
6.5.5. Density discontinuity at the ICB
6.6. Summary
References
Chapter 7: Inner core dynamics
7.1. Solidification of the inner core
7.1.1. Morphological instability and dendritic growth
7.1.2. The solidification microstructure and texture of the inner core
7.1.3. The origin of the F layer, inner core translation, the ``snowing´´ core model, and inner core nucleation
7.2. Deformation in the inner core
7.2.1. Stress/strain
7.2.1.1. Convection
7.2.1.2. Other causes for stress/strain
7.2.2. Deformation mechanisms
7.2.2.1. Dislocation creep
7.2.2.2. Slip systems
7.2.2.3. Diffusion creep
7.3. Annealing: Recovery, recrystallization, grain growth, and coarsening
7.4. Grain size and the deformation mechanism map of the inner core
7.5. Inner core viscosity
7.6. Inner core elastic anisotropy, attenuation, and isotropic heterogeneity
7.6.1. Elastic anisotropy
7.6.2. Attenuation and isotropic heterogeneity
7.7. Summary
References
Further reading
Chapter 8: Formation and evolution of the core
8.1. Formation of the core
8.1.1. Energetics of Earth formation
8.1.2. Genesis of the core-forming elements
8.1.3. Origin, composition, and early evolution of the solar system
8.1.4. Evidence from meteorites
8.1.5. Terrestrial planet formation models
8.1.6. Core formation processes
8.1.7. Isotopic evidence
8.1.8. Evidence from siderophile elements
8.1.9. Effects of Moon formation
8.2. Core evolution
8.2.1. The equilibrium model
8.2.2. Core evolution inputs
8.2.3. Inner core growth histories
8.2.4. Inner core nucleation age
8.2.5. Dynamo model predictions
8.2.6. Long-term core cooling
8.2.7. Convection prior to inner core nucleation
8.2.8. Buoyancy flux from light element exsolution
8.3. The geodynamo in the deep past
8.3.1. How old is the geodynamo?
8.3.2. Numerical models of the ancient geodynamo
8.4. Seeding the early geodynamo
8.4.1. Seed magnetic fields
8.4.1.1. Astrophysical batteries
8.4.1.2. Solar nebula seeding
8.4.2. Geodynamo seeding times
8.4.3. Geodynamo initiation
8.4.3.1. Electromagnetic implantation
8.4.3.2. Tidal stirring
8.5. Summary
Appendix
Appendix 8.1. Core evolution model
Appendix 8.2. Dynamo seeding times
References
Chapter 9: Future research goals
9.1. Introduction
9.2. Seismology
9.2.1. Station coverage
9.2.2. Seismic instrumentation
9.2.3. Ambient noise, wavefield correlation, and coherence
9.2.4. Source-time functions
9.2.5. Numerical synthetic seismograms
9.3. Mineral physics
9.3.1. High-pressure experiments
9.3.2. Ab initio calculations
9.3.3. Analogs and processes
9.4. Core dynamics
9.4.1. Liquid metal numerical dynamos
9.4.2. Laboratory experiments on thermochemical convection
9.4.3. Core-mantle boundary heat flow and the age of the inner core
References
Notation tables
Core properties and parameters
Glossary
Index
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