Louis Lliboutry

Quantitative Geophysics and Geology

Published in association with Springer Praxis Publishing PR Chichester, UK Contents

Preface xiii

1 RATIONALE 1 1.1 Geological sciences and geophysical sciences 1 1.2 Geological rules reduced to the laws of physics 2 1.3 Usefulness of physical modeis 3 1.4 Baconian and Popperian approaches to reality 4

2 EARTHQUAKES AND SEISMIC EXPLORATION 6 2.1 Tectonic earthquakes. Faults 6 2.2 Induced, volcanic and other types of earthquakes 8 2.3 Macroseismics: seismic intensity in a given location 9 2.4 Seismic waves: generalities 11 2.5 Seismometers 13 2.6 Dissipated energy, seismic efficiency, seismic moment 15 2.7 Magnitude of an earthquake 17 2.8 Ray renection and refraction; head and surface waves 19 2.9 Inner Constitution of the Earth and seismic phases 22 2.10 Techniques of seismic exploration 25 2.11 Focal mechanisms. Synthetic seismograms 27

3 PETROGRAPHY AND METAMORPHISM 29 3.1 Main minerals in crystalline rocks 29 3.2 Rocks - Generalities 32 3.3 Main crystalline rocks 34 3.4 Magma formation and intrusion 35 3.5 Nature of the oceanic crust and upper mantle 39 3.6 Metamorphic rocks 40 vi Contents

3.7 Geothermo-barometers 42 3.8 Facies and metamorphic rocks 43 3.9 Nature of the Continental crust 46

4 GEOMAGNETISM AND ROCK MAGNETIZATION 49 4.1 Magnetic fields produced by magnetic materials 49 4.2 Magnetic fields produced by electric currents 53 4.3 Measuring Instruments 55 4.4 Origin of the regulär terrestrial magnetic field 57 4.5 Outer geomagnetic field and magneto-telluric exploration 58 4.6 Spherical harmonics of geomagnetic potential 60 4.7 Magnetization produced by a magnetic excitation 61 4.8 Microscopic processes of ferromagnetism 63 4.9 Single-domain ferromagnetism of small inclusions 64 4.10 Magnetic mineralogy, ferro- and anti-ferromagnetism 65 4.11 Thermo-remanent and chemical remanent magnetization 66 4.12 Archaeomagnetism 67 4.13 Geomagnetic field reversals 68 4.14 Remanent magnetization of Sediments 70

5 MID-OCEAN RIDGES AND HOT SPOTS 72 5.1 Geophysical exploration of the oceans 72 5.2 Mid-ocean ridges 72 5.3 Magnetic anomaly stripes 76 5.4 Transform faults and spreading direction 79 5.5 The model of lithospheric plates (shells) 80 5.6 Limits of traditional plate theory 82 5.7 Mid-ocean ridge processes 84 5.8 Evolution of mid-ocean ridges with time 85 5.9 Passive continental margins 89 5.10 Intra-plate volcanism and hot spots 91

6 MOVEMENT OF LITHOSPHERIC SHELLS 97 6.1 Kinematics of a rigid figure in the plane or on the sphere 97 6.2 Equations of 'instantaneous' plate kinematics 99 6.3 Determination of the relative angular velocities 102 6.4 Extending the palaeomagnetic chronology 103 6.5 No-net-rotation frame of reference and NNR absolute velocities . . 104 6.6 Hot-spot frame of reference and HS absolute velocities 106 6.7 Evolution of the Pacific plate 109 6.8 Spatial geodesy techniques 112 6.9 Relative movements of lithospheric shells on the decennial scale . . 115 6.10 Movements in the boundary zones 117 Contents vii

