The Magnetic Field of the Earth

Transcription

1 The Magnetic Field of the Earth Paleomagnetism, the Core, and the Deep Mantle RONALD T. MERRILL Department of Geophysics University of Washington Seattle, Washington MICHAEL W. McELHINNY Gondwana Consultants Hat Head, New South Wales Australia PHILLIP L. McFADDEN Australian Geological Survey Organisation Canberra, Australia ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto

2 Contents Preface Chapter 1 History of Geomagnetism and Paleomagnetism 1.1 Discovery of the Main Magnetic Elements The Magnetic Compass Declination, Inclination, and Secular Variation The Experiments of William Gilbert Magnetic Charts and the Search for the Poles Fossil Magnetism and the Magnetic Field in the Past Early Observations Reversais of the Magnetic Field Secular Variation Continental Drift Investigations of the External Magnetic Field Transient Magnetic Variations Early Theories of Magnetic Storms and Auroras The Magnetosphere Origin of the Earth's Magnetic Field 17 Chapter 2 The Present Geomagnetic Field: Analysis and Description from Historical Observations 2.1 Magnetic Elements and Charts Spherical Harmonie Description of the Earth's Magnetic Field 25

3 VI The Magnetic Field ofthe Earth Scalar Potential for the Magnetic Field Basics of Spherical Harmonics Application of Spherical Harmonics to the Earth's Magnetic Field Determination ofthe Gauss Coefficients Interpretation of Spherical Harmonie Terms Uniqueness and Other Mathematical Problems Application of Laplace's Equation to the Earth Approximation with a Truncated Series Uniqueness of Source Nonspherical Harmonie Representation ofthe Earth's Magnetic Field Magnetic Annihilator Geomagnetic Secular Variation Overview The Magnetic Jerk and Screening by the Mantle Methods Used to Determine the Secular Variation Drift ofthe Nondipole Field Variations ofthe Dipole Field with Time The External Magnetic Field The Magnetosphere The Ionosphere Transient Magnetic Variations, Storms, and Substorms Magnetic Indices 66 Chapter 3 Foundations of Paleomagnetism 3.1 Rock Magnetism Types of Magnetization Acquired by Rocks Magnetic Hysteresis The Demagnetizing Field and Magnetic Anisotropy Single-Domain Theory for TRM Classical Magnetic Domains Modern Domain Concepts Magnetic Mineralogy Properties of Magnetic Minerals The Magnetic Record in Rocks Paleomagnetic Directions and Poles Demagnetization Procedures, Remagnetization, and Consistency Checks 89

4 3.3.2 The Geocentric Axial Dipole Field Hypothesis Standard Statistical Methods in Paleomagnetism Paleointensity Methods The Problem Absolute Paleointensities I: The Modified Thellier Method Absolute Paleointensities II: Shaw's Method Relative Paleointensity Measurements Dipole Moments Age Determinations Potassium-Argon and Argon Isotope Dating Relative Age Determinations 113 vii Chapter 4 The Recent Geomagnetic Field: Paleomagnetic Observations 4.1 Archeomagnetic Results Evidence for Westward Drift Motion ofthe Dipole Axis Variations in the Dipole Moment Deductions from Carbon-14 Variations Dipole Moments before 10,000 yr B.P Analysis of Recent Lake Sediments The Recording Mechanism in Lake Sediments Relative Paleointensities Analysis of Declination and Inclination Westward Drift and Runcorn's Rule Interpretations in Terms of Dipole Sources Interpretations Using Spherical Harmonie Analysis Interpretations in Terms of Dynamo Waves Uncertainties in Interpretations of Secular "Variation Geomagnetic Excursions Definition of Excursions The Laschamp Excursion Excursions Observed in Lake and Deep-Sea Sediments Reversais or Excursions during the Brunnes Chron? Models of Geomagnetic Excursions The Geomagnetic Power Spectrum Time Series Analysis Spectrum from Historical Records 158

