Complexity of Seismic Time Series: Measurement and Application

Front-matter
Front-matter
Complexity of Seismic Time Series
Complexity of Seismic Time Series
Copyright
List of Contributors
Introduction
References
Foreword
1 Analysis of the Complexity of Seismic Data Sets: Case Study for Caucasus
1.1 Introduction
1.2 Data
1.2.1 Waiting Times and Earthquake Interdistances
1.2.2 Ambient Seismic Noise
1.3 Methods of Analysis
1.4 Results of Analysis
1.4.1 Waiting Times and Earthquake Interdistance Analysis
1.4.2 Ambient Seismic Noise Data Analysis
1.5 Conclusions
Acknowledgement
References
2 Nonextensive Statistical Seismology: An Overview
2.1 Introduction
2.2 The Phenomenology of Earthquake Populations
2.2.1 Frequency–Size Distribution of Earthquakes
2.2.2 Spatiotemporal Properties of Seismicity
2.3 Statistical Physics of Earthquakes
2.3.1 Critical Phenomena and Self-Organized Criticality
2.3.2 Statistical Mechanics and Information Theory
2.4 Nonextensive Statistical Seismology
2.4.1 The Nonadditive Entropy Sq
2.4.2 Optimizing Sq
2.4.3 The Fragment–Asperity Model for Earthquake Magnitudes
2.5 Applications of Nonextensive Statistical Seismology
2.5.1 The Frequency–Magnitude Distribution of Seismicity
2.5.2 Temporal Variations and the Evolution of Seismicity
2.5.3 Spatiotemporal Properties of Seismicity and Nonextensive Statistical Mechanics
2.5.3.1 Spatial Properties of Seismicity
2.5.3.2 Temporal Properties of Seismicity and the Risk Function
2.6 Discussion – Quo Vademus?
Acknowledgements
References
3 Spatiotemporal Clustering of Seismic Occurrence and Its Implementation in Forecasting Models
3.1 Introduction
3.2 A Physical Interpretation of the ETAS Model
3.2.1 Rate-and-State Friction
3.2.2 Viscous Coupling With the Asthenosphere
3.3 Short-Term Aftershock Incompleteness and Its Implementation in the ETAS Model
3.3.1 Mechanisms Responsible for STAI
3.3.2 The Dynamic Scaling ETAS Model
3.3.3 The ETAS Incomplete Model
3.4 Foreshock Occurrence in the ETAS Model
3.4.1 The Foreshock Productivity Law and the Inverse Omori Law
3.4.2 The Foreshock Spatial Distribution
3.4.3 The ETAFS Model
3.5 Numerical Implementation of the ETAS Model
References
4 Fractal, Informational and Topological Methods for the Analysis of Discrete and Continuous Seismic Time Series: An Overview
4.1 Introduction
4.2 Fractal Methods
4.2.1 Coefficient of Variation
4.2.2 Detrended Fluctuation Analysis
4.2.3 Multifractal Detrended Fluctuation Analysis
4.2.4 Allan Factor
4.3 Informational Methods
4.4 Topological Methods
4.5 Conclusions
References
5 Modelling of Persistent Time Series by the Nonlinear Langevin Equation
5.1 Introduction
5.2 Modified Langevin Equation
5.3 Reconstruction Procedures
5.3.1 Modified Numerical Reconstruction Procedure (MNRP)
5.3.2 Modified Semianalytical Reconstruction Procedure (MsARP)
5.4 Testing of the Reconstruction Procedures
5.5 Conclusions
Appendix: Derivation of the Fokker–Planck Equation Associated With the Modified Langevin Equation
Acknowledgements
References
6 Synchronization of Geophysical Field Fluctuations
6.1 Introduction
6.2 Wavelet-Based Robust Coherence Measure
6.3 Multiple Spectral Coherence Measure
6.4 Statistics of Time Fragments
6.5 First Principal Component
6.6 Properties of Global Low-Frequency Seismic Noise
6.7 Low-Frequency Seismic Noise at Japan Islands
6.8 Results for Surrogate Time Series
6.9 Conclusion
Acknowledgement
References
Further Reading
7 Natural Time Analysis of Seismic Time Series
7.1 Introduction
7.2 A Brief Overview of Natural Time Analysis
7.2.1 Background of Natural Time Analysis
7.2.2 The Seismic Data Used
7.2.3 The Two Origins of Self-Similarity and Their Distinction in the Case of Seismicity
7.2.4 Temporal Correlations Between Earthquake Magnitudes by Means of Detrended Fluctuation Analysis
7.3 The Order Parameter of Seismicity in Natural Time
7.3.1 Definition of the Order Parameter and the Construction of Its Probability Density Function
7.3.2 Universal Curve of Seismicity
7.3.3 Similarity of Fluctuations in Correlated Systems Including Seismicity
7.3.4 Identifying the Occurrence Time of a Mainshock Using the Value of the Order Parameter Itself
7.3.5 The Two Types of Complexity Measures Involving Order Parameter Fluctuations and Their Complementarity
7.4 Order Parameter Fluctuations Upon Varying the Natural Time Window Length