Earthquake Thermodynamics and Phase Transformation in the Earth's Interior (eBook)

Front Cover 1
Earthquake Thermodynamics and Phase Transformations in the Earth's Interior 4
Copyright Page 5
Contents 6
Contributors 16
Preface 18
Introduction 20
PART I: THERMODYNAMICS AND PHASE TRANSFORMATIONS IN THE EARTH'S INTERIOR 24
Chapter 1. The Composition of the Earth 26
1.1 Structure of the Earth 28
1.2 Chemical Constraints 30
1.3 Early Evolution of the Earth 43
References 44
Chapter 2. Thermodynamics of Chaos and Fractals Applied: Evolution of the Earth and Phase Transformations 48
2.1 Evolution of the Universe 48
2.2 Evolution of the Earth 51
2.3 Evolution Equations and Nonlinear Mappings 53
2.4 Strange Attractors 54
2.5 Examples of Maps 55
2.6 Concept of Temperature in Chaos Theory 56
2.7 Static and Dynamic States 56
2.8 Measures of Entropy and Information 58
2.9 The Lyapounov Exponents 62
2.10 Entropy Production 63
2.11 Entropy Budget of the Earth 66
2.12 The Evolution Criterion 71
2.13 The Driving Force of Evolution 72
2.14 Self-Organization Processes in Galaxies 73
2.15 Fractals 74
2.16 Thermodynamics of Multifractals 78
2.17 The Fractal Properties of Elastic Waves 81
2.18 Random Walk of Dislocations 84
2.19 Chaos in Phase Transformations 88
2.20 Conclusions 100
References 100
Chapter 3. Nonequilibrium Thermodynamics of Nonhydrostatically Stressed Solids 104
3.1 Introduction 104
3.2 Review of Hydrostatic Thermodynamics 105
3.3 Conservation Equations 107
3.4 Constitutive Assumptions 109
3.5 Chemical Potential in Stress Fields 111
3.6 Driving Force of Diffusion and Phase Transition 115
3.7 Phase Equilibria under Stress 118
3.8 Flow Laws of Diffusional Creeps 122
3.9 Summary 123
References 124
Chapter 4. Experiments on Soret Diffusion Applied to Core Dynamics 126
4.1 Review of Experiments Simulating the Core–Mantle Interactions 126
4.2 Experiments on Soret Diffusion 137
4.3 Thermodynamic Modeling of the Core–Mantle Interactions 142
4.4 Concluding Discussion 159
References 160
PART II: STRESS EVOLUTION AND THEORY OF CONTINUOUS DISTRIBUTION OF SELF-DEFORMATION NUCLEI 164
Chapter 5. Deformation Dynamics: Continuum with Self-Deformation Nuclei 166
5.1 Self-Strain Nuclei and Compatibility Conditions 166
5.2 Deformation Measures 167
5.3 Thermal Nuclei 170
5.4 Thermal Nuclei and Dislocations in 2D 172
5.5 Defect Densities and Sources of Incompatibility 174
5.6 Geometrical Objects 176
5.7 Constitutive Relations 179
5.8 Constitutive Laws for Bodies with the Electric-Stress Nuclei 184
References 187
Chapter 6. Evolution, Propagation, and Diffusion of Dislocation Fields 190
6.1 Dislocation Density Flow 190
6.2 Dislocation-Stress Relations 194
6.3 Propagation and Flow Equations for the Dislocation-Related Stress Field 198
6.4 Splitting the Stress Motion Equation into Seismic Wave and Fault-Related Fields 212
6.5 Evolution of Dislocation Fields: Problem of Earthquake Prediction 217
References 219
Chapter 7. Statistical Theory of Dislocations 222
7.1 Introduction 222
7.2 Dynamics and Statistics of Discrete Defects 224
7.3 The Field Equations 226
7.4 Field Equations of Interacting Continua 237
7.5 Approximate Solutions (Multiscale Method) in the One-Dimensional Case 241
7.6 Continuous Distributions of Vacancies 247
References 249
PART III: EARTHQUAKE THERMODYNAMICS AND FRACTURE PROCESSES 252
Chapter 8. Thermodynamics of Point Defects 254
8.1 Formation of Vacancies 254
8.2 Formation of Other Point Defects 264