5 vüi The Magnetic Field ofthe Earth Spectrum from Lake Sediment Data 160 Chapter 5 Reversais ofthe Earth's Magnetic Field 5.1 Evidence for Field Reversal Definition of a Reversal Self-Reversal in Rocks Baked Contacts Development ofthe Polarity Time Scale for the Past 5 Myr Terminology in Magnetostratigraphy Marine Magnetic Anomalies Measurement and Calculation Sea-Floor Spreading Aspects of Magnetic Anomaly Interpretation Extension ofthe Polarity Time Scale to 160 Ma Analysis of Reversal Sequences Independence of Polarity Intervals Statistical Analysis of Reversal Sequences Superchrons Stability of Polarity States Nonstationarity and Inhibition in the Reversal Record Paleointensity and Reversais Summary Polarity Transitions Recording Polarity Transitions Intensity Changes Directional Changes and Interpretations Reversais and Secular Variation 214 Chapter 6 The Time-Averaged Paleomagnetic Field 6.1 Geocentric Axial Dipole Hypothesis The Past Few Million Years The Past 600 Million Years Paleoclimatic Evidence Longevity of the field Second-Order Terms The Problems in Time Averaging Spherical Harmonie Analyses 228

6 Contents ix The Past Five Million Years Extension to 200 Ma Variation in the Earth's Dipole Moment Paleointensities and Dipole Moments Absolute Paleointensities The Past 10 Million Years Relative Paleointensities The Past Four Million Years Variation with Geological Time Paleosecular Variation from Lavas (PSVL) Angular Dispersion of the Geomagnetic Field Models of PSVL Angular Dispersion of the Present Geomagnetic Field The Past Five Million Years A Pacific Dipole Window? Variation with Geological Time 261 Chapter 7 Processes and Properties of the Earth's Deep Interior: Basic Principles 7.1 Seismic Properties of the Earth's Interior Chemical and Physical Properties Composition Physical Properties Electrical Properties of the Lower Mantle Thermodynamic Properties of the Earth's Deep Interior Thermal History Models Nondynamo Models for the Earth's Magnetic Field Permanent Magnetization Thermoelectric Effects Other Mechanisms Fluid Mechanics Fundamentals The Navier-Stokes Equation and Boundary Conditions Dimensionless Numbers Instabilities Turbulence Energy Sources 300

7 X The Magnetic Field ofthe Earth Chapter 8 Introduction to Dynamo Theory 8.1 The Dynamo Problem Disc Dynamos Magnetohydrodynamics and Plasma Physics The Earth Dynamo Problem The Magnetic Induction Equation Introduction Physical Insight The a- and co-effects of Dynamo Theory a-effect The co-effect and a Heuristic ctco-dynamo Dynamo numbers and oc 2 - and a 2 G)-Dynamos Waves in Dynamo Theory MHDWaves Planetary Waves Symmetries in Dynamo Theory The Importance of Symmetries The Dynamo Families Theories for Geomagnetic Secular Variations and Magnetic Field Reversais Secular Variation Reversais 336 Chapter 9 Dynamo Theory 9.1 Vector Spherical Harmonics The Helmholtz Theorem Helmholtz Scalar Equation Helmholtz Vector Equation Free-Decay Modes Kinematic Dynamos Toroidal and Poloidal Fields Bullard-Gellman Models Fast Dynamos Cowling's Theorem and Other Constraints Turbulence in the Core The et- and ß-Effects 356

8 Contents xi a 2 -Dynamos Dynamo Waves Dynamics of the Geodynamo Taylor-State versus Model-Z Dynamos Weak-Field Hydromagnetic Models Strong-Field Models The Role of the Inner Core 372 Chapter 10 The Magnetic Fields of the Sun, Moon, and Planets 10.1 Origin of the Solar System The Sun General Properties Solar Magnetic Field Solar Magnetic Field Theory The Moon General Properties The Lunar Magnetic Field Lunar Rock Magnetism Origin of the Ancient Lunar Magnetic Field Meteorites Magnetic Fields of the Planets Planetary Magnetism Solar System Dynamos Geomagnetic Relevance 407 Chapter 11 Examples of Synthesis 11.1 Fluid Velocities in the Core Overview The Uniqueness Problem Models and Results Core-Mantle Coupling: Length of Day Nutation and Wobble Electromagnetic Coupling Topographical Coupling 421

9 XÜ The Magnetic Field ofthe Earth 11.3 Paleomagnetism and Dynamo Theory Testing Geodynamo Theory Constraints on Dynamo Theory Variations at the Core-Mantle Boundary and the Earth's Surface Spatial Variation at the CMB Variations ofthe CMB Boundary Conditions with Time 432 Appendix A SI and Gaussian CGS Units and Conversion Factors 437 Appendix B Functions Associated with Spherical Harmonics B.1 The Scalar Potential 439 B.2 The Legendre Functions P/ 440 B.3 The Associated Legendre Functions P/ m 441 B.4 Normalization of the Associated Legendre Functions 441 B.5 Inclination Anomaly Model for Zonal Harmonics 443 References 445 Author Index 509 Index 523