Mantle Convection in the Earth and Planets (Cambridge Monographs on Mechan)

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 15
1.1 Introduction......Page 19
1.2 Continental Drift......Page 23
1.3 The Concept of Subsolidus Mantle Convection......Page 26
1.4 Paleomagnetism......Page 29
1.5 Seafloor Spreading......Page 30
1.6 Subduction and Area Conservation......Page 31
2.1 Introduction......Page 34
2.2 The Lithosphere......Page 43
2.3 Accretional Plate Margins (Ocean Ridges)......Page 44
2.4 Transform Faults......Page 46
2.5 Subduction......Page 47
2.5.1 Rheology of Subduction......Page 51
2.5.2 Dip of Subduction Zones......Page 52
2.5.4 Why Are Island Arcs Arcs?......Page 53
2.5.5 Subduction Zone Volcanism......Page 54
2.5.6 Back-arc Basins......Page 56
2.6 Hot Spots and Mantle Plumes......Page 57
2.7.1 Composition......Page 60
2.7.2 Delamination and Recycling of the Continents......Page 62
2.7.3 Continental Crustal Formation......Page 65
2.8 Plate Motions......Page 66
2.9 The Driving Force for Plate Tectonics......Page 70
2.10 The Wilson Cycle and the Time Dependence of Plate Tectonics......Page 75
3.2 Spherically Averaged Earth Structure......Page 81
3.3 The Crust......Page 86
3.3.1 Oceanic Crust......Page 87
3.3.2 Continental Crust......Page 89
3.4 The Upper Mantle......Page 92
3.4.1 Radial Structure of the Upper Mantle......Page 93
3.4.2 Upper Mantle Composition......Page 98
3.5.1 The 410 km Seismic Discontinuity......Page 102
3.5.2 The 660 km Seismic Discontinuity......Page 104
3.6 The Lower Mantle......Page 110
3.7 The D\" Layer and the Core–Mantle Boundary......Page 112
3.8 The Core......Page 115
3.9 Three-dimensional Structure of the Mantle......Page 119
3.9.1 Upper Mantle Seismic Heterogeneity and Anisotropy......Page 121
3.9.2 Extensions of Subducted Slabs into the Lower Mantle......Page 124
3.9.3 Lower Mantle Seismic Heterogeneity......Page 131
3.9.4 Topography of the Core–Mantle Boundary......Page 134
4.1.1 Cooling of an Isothermal Earth......Page 136
4.1.2 Cooling of a Molten Earth......Page 141
4.1.3 Conductive Cooling with Heat Generation......Page 143
4.1.4 Mantle Convection and Mantle Temperatures......Page 145
4.1.5 Surface Heat Flow and Internal Heat Sources......Page 146
4.2.1 Half-space Cooling Model......Page 150
4.2.2 Plate Cooling Model......Page 157
4.3 Temperatures in the Continental Lithosphere......Page 161
4.4 Partial Melting and the Low-velocity Zone......Page 169
4.5 Temperatures, Partial Melting, and Melt Migration Beneath Spreading Centers......Page 171
4.5.1 Melt Migration by Porous Flow......Page 172
4.5.2 Melt Migration in Fractures......Page 184
4.6.1 Frictional Heating on the Slip Zone......Page 194
4.6.2 Phase Changes in the Descending Slab......Page 198
4.6.3 Metastability of the Olivine–Spinel Phase Change in the Descending Slab......Page 203
4.7 The Adiabatic Mantle......Page 206
4.8 Solid-state Phase Transformations and the Geotherm......Page 209
4.9 Temperatures in the Core and the D Layer......Page 218
4.10 Temperatures in the Transition Zone and Lower Mantle......Page 222
4.11.1 Thermal Expansion......Page 225
4.11.3 Adiabatic Temperature Scale Height......Page 227
4.11.4 Thermal Conductivity and Thermal Diffusivity......Page 228
5.1.2 Viscoelasticity......Page 230
5.1.3 Postglacial Rebound......Page 231
5.1.6 Laboratory Experiments......Page 233
5.2 Global Isostatic Adjustment......Page 234
5.2.1.1 Half-space Model......Page 235
5.2.1.2 Spherical Shell Model......Page 240
5.2.1.3 Postglacial Relaxation Time and Inferred Mantle Viscosity......Page 241
5.2.2 Ice Load Histories and Postglacial Sea Levels......Page 242
5.2.3 Evidence for a Low-viscosity Asthenosphere Channel......Page 245
5.3 Changes in the Length of Day......Page 248
5.4 True Polar Wander......Page 249
5.5 Response to Internal Loads......Page 250
5.6 Incorporation of Surface Plate Motion......Page 255
5.7 Application of Inverse Methods......Page 256
5.9 Physics of Mantle Creep......Page 258
5.10 Viscosity Functions......Page 266
6.2 Conservation of Mass......Page 269
6.3 Stream Functions and Streamlines......Page 271
6.4 Conservation of Momentum......Page 272
6.5 Navier–Stokes Equations......Page 273
6.7 Stream Function Equation......Page 275
