Synchronization and Triggering: from Fracture to Earthquake Processes (eBook)

Contents 10
Introduction 14
Part I Theoretical Studies 18
Chapter 1: Nonlinear Dynamics as a Tool for Revealing Synchronization and Ordering in Geophysical Time Series: Application to Caucasus Seismicity 19
1.1 Introduction 19
1.2 Overview of nonlinear data analysis methods 20
1.3 Investigation of dynamics of complex natural process: Caucasus seismicity 29
References 35
Chapter 2: Models of Stick-Slip Motion: Impact of Periodic Forcing 38
2.1 Introduction 38
2.2 Main details of experimental stick-slip results 39
2.3 Mathematical models of friction 42
References 47
Chapter 3: Shear Oscillations, Rotations and Interactions in Asymmetric Continuum 49
3.1 Introduction 49
3.2 Asymmetric Continuum 50
3.3 Rotation and shear-twist motions 52
3.4 Dislocations and disclinations: fragmentation and cracks 55
3.5 Interaction fields 56
3.6 Direct relations between defect and electric fields 58
3.7 Interaction examples 58
3.7.1 Thermal interaction 58
3.7.2 Piezoelectric effects 59
3.7.3 Polarization gradient theory 59
3.7.4 Interaction chains: electric and acoustic effects 61
3.8 Conclusions 61
References 62
Chapter 4: Processes in Micro-Fracture Continuum 64
4.1 Introduction 64
4.2 Asymmetric Continuum 65
4.2.1 Standard asymmetric continuum 65
4.3 Slip and fragmentation transport in fracture micro-continuum 67
4.4 Local transport in sources of asymmetric elastic continuum 69
4.5 Shear and confining loads 70
4.6 Conclusions 72
References 73
Chapter 5: On a Simple Stochastic Cellular Automaton with Avalanches: Simulation and Analytical Results 75
5.1 Introduction 75
5.2 The random domino automaton 77
5.3 Quasi-equilibrium equations 78
5.4 Summary and discussion 84
References 87
Chapter 6: Ito Equations as Macroscopic Stochastic Models of Geophysical Phenomena - Construction of the Models on the Basis of Time Series 88
6.1 Introduction 88
6.2 What do a(y) and b(y) consist of? 90
6.3 Extracting microscopic information from a(y) and b(y) 97
6.4 Analytical derivation of a(y) and b(y) 99
6.5 Stochastic control in Ito models 104
6.6 Conclusions 105
References 106
Chapter 7: The Importance of Privilege for the Appearance of Long-Tail Distributions 108
7.1 Introduction 108
7.2 Nonlinear Transformations 109
7.2.1 Transformation y = g(x) of a random variable x 110
7.2.2 Transformations given by solutions of random differential equations 111
7.3 The Master Equation and the Privilege Concept 112
7.3.1 The Pure Birth Master equation 113
7.3.2 The Fokker-Planck equation 115
7.4 The Role of Boundary Conditions 116
7.5 Ito Equations and the Privilege 118
7.6 Multiplicative Processes and the Privilege 120
7.7 Applications 121
7.7.1 Transformation y = g(x) 121
7.7.2 Multiplication of probabilities 122
7.7.3 The Master equation 122
7.7.4 Multiplicative processes 126
7.7.5 Ito equations 127
7.8 Conclusions 127
References 128
Part II Laboratory Experiments 131
Chapter 8: Triggering and Synchronization of Stick-Slip: Experiments on Spring-Slider System 132
8.1 Introduction 132
8.2 Electromagnetic Triggering of Slip 133
8.2.1 EM Triggering - Experimental Setup 134
8.2.2 EM Triggering Experiments 135
8.2.3 Experimental Procedure and Case Stories 135
8.2.4 EM Triggering - The First Mode 136
8.2.5 EM Triggering - The Second Mode 136
8.2.6 Finding Mechanical Equivalent of EM Impact 137
8.3 Analysis of Recorded Acoustic Waveforms 138
8.4 The Elementary Theory of EM Coupling with the Friction Force 139
8.5 Synchronization of Stick-slip 141
8.5.1 Synchronization: Experimental Setup 141
8.5.2 Signal Processing: Separation of AE Wave Trains 142
8.5.3 Synchronization: Results 144
8.6 Synchronization: Quantitative Analysis 151
8.7 Phase Time Delay 156
8.8 Synchronization by Mechanical Forcing 157
8.9 High Order Synchronization of Stick-Slip Process: Experiments on Spring-Slider System 158
8.9.1 High Order Synchronization 159
