Electromagnetism and the Earth's Interior

Electromagnetism and the Earth's Interior reviews the earth's magnetic fields in terms of physical processes that are occurring in the earth's interior.

The book describes the distribution of the earth's magnetic field in terms of declination, horizontal intensity, and vertical intensity. The dynamo theory concerns the self-exciting electric generation in the interior of the earth, and can account for any geomagnetic secular variation. A workable laboratory model-a dynamo mechanism of Lowes and Wilkinson (1963) has a significant role on the dynamo theory for the model actually demonstrated Herzenberg's proof that was developed mathematically. The text also describes various aspects of long-term geomagnetic variations, such as the decrease in the dipole moment, the reversal of the geomagnetic field, the drift of eccentric dipole, the fluctuation in the length of day, and the geomagnetic secular variation. The book also investigates the possible effects of the ocean on geomagnetic variations. The characteristics of transient geomagnetic variations on islands can point to a possible special underground structure.

The book is suitable for geologists, astrophysicists, seismologists, and students of the natural sciences.

Contenu

Preface

Chapter 1. Introductory Remarks

Chapter 2. Main Magnetic Field of the Earth

World's Distribution of the Geomagnetic Field

Elements of the Geomagnetic Field

Magnetic Charts

Spherical Harmonic Analysis of the Main Field

Dipole Field

Eccentric Dipole

Chapter 3. Theory of Steady Dynamo

Theories of the Origin of the Earth's Magnetism

Permanent Magnetization

Free Decay of Electric Current

Gyromagnetic Effect

Rotating Electric Charge

Electromagnetic Induction by Magnetic Storms

Thermoelectric Effect

Hall Effect

Compression Effect

Rotation of a Massive Body

Twisted-Kink Theory

Basic Idea of the Dynamo

Equations for a Homogeneous Dynamo

Physical Discussions Relating to the Homogeneous Dynamo

Convection Current and Magnetic Lines of Force

Bullard Process

Feedback Mechanism Proposed by Bullard

Eigen-Value Problem

Additional Discussion

Inglis Model

Visual Aid by Inglis

Equations for the Inglis Model

Non-Dimensional form of the Equations

Steady-State Solution

Steady State of a Model of Manageable Size in a Laboratory

Inglis Model with the Size of the Earth's Core

Backus and Herzenberg Dynamos

Lowes and Wilkinson's Experiment

Chapter 4. Stability of the Dipole Field

Fundamental Equations for Small M.H.D. Disturbances Given to a Conducting Fluid Body

M.H.D. Oscillation of a Perfectly Conducting Fluid Sphere Placed in a Uniform Magnetic Field

Effect of the Coriolis Force

Stability of the Earth's Dynamo

Chapter 5. Theory of Non-Steady Dynamo

Finite-Amplitude Oscillation of a Disk Dynamo

Oscillation of a System of Disk Dynamo

Disk Dynamo with a Heat Engine

Time-Dependent Behaviour of the Inglis Model

Chapter 6. Geomagnetic Secular Variation

Secular Variation as Observed by Instruments

Analysis of the Secular Variation

Decrease in the Dipole Moment

Secular Variation During Historical and Geological Times

Reversal of the Geomagnetic Dipole

Evidence from Palaeomagnetic Studies

Field Intensity During a Reversal

Westward Drift of the Geomagnetic Field

Non-Drifting Secular Variation

Drift of the Eccentric Dipole

Fluctuation in the Length of Day and Geomagnetic Secular Variation

Chapter 7. Theory of Secular Variation

Core-Mantle Coupling and the Westward Drift

Rigid-Sphere Model

Diffusion of Toroidal Field

Mechanical Couple Exerted to the Mantle

Time-Dependent Core-Mantle Coupling

Oscillation of the Quadrupole Field in Relation to the Northward Shift

Growth and Decay of Non-Drifting Field

Rigid-Rotator Model

Poloidal Fields Associated with Uplifting of Toroidal Field by Convective Motion

Chapter 8. Electromagnetic Induction within the Earth by Daily Variation

Analysis of Solar Daily Variation (Sq)

Analysis of Lunar Daily Variation (L)

Numerical Method for Calculating a Magnetic Potential

Method of Graphical Integration

Method of Residuals

Surface Integral Method for the Analysis of a Potential

Chapter 9. Theory of Electromagnetic Induction in a Spherical Body

Fundamental Equations in a Non-Uniform Conductor

Conductors with Spherical Symmetry

Uniform Sphere Model

Non-Uniform Sphere Model when s=s0ß-l

Spherical Shell

Use of High-Speed Computer

Chapter 10. Electromagnetic Induction by Various Variations

Sudden Storm Commencement (s.s.c.)

Storm Main Phase (Dst)

Geomagnetic Bay

Solar Flare Effect (s.f.e.)

Auroral Jet

Other Variations

Chapter 11. Theory of Electromagnetic Induction in an Earth Having a Plane Surface

Fundamental Equations

Elementary Solutions

Elementary Solutions of the First Type

Elementary Solutions of the Second Type

Indeterminate Case for Induction by a Uniform Field

Relation Between External and Internal Parts of the Geomagnetic Field Over a Plane Earth

Line of Magnetic Dipoles Over a Uniform Earth-a Two-Dimensional Problem

Chapter 12. Theory of Electromagnetic Induction in a Thin Sheet of Conductor

General Equations

Plane Sheet

Fundamental Characteristics of Electromagnetic Induction in a Uniform Plane Sheet

Electromagnetic Induction in a Uniform Plane Sheet by a Magnetic Dipole

Non-Uniform Plane Sheet Over a Uniform Semi-Infinite Conductor

Anisotropic Plane Sheet Over a Uniform Semi-Infinite Conductor

Spherical Sheet

Uniform Spherical Sheet

Non-Uniform or Anisotropic Spherical Sheets

Hemispherical Sheet

Electromagnetic Coupling Between a Hemispherical Sheet and an Underlying Conductor

Hemispherical Ocean and Sq

Induction in a Disk

Use of Relaxation Method

Two-Dimensional Problem

Axisymmetric Problem

Hole-in-a-Plate Problem

Model Experiment

Chapter 13. Theory of Electromagnetic Induction in a Cylinder: Two-Dimensional Problems

Circular Cylinder

Electromagnetic Coupling Between a Circular Cylinder and an Underlying Layer

Elliptic Cylinder

Small Flattening and Moderate Conductivity

Thin Elliptic Cylinder

Highly Conducting Elliptic Cylinder

Chapter 14. Shielding Effect of the Mantle and Secular Variation

Plane Slab Model

Time-Dependent Dipole at the Core-Mantle Boundary

Chapter 15. Overall Distribution of the Electrical Conductivity in the Mantle

Conductivity Distribution as Inferred from Geomagnetic Variations Arising from External Sources

Uniform Core Model

Second Approximation of the Conductivity Distribution

Results from Secular Variation

Overall Distribution of the Conductivity

Conduction Mechanism

Geophysical Significance of the Conductivity Distribution

Temperature Distribution in the Mantle Derived from the Conductivity Distribution

Olivine-Spinel Transition in the Upper Mantle

Chapter 16. Electrical Conductivity in the Core

Physical State in the Core

Geophysical Discussions

Chapter 17. Possible Effect of the Ocean on Geomagnetic Variations

Time Constant of an Ocean

Observation on a Floating Ice Station

Edge Effect at the Margin of an Ocean

Observation on Islands

Chapter 18. Earth-Currents and Magneto-Tellurics

Earth-Current Observation

Electric and Magnetic Fields at the Surface of a Uniform Plane Earth

Earth-Currents in a Layered Earth
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