6.8 Thermodynamics......Page 277
6.9 Conservation of Energy......Page 280
6.10 Approximate Equations......Page 283
6.12 Reference State......Page 292
6.13 Gravitational Potential and the Poisson Equation......Page 297
6.14 Conservation of Momentum Equations in Cartesian, Cylindrical, and Spherical Polar Coordinates......Page 298
6.15 Navier–Stokes Equations in Cartesian, Cylindrical, and Spherical Polar Coordinates......Page 299
6.16 Conservation of Energy Equation in Cartesian, Cylindrical, and Spherical Polar Coordinates......Page 304
7.2 Summary of Basic Equations......Page 306
7.3 Plane Layer Heated from Below......Page 308
7.4 Plane Layer with a Univariant Phase Transition Heated from Below......Page 315
7.5 Plane Layer Heated from Within......Page 321
7.6 Semi-infinite Fluid with Depth-dependent Viscosity......Page 325
7.7 Fluid Spheres and Spherical Shells......Page 326
7.7.1 The Internally Heated Sphere......Page 331
7.7.2 Spherical Shells Heated Both from Within and from Below......Page 334
7.7.3 Spherical Shell Heated from Within......Page 336
7.7.4 Spherical Shell Heated from Below......Page 338
7.8 Spherical Harmonics......Page 341
8.1 Introduction......Page 348
8.2 Eigenmode Expansions......Page 349
8.3 Lorenz Equations......Page 350
8.4 Higher-order Truncations......Page 355
8.5 Chaotic Mantle Mixing......Page 362
8.6.1 Boundary Layer Stability Analysis......Page 368
8.6.2 Boundary Layer Analysis of Cellular Convection......Page 371
8.7 Single-mode Mean Field Approximation......Page 379
8.8.1 Two-dimensional Convection......Page 385
8.8.2 Three-dimensional Convection, Hexagons......Page 388
9.1 Introduction......Page 394
9.2 Steady Convection at Large Rayleigh Number......Page 396
9.3 Internal Heat Sources and Time Dependence......Page 400
9.4 Convection with Surface Plates......Page 403
9.5 Role of Phase and Chemical Changes......Page 408
9.6 Effects of Temperature-and Pressure-dependent Viscosity......Page 411
9.7 Effects of Temperature-dependent Viscosity: Slab Strength......Page 414
9.8 Mantle Plume Interaction with an Endothermic Phase Change......Page 419
9.9 Non-Newtonian Viscosity......Page 422
9.10 Depth-dependent Thermodynamic and Transport Properties......Page 423
9.12 Continents and Convection......Page 426
9.13 Convection in the D\" Layer......Page 431
10.1 Introduction......Page 435
10.2.1 Spherical Shell Convection......Page 436
10.2.2 Rectangular Box Convection......Page 446
10.3 Unsteady, Asymmetric Modes of Convection......Page 458
10.4 Mantle Avalanches......Page 472
10.5 Depth-dependent Viscosity......Page 488
10.6 Two-layer Convection......Page 491
10.7 Compressibility and Adiabatic and Viscous Heating......Page 495
10.8 Plate-like Rheology......Page 506
10.9 Three-dimensional Models of Convection Beneath Ridges and Continents......Page 516
11.1 Introduction......Page 517
11.2 Hot Spot Tracks......Page 519
11.3 Hot Spot Swells......Page 523
11.4 Hot Spot Basalts and Excess Temperature......Page 526
11.5 Hot Spot Energetics......Page 528
11.6 Evidence for Mantle Plumes from Seismology and the Geoid......Page 532
11.7 Plume Generation......Page 536
11.8 Plume Heads and Massive Eruptions......Page 543
11.9 Plume Conduits and Halos......Page 547
11.10 Instabilities and Waves......Page 551
11.11 Dynamic Support of Hot Spot Swells......Page 555
11.12 Plume–Ridge Interaction......Page 561
11.13 Massive Eruptions and Global Change......Page 563
12.2 Geochemical Reservoirs......Page 565
12.3 Oceanic Basalts and Their Mantle Reservoirs......Page 567
12.4.1 Radioactivity......Page 569
12.4.2 A Two-reservoir Model with Instantaneous Crustal Differentiation......Page 571
12.4.3 Application of the Two-reservoir Model with Instantaneous Crustal Addition to the Sm–Nd and Rb–Sr Systems......Page 573
12.4.4 A Two-reservoir Model with a Constant Rate of Crustal Growth......Page 574
12.4.5 Application of the Two-reservoir Model with Crustal Growth Linear in Time to the Sm–Nd System......Page 576
12.4.6 A Two-reservoir Model with Crustal Recycling......Page 579
12.4.7 Application of the Two-reservoir Model with Crustal Recycling to the Sm–Nd System......Page 581
12.5.1 Lead Isotope Systematics......Page 583
12.5.2 Application to the Instantaneous Crustal Differentiation Model......Page 587