7 SUBDUCTION ZONES AND ISLAND ARCS 119 7.1 Oceanic trenches and island arcs of the Pacific 119 7.2 Wadati-Benioff surfaces 121 7.3 Volcanism and geothermal flux 127 7.4 Extension phases of back-arc basins 128 7.5 Accretion prisms and fore-arc troughs 130 7.6 Ablative subduction 132 7.7 Ophiolite overthrust sheets 132 7.8 Subduction of oceanic back-arc basins below continental island arcs 134 7.9 Initiation of subduction 135 7.10 Subduction of the Australian continent below the Banda sea oceanic plate 136 8 EARTH ROTATION, GRAVIMETRY, AND ISOSTASY 140 8.1 Earth rotation and the Coriolis force 140 8.2 Newtonian potential in a Galilean frame of reference 142 8.3 Gravity potential and geoid 145 8.4 Geoid determination 146 8.5 Altitude of a place 148 8.6 Gravimetry 148 8.7 Isostasy 150 8.8 Isostatic equilibrium and Archimedes thrust 152 8.9 Vertical movements due to erosion or Sedimentation 154 8.10 Time necessary for the isostatic adjustment 156 8.11 Earth-Moon angular momentum 156 8.12 Slowing down of the Earth's rotation and increasing distance to the Moon 158 8.13 Non-tidal variations in the angular velocity 161 8.14 Earth and Moon formation 162 9 TERRESTRIAL HEAT 163 9.1 Heat diffusion 163 9.2 Measuring the geothermal flux 165 9.3 Influence of the topography: Case with an analytical Solution. . . . 166 9.4 Temperatures in a moving medium 168 9.5 Solutions of the form T =f(z) x g(nt) 169 9.6 Solutions for a half-space with a singular point 171 9.7 Temperatures in a polar ice cap 172 9.8 Subsidence of the oceanic lithosphere 174 9.9 Modelling the cooling of oceanic plates 176 9.10 Crossing of a partially molten LVZ by the geothermal flux 179 9.11 Estimation of geothermal fluxes 180 9.12 Origins of terrestrial heat 181 9.13 Concentration of radioactivity in granitic terrains 183 9.14 Lithospheric thickness and basin subsidence 185 9.15 LVZ below the continents 187

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10 ELASTIC AND ISOVISCOUS MEDIA 189 10.1 Definition of stress in a continuous medium 189 10.2 Elastic strains and viscous Stresses 190 10.3 Stress tensor and equilibrium equations 191 10.4 Stress invariants and deviatoric stress 194 10.5 Small strains and strain rates 195 10.6 Isotropie elasticity 197 10.7 The Navier equation and its consequences 200 10.8 Solution to some elastic problems 202 10.9 Isotropie Newtonian viscosity 205 10.10 Load distributed over an elastic or isoviscous layer 206 10.11 Flow of an isoviscous fluid in a cylinder 207 10.12 Permeability and porosity of soils 210

11 ROCK CREEP 212 11.1 Plasticity and creep 212 11.2 Rock textures and deformation 213 11.3 Ideal plasticity and n-power law isotropic viscosity 217 11.4 Dislocations in crystals 220 11.5 Role of point defects in creep 222 11.6 From microscopic to macroscopic creep 224 11.7 Fabrics and superficial energy of grains 225 11.8 Transient creep 228 11.9 Anisotropie materials 231

12 ROCK FRACTURE AND EARTHQUAKE PREDICTION 234 12.1 Normal stress and shear stress on any plane 234 12.2 Different states of stress 235 12.3 Tensile strength in mechanical tests 237 12.4 Theory of the Mohr envelope 238 12.5 Microscopic fracture mechanisms 240 12.6 Plastic bodies in mechanics 242 12.7 Soil plasticity, consolidation and dilatancy 245 12.8 Rock fracture, joints and faults 248 12.9 Focal mechanism and real fracture mechanism 249 12.10 Stick-slip motion and earthquake recurrence 252 12.11 Aseismic slip and silent earthquakes 253 12.12 Intermediate and deep earthquakes 256 12.13 Seismic hazard estimation from historical earthquakes 256 12.14 Palaeoseismicity 259 12.15 Long- and medium-term seismic prediction 260 12.16 Short-term seismic prediction 261 Contents ix

13 MECHANICS OF LITHOSPHERIC PLATES 263 13.1 Homogeneous elastic plate model 263 13.2 Bending of an oceanic plate 267 13.3 Correlation between topography and Bouguer anomaly 270 13.4 Elastic lithosphere thickness 273 13.5 Measuring Stresses in the crust 275 13.6 Driving mechanism of lithospheric shells 276 13.7 Equilibrium of the forces acting on plates 279 13.8 Forces acting on the subducted plates 281 13.9 Lateral extrusions and the perfect plastic model 282

