ESSENTIALS OF PALEOMAGNETISM

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1 ESSENTIALS OF PALEOMAGNETISM LISA TAUXE With Contributions from Robert F. Butler, R. Van der Voo, and Subir K. Banerjee

2 CONTENTS PREFACE xiii 1 THE PHYSICS OF MAGNETISM What is a magnetic field? Magnetic moment 2 '1.3 Magnetic flux ; Magnetic energy Magnetization and magnetic susceptibility Relationship of B and H 6 17 A brief tour of magnetic units in the cgs system The magnetic potential Origin of the geomagnetic field Problems 13 2 THE GEOMAGNETIC FIELD Components of magnetic vectors Reference magnetic field Geocentric axial dipole (GAD) and other poles.23 '2.4 Plotting magnetic directional data.26 - / D, I transformation Virtual geomagnetic poles Virtual dipole moment Problems.31 3 INDUCED AND REMANENT MAGNETISM * Magnetism at the atomic level Induced magnetization Orbital contribution and diamagnetism Role of electronic spins and paramagnetism Ferromagnetism Problems 45

3 4 MAGNETIC ANISOTROPY AND DOMAINS The magnetic energy of particles Exchange energy Magnetic moments and external fields Magnetocrystalline anisotropy energy Magnetostriction: stress anisotropy Magnetostatic (shape) anisotropy Magnetic energy and magnetic stability Magnetic domains Thermal energy Putting it all together Problems 64 5 MAGNETIC HYSTERESIS The "flipping" field Hysteresis loops Uniaxial anisotropy Magnetic susceptibility Cubic anisotropy Superparamagnetic particles Particles with domain walls Hysteresis of mixtures of SP, SD, and MD grains First-order reversal curves Problems 83 6 MAGNETIC MINERALOGY Iron-oxides Titanomagnetites Fe 3x Ti x Hematite-ilmenite Fe Ti O Oxidation of (titano)magnetites to (titano)maghemites Iron-oxyhydroxides and iron-sulfides FeTi oxides in igneous rocks Magnetic mineralogy of soils and sediments Problems 98 7 HOW ROCKS GET AND STAY MAGNETIZED The concept of dynamic equilibrium Essential Neel theory.' Viscous remanent magnetization Thermal remanent magnetization Chemical remanent magnetization Detrital remanent magnetization Physical alignment of magnetic moments in viscous fluids 116

4 7.6.2 Post-depositional processes ; Inclination error Isothermal remanent magnetization Thermo-viscous remanent magnetization Natural remanent magnetization Artificial remanences Problems APPLIED ROCK (ENVIRONMENTAL) MAGNETISM Images Critical temperatures Magnetic susceptibility Measurement of magnetic susceptibility Temperature dependence Frequency dependence Outcrop measurements Magnetization Magnetic interactions: IRM and ARM techniques IRM "unmixing" Combining thermal and isothermal information for rock magnetic characterization Hysteresis parameters The building blocks of hysteresis loops Hysteresis behavior of mixtures Trends in parameters with grain size Ratios Applications of rock magnetism Paleoclimatic information from lake sediments Paramagnetic contributions to magnetic susceptibility Separation of two superparamagnetic particle size distributions Identification of biogenic magnetite in natural samples Concluding remarks Problems GETTING A PALEOMAGNETIC DIRECTION Paleomagnetic sampling Types of samples Orientation in the field A note on terminology Measurement of magnetic remanence Changing coordinate systems Demagnetization techniques Estimating directions from demagnetization data Vector difference sum Best-fit lines and planes 176

5 9.8 Field strategies Problems PALEOINTENSITY Paleointensity with TRMs Step-wise heating family of experiments Reducing the effect of heating Quality assurance and data selection Paleointensity with DRMs Problems FISHER STATISTICS The normal distribution Statistics of vectors Estimation of Fisher statistics Some illustrations Significance tests Watson's test for randomness Comparison of precision Comparing known and estimated directions Comparing two estimated directions Combining directions and great circles Inclination-only data Is a given data set Fisher distributed? Problems BEYOND FISHER STATISTICS Non-Fisherian parametric approaches The Kent distribution The Bingham distribution The Bingham-LeGoff approximation The bi-gaussian distribution The simple (naive) bootstrap The parametric bootstrap, When are two data sets distinct? Application to the "reversals test" Application to the "fold test" Problems PALEOMAGNETIC TENSORS Anisotropy of magnetic susceptibility Hext statistics Hext confidence ellipses Hext F statistics for significance of eigenvalue ratios.252