12.6 Noble Gas Systems......Page 591
12.6.1 Helium......Page 592
12.6.2 Argon......Page 595
12.6.3 Xenon......Page 597
12.7 Isotope Systematics of Ocean Island Basalts......Page 598
12.8 Summary......Page 601
13.1 Introduction......Page 604
13.2.1 Initial State......Page 605
13.2.2 Energy Balance and Surface Heat Flow Parameterization......Page 606
13.2.3 Temperature Dependence of Mantle Viscosity and Self-regulation......Page 608
13.2.4 Model Results......Page 609
13.2.5 Surface Heat Flow, Internal Heating, and Secular Cooling......Page 612
13.2.6 Volatile Dependence of Mantle Viscosity and Self-regulation......Page 614
13.3.1 A Model of Coupled Core–Mantle Thermal Evolution......Page 620
13.3.2 Core Evolution and Magnetic Field Generation......Page 625
13.4 Two-layer Mantle Convection and Thermal Evolution......Page 629
13.5 Scaling Laws for Convection with Strongly Temperature Dependent Viscosity......Page 635
13.6 Episodicity in the Thermal Evolution of the Earth......Page 643
13.7 Continental Crustal Growth and Earth Thermal History......Page 645
14.1 Introduction......Page 651
14.1.1 The Role of Subsolidus Convection in the Solar System......Page 652
14.1.2 Surface Ages and Hypsometry of the Terrestrial Planets......Page 653
14.2.1 Comparison of Two Sisters: Venus versus Earth......Page 658
14.2.2 Heat Transport in Venus......Page 665
14.2.3 Venusian Highlands and Terrestrial Continents......Page 674
14.2.4 Models of Convection in Venus......Page 675
14.2.5 Topography and the Geoid: Constraints on Convection Models......Page 679
14.2.6 Convection Models with a Sluggish or Stagnant Lid......Page 682
14.2.7 Convection Models with Phase Changes and Variable Viscosity......Page 685
14.2.8 Thermal History Models of Venus......Page 690
14.2.9 Why is There no Dynamo in Venus?......Page 696
14.3.1 Surface Tectonic and Volcanic Features......Page 699
14.3.2 Internal Structure......Page 704
14.3.3 The Martian Lithosphere......Page 705
14.3.4 Radiogenic Heat Production......Page 708
14.3.5 Martian Thermal History: Effects of Crustal Differentiation......Page 709
14.3.6 Martian Thermal History: Magnetic Field Generation......Page 716
14.3.7 Martian Thermal History Models with a Stagnant Lid......Page 724
14.3.8 Convection Patterns in Mars......Page 726
14.3.9 Summary......Page 733
14.4.1 The Lunar Crust: Evidence from the Apollo Missions......Page 734
14.4.2 Differentiation of the Lunar Interior: A Magma Ocean......Page 736
14.4.3 Lunar Topography and Gravity......Page 737
14.4.4 Early Lunar History......Page 740
14.4.6 Crustal Magnetization: Implications for a Lunar Core and Early Dynamo......Page 744
14.4.8 Lunar Heat Flow and Convection......Page 745
14.4.9 Lunar Thermal Evolution with Crustal Differentiation......Page 746
14.4.10 Lunar Isotope Ratios: Implications for the Moon’s Evolution......Page 749
14.5.1 Volcanism and Heat Sources: Tidal Dissipation......Page 754
14.5.2 Some Consequences of Tidal Dissipation......Page 757
14.5.3 Io’s Internal Structure......Page 758
14.5.4 Models of Tidal Dissipation in Io......Page 760
14.5.5 Models of the Thermal and Orbital Dynamical History of Io......Page 764
14.6.1 Composition and Internal Structure......Page 766
14.6.2 Accretion, Core Formation, and Temperature......Page 768
14.6.3 Thermal History......Page 770
14.7.2 Europa......Page 774
14.7.3 Ganymede......Page 778
14.7.4 Callisto......Page 779
14.7.5 Convection in Icy Satellites......Page 781
15.1 Introduction......Page 785
15.2.1 Subduction......Page 792
15.3.1 Accretional Plate Margins......Page 796
15.3.2 Mantle Plumes......Page 798
15.4.1 The Lithosphere......Page 800
15.4.2 The D\" Layer......Page 801
15.5 The General Circulation......Page 802
15.6 Time Dependence......Page 804
15.7 Special Effects in Mantle Convection......Page 805
15.7.1 Solid-state Phase Transformations......Page 806
15.7.3 Nonlinear Viscosity......Page 807
15.7.4 Compressibility......Page 808
15.8.1 Plates......Page 809
15.9 Comparative Planetology......Page 810
15.9.1 Venus......Page 811
15.9.3 The Moon......Page 812
15.9.5 Icy Satellites......Page 813
References......Page 815
Appendix: Table of Variables......Page 893
Author Index......Page 911
Subject Index......Page 931