8.3 Thermodynamics of the Specific Heat 267
8.4 Self-Diffusion 270
8.5 Relation of the Defect Parameters with Bulk Properties 275
References 282
Chapter 9. Thermodynamics of Line Defects and Earthquake Thermodynamics 284
9.1 Introduction 284
9.2 Dislocation Superlattice 286
9.3 Equilibrium Distribution of Vacant Dislocations 288
9.4 Thermodynamic Functions Related to Superlattice 289
9.5 Gibbs Free Energy 291
9.6 The Cµ..2 Model 293
9.7 Earthquake Thermodynamics 294
9.8 Premonitory and Earthquake Fracture Theory 297
9.9 Discussion 299
References 300
Chapter 10. Shear Band Thermodynamic Model of Fracturing 302
10.1 Introduction 302
10.2 Jogs and Kinks 304
10.3 Shear Band Model 305
10.4 Energy Release and Stresses 306
10.5 Source Thickness and Seismic Efficiency 310
10.6 Shear and Tensile Band Model: Mining Shocks and Icequakes 311
10.7 Results for Earthquakes, Mine Shocks, and Icequakes 314
10.8 Discussion 314
References 315
Chapter 11. Energy Budget of Earthquakes and Seismic Efficiency 316
11.1 Introduction 316
11.2 Energy Budget of Earthquakes 316
11.3 Stress on a Fault Plane 317
11.4 Seismic Moment and Radiated Energy 318
11.5 Seismic Efficiency and Radiation Efficiency 319
11.6 Relation between Efficiency and Rupture Speed 320
11.7 Efficiency of Shallow Earthquakes 322
11.8 Deep-Focus Earthquakes 326
References 327
Chapter 12. Coarse-Grained Models and Simulations for Nucleation, Growth, and Arrest of Earthquakes 330
12.1 Introduction 330
12.2 Physical Picture 332
12.3 Two Models for Mainshocks 333
12.4 Consequences, Predictions, and Observational Tests 340
12.5 Final Remarks 342
References 343
Chapter 13. Thermodynamics of Fault Slip 346
13.1 Introduction 346
13.2 Fault Entropy 347
13.3 Physical Interpretation 349
13.4 Conclusions 350
References 350
Chapter 14. Mechanochemistry: A Hypothesis for Shallow Earthquakes 352
14.1 Introduction 352
14.2 Strain, Stress, and Heat Flow Paradoxes 352
14.3 Chemistry: Mineral Alteration and Chemical Transformation 356
14.4 Dynamics: Explosive Release of Chemical Energy 359
14.5 Dynamics: The Genuine Rupture 366
14.6 Consequences and Predictions 368
Appendix 1: Explosive Shock Neglecting Electric Effects 371
Appendix 2: Elastic–Electric Coupled Wave 377
Appendix 3: Structural Shock Including Electric Effects 380
References 383
Chapter 15. The Anticrack Mechanism of High-Pressure Faulting: Summary of Experimental Observations and Geophysical Implications 390
15.1 Introduction 390
15.2 New Results 391
15.3 Discussion 394
References 399
Chapter 16. Anticrack-Associated Faulting and Superplastic Flow in Deep Subduction Zones 402
16.1 Introduction 402
16.2 Antidislocations 405
16.3 Anticrack Formation 409
16.4 Anticrack Development and Faulting 411
16.5 Conclusions 419
References 419
Chapter 17. Chaos and Stability in the Earthquake Source 422
17.1 Introduction 422
17.2 Types of Lattice Defects in the Earthquake Source 423
17.3 Chaos in the Earthquake Source: Observational Evidence 426
17.4 Modeling the Defect Interactions 427
17.5 Stability 434
17.6 Statistical Approach 439
17.7 Concluding Discussion 443
References 444
Chapter 18. Micromorphic Continuum and Fractal Properties of Faults and Earthquakes 448
18.1 Introduction 448
18.2 Micromorphic Continuum 449
18.3 Rotational Effects at the Epicenter Zones 451
18.4 Equation of Equilibrium in Terms of Displacements: Navier Equation and Laplace Equations 452