14 OROGENIC PROCESSES 286 14.1 Dating of events 286 14.2 The old geosyncline concept 287 14.3 Orogenic phases and orogenies 289 14.4 Folding 290 14.5 Theory of folding initiation 293 14.6 Gravitational nappes 295 14.7 Large overthrusts of the basement 296 14.8 Warming of a plate suddenly shortened horizontally 299 14.9 Mechanical properties of Continental lithosphere 301 14.10 Consequences of the existence of a crustal asthenosphere 302 14.11 Post-orogenic subsidence 304 14.12 Post-orogenic tectonic stress 307 14.13 Exhumation by retro-subduction 308

15 A SHORT HISTORY OF THE MESOZOIC AND CENOZOIC .... 330 15.1 Formation and breaking up of Pangaea 320 15.2 Formation of Asia 323 15.3 Punching by India and its consequences 328 15.4 Tethys and the Mediterranean mountain chains 330 15.5 The Western Alps 339 15.6 The Apennines and the Tyrrhenian Basin 346 15.7 Other arcs and basins in the Mediterranean 351 15.8 Krikogenic mechanisms in the Western Mediterranean 353 15.9 West Indies arc 354 15.10 Progressive isolation of Antarctica 356

16 POLAR WANDER AND CONTINENTAL DRIFT DURING THE PALAEOZOIC 358 16.1 Astronomical climate factors 358 16.2 Wander of the geographical pole 360 16.3 Causes of the HS absolute wanders of NP and MGP 363

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16.4 Core and terrestrial dynamo 363 16.5 Geomagnetic palaeopoles 366 16.6 MGP wandering from Ordovician to Permian 367 16.7 Orogenic phases in the Palaeozoic 369 16.8 Continental drift between 1,000 and 500 Ma B.P 375

17 MANTLE CHEMISTRY AND CONTINENT FORMATION 376 17.1 Very high pressure studies 376 17.2 Mantle density and phase changes 379 17.3 Penetration of subducted plates into the lower mantle 381 17.4 Seismic tomography 383 17.5 Nucleosynthesis and natural radioactivity 386 17.6 Radiochronology up to 300,000 years 388 17.7 Dating of rock materials 389 17.8 Lead dating 391 17.9 Age of the Earth 392 17.10 Marking by trace elements or isotopic ratios 393 17.11 Formation of the Earth 397 17.12 Chondrites 399 17.13 Progressive appearance of the continents 401 17.14 Continental crust evolution and recycling 402 17.15 Recycling of the oceanic crust 404

18 GLACIATIONS, GLACIO-ISOSTASY AND SEA LEVEL 405 18.1 Sea ice, ice shelves and ice sheets 405 18.2 Glaciations prior to the Pleistocene 406 18.3 Pleistocene stratigraphy 408 18.4 Stages of the last deglaciation 412 18.5 Glacio-isostasy 413 18.6 First modeis of the glacio-isostatic rebound 414 18.7 Modelling with visco-elasitic spherical layers 418 18.8 Inverse problem Solution for a Maxwell earth 420 18.9 Ice cap thickness 421 18.10 Objections to the traditional model of a visco-elastic Earth .... 422

19 THERMAL CONVECTION IN THE MANTLE 428 19.2 Benard-Boussinesq convection 428 19.3 Lorenz equations 431 19.4 Bifurcations and attractors 433 19.5 Experimental studies of Benard-Boussinesq convection 436 19.6 Heat transfer by convection: Nusselt number 437 19.7 Super-adiabatic temperatures and Rayleigh number in the mantle 438 19.8 Influence of plates and variable viscosity on convection 441 Contents xi

19.9 'Hard' turbulence and mantle mixing 443 19.10 D" layer and hot spot origin 445 19.11 Exploitation of seismic tomography data 447

APPENDIX: MATHEMATICAL COMPLEMENTS 450 A.l Invariants of space functions and vector nelds 450 A.2 Spherical harmonics 453 A.3 Error function 454 A.4 Fourier transform 455 A.5 Impulse response and Laplace transform 457

CHRONOSTRATIGRAPHIC UNITS 459 Synoptic table of the Earth's history 459 Palaeomagnetic chronology 460

Bibliography 461

Index 471

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