6 13.3 Limitations of Hext statistics Bootstrap confidence ellipses Comparing mean eigenvectors with other axes Shape Anisotropy of magnetic remanence Anisotropy of ARM andtrm Anisotropy of DRM Problems ; THE ANCIENT GEOMAGNETIC FIELD Historical measurements Archaeo- and paleomagnetic records Pioneers in paleomagnetism The last seven millenia Westward drift The more distant past Time series of paleomagnetic data Excursions Reversals Geomagnetic polarity time scale a first look The time-averaged field Long-term changes in paleointensity Statistical models of paleosecular variation Problems THE GPTS AND MAGNETOSTRATIGRAPHY Early efforts in defining the GPTS The addition of biostratigraphy Astrochronology A note on terminology Current status of the geological time scale Applications Dating geological sequences Measuring rates Tracing of magnetic isochrons Problems TECTONIC APPLICATIONS OF PALEOMAGNETISM Essentials of plate tectonic theory Poles and apparent polar wander The Gondwana APWP Inclination shallowing and GAD Paleomagnetism and plate reconstructions Discordant poles and displaced terranes 331

7 16.7 Inclination-only data and APWPs Concluding remarks Problems 335 APPENDIX A: DEFINITIONS, DERIVATIONS, AND TRICKS 339 A.1 Definitions 339 A.2 Derivations 343 A.2.1 Langevin function for a paramagnetic substance.343 A.2.2 Superparamagnetism.344 A.3 Useful tricks 345 A.3.1 Spherical trigonometry 345 A.3.2 Vector addition 346 A.3.3 Vector subtraction 346 A.3.4 Vector multiplication 347 A.3.5 Tricks with tensors.347 A.3.6 Upside down triangles, V.357 A.3.7 The statistical bootstrap.361 A.3.8 Directions using a sun compass.362 APPENDIX B: PLOTS USEFUL IN PALEOMAGNETISM.365 B.1 Equal-area projections.365 B.1.1 Calculation of an equal-area projection.365 B.1.2 Plotting directions 365 B.1.3 Bedding tilt corrections 367 B.1.4 Reading ternary diagrams.368 B.1.5 Quantile-Quantile plots 369 APPENDIX C: PALEOMAGNETIC STATISTICS AND PARAMETER ESTIMATION 373 C.1 Hysteresis parameters 373 C.2 Directional statistics 375 C.2.1 Calculation of Watson's V n 375 C.2.2 Combining lines and planes 375 C.2.3 Inclination-only calculation 376 C.2.4 Kent 95% confidence ellipse : 378 C.2.5 Bingham95% confidence parameters 379 C.3 Paleointensity statistics.380 APPENDIX D: ANISOTROPY IN PALEOMAGNETISM 385 D.1 The 15-measurement protocol 385

8 D.2 The spinning protocol 386 D.3 Correction of inclination error with AARM 387 APPENDIX E: THE MagIC DATABASE '. 391 E.1 Introduction 391 E.2 Getting started 392 E.3 Perusing the existing data 392 E.4 Uploading data to the database.392 E.5 Structure of the database tables.393 E.6 A word about method codes 393 APPENDIX F: COMPUTER SKILLS 397 F.1 Programming Python for paleomagnetism 397 F.1.1 Why Python? 397 F.1.2 Installing and starting Python.398 F.1.3 Finding the command line window.398 F.1.4 Programming essentials.398 F.1.5 A first program 400 F.1.6 Variables 400 F.1.7 Data structures 400 F. 1.8 Operations and comparisons.402 F.1.9 Conditionals and flow control.402 R1.10 Input/output 403 F.1.11 Functions and modules,.405 F.1.12 Plotting 405 F.2 Survival *NIX 407 F.2.1 Redirecting input and output.408 F.2.2 Wildcards 408 F.2.3 *NIX commands 409 F.2.4 Text editors 411 F.3 The PmagPy software package.411 F.3.1 Downloading and installing PmagPy.411 F.3.2 General characteristics of PmagPy programs.411 F.3.3 Examples of how to use PmagPy programs.412 R4 Complaints department 461 BIBLIOGRAPHY 463 INDEX 479

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