18.5 Propagation of Deformation along Elastic Plate Boundaries Overlying a Viscoelastic Foundation: Macroscale Governing Equation 454
18.6 Navier Equation, Laplace Field, and Fractal Pattern Formation of Fracturing 456
18.7 Size Distributions of Fractures in the Lithosphere 457
18.8 Relationship between Two Fractal Dimensions 457
18.9 Application of Scaling Laws to Crustal Deformations 458
18.10 Discussion 460
References 461
Chapter 19. Physical and Chemical Properties Related to Defect Structure of Oxides and Silicates Doped with Water and Carbon Dioxide 464
19.1 Introduction 464
19.2 General Properties of Magnesium and Other Metal Oxides 465
19.3 Symbols and Classification of Defects in Magnesium Oxide 468
19.4 Hydrogen and Peroxy Group Formation 471
19.5 Atomic Carbon in MgO Crystals 474
19.6 Dissolution of CO2 in MgO 476
19.7 Dissolution of O2 in MgO 476
19.8 Mechanism of Water Dissolution in Minerals 478
19.9 Formation of Peroxy Ions and Positive Holes in Silicates 480
References 481
PART IV: ELECTRIC AND MAGNETIC FIELDS RELATED TO DEFECT DYNAMICS 484
Chapter 20. Electric Polarization Related to Defects and Transmission of the Related Signals 486
20.1 Generation of Electric Signals in Ionic Crystals 486
20.2 Analytical Calculations for the Transmission of Electric Signals 493
20.3 Numerical Calculations 512
20.4 Conclusions 521
References 521
Chapter 21. Laboratory Investigation of the Electric Signals Preceding the Fracture of Crystalline Insulators 524
21.1 Introduction 524
21.2 Experimental Setup 525
21.3 Results 528
21.4 Interpretation 536
21.5 Conclusions 538
References 539
Chapter 22. Diffusion and Desorption of O- Radicals: Anomalies of Electric Field, Electric Conductivity, and Magnetic Susceptibility as Related to Earthquake Processes 542
22.1 Introduction 542
22.2 Water Dissolved in the Earth's Mantle 543
22.3 Emission of O- Radicals 544
22.4 Hole Electric Current and Conductivity Anomalies 545
22.5 Earthquake-Related Effects 550
22.6 Paramagnetic Anomaly 551
22.7 Diffusion of O° and Other Charge Carriers 552
References 556
Chapter 23. Electric and Electromagnetic Fields Related to Earthquake Formation 558
23.1 Introduction 558
23.2 Charged Dislocations and Thermodynamic Equilibrium of Charges 559
23.3 Electric Field Caused by Polarization and Motion of Charge Carriers 560
23.4 Dipole Moments and Electromagnetic Field Radiation 567
23.5 Simulations of Electric Current Generation and of Electromagnetic Fields 568
23.6 Discussion 571
References 573
Chapter 24. Tectono- and Chemicomagnetic Effects in Tectonically Active Regions 576
24.1 Introduction 576
24.2 Finslerian Continuum Mechanics for Magnetic Material Bodies 576
24.3 Reversible Modeling for Piezomagnetization 579
24.4 A Tectonomagnetic Model for Fault Creep 579
24.5 Chemical Reactions and Magnetic Properties of Rocks by Irreversible Thermodynamics 581
24.6 Geomagnetic Field Anomaly by the Induced Magnetization Changes 582
24.7 Implications for Tectono- and Chemicomagnetic Effects in Tectonically Active Regions 583
References 585
PART V: THERMODYNAMICS OF MULTICOMPONENT CONTINUA 588
Chapter 25. Thermodynamics of Multicomponent Continua 590
25.1 Multicomponent Models in Geophysics 590
25.2 Thermodynamical Foundations of Fluid Mixtures 591
25.3 Some Models of Porous Materials 607
25.4 On Constraints in Models of Porous Materials 641
25.5 Wave Propagation in Porous Materials 654
25.6 Concluding Remarks 675
References 676
Index 680
Previous Volumes in Series 694