8.9.2 HOS Synchronization by Electromagnetic Forcing 160
8.9.3 HOS by Mechanical Forcing 162
8.9.4 Synchronization of AE Signal Terminations 166
8.10 EM Synchronization: Physical Mechanism of Period Doubling 169
8.11 Conclusions 171
References 171
Chapter 9: Oscillating Load-Induced Acoustic Emission in Laboratory Experiment 174
References 185
Chapter 10: Acoustic Emission Dynamics Initiated by Fluid Infusion on Laboratory Scale 187
10.1 Introduction 187
10.2 Experiment procedure 188
10.3 Experiment results 188
10.3.1 Initiation #1 188
10.3.2 Initiation #2 192
10.3.3 Initiation #3 194
10.4 Discussion 197
10.5 Conclusions 206
References 207
Chapter 11: Acoustic Emission Spectra Classification from Rock Samples of Etna Basalt in Deformation-Decompression Laboratory Experiments 209
11.1 Introduction 210
11.2 The data set 211
11.3 Method 212
11.4 Results and discussion 214
11.5 Conclusions 217
References 218
Chapter 12: Phase-Shifted Fields: Some Experimental Evidence 220
12.1 Introduction 220
12.2 Synchronization and interaction: experimental evidence 221
12.3 Theoretical interpretation of co-action and synchronization effects 224
12.3.1 Conclusions 227
References 227
Part III Field Observations 228
Chapter 13: Periodical Oscillations of Microseisms before the Sumatra Earthquake of December 26, 2004 229
13.1 Introduction 229
13.2 Microseismic data 231
13.3 Results 234
13.4 Discussion 244
13.5 Conclusion 246
References 246
Chapter 14: Synchronizations of Microseismic Oscillations as the Indicators of the Instability of a Seismically Active Region 248
14.1 Introduction 248
14.2 Initial data 249
14.2.1 Brief description of the methods 250
14.2.1.1 Transforming to generalized Hurst exponent variations 250
14.2.1.2 Spectral measure of synchronization 252
14.3 Synchronization of microseismic oscillations within minute range of periods 252
14.4 Conclusion 256
References 256
Chapter 15: Multifractal Parameters of Low-Frequency Microseisms 258
15.1 Introduction 258
15.2 Initial Data: F-net Network 260
15.3 Parameters of the Singularity Spectrum of Low-frequency Microseisms 261
15.4 Variations in the Singularity Spectrum Support Width 264
15.5 Variations in the Generalized Hurst Exponent 266
15.6 Variations in the Products of Cluster Canonical Correlations 267
15.7 Variations in the Cluster Spectral Measure of Coherence 271
15.8 Conclusions 275
References 276
Chapter 16: Changes in Dynamics of Seismic Processes Around Enguri High Dam Reservoir Induced by Periodic Variation of Water Level 278
16.1 Introduction 279
16.2 Data and Methods Used 280
16.3 Results and Discussions 284
16.4 Conclusions 289
References 290
Chapter 17: Earthquakes´ Signatures in Dynamics of Water Level Variations in Boreholes 292
17.1 Introduction 293
17.2 Methods of analysis 293
17.3 Results and discussion 294
17.4 Conclusions 307
References 308
Chapter 18: Detecting Quasi-Harmonic Factors Synchronizing Relaxation Processes: Application to Seismology 309
18.1 Introduction 310
18.2 The model of relaxation oscillator synchronization 312
18.3 The compliance of synchronization model with statistical requirements of data processing 316
18.4 The study of strong earthquake synchronization 317
18.5 The study of synchronization of weak earthquakes 320
18.6 Synchronization in model laboratory experiments 322
18.7 Discussion 323
18.8 Conclusions 324
References 325
Chapter 19: Stacked Analysis of Earthquake Sequences: Statistical Space-Time Definition of Clustering and Omori Law Behavior 327
19.1 Introduction 328
19.1.1 Data 329
19.2 Space-Time Fractal Dimensions of Seismicity 331
19.3 Omori law analysis 335
19.4 Conclusions 339
References 340
Chapter 20: Dynamical Changes Induced by Strong Electromagnetic Discharges in Earthquakes´ Waiting Time Distribution at the Bishkek Test Area (Central Asia) 342
20.1 Introduction 343
20.2 Methods 343
20.3 Data and Analysis 346
20.4 Results and discussion 347
20.5 Conclusion 360
References 361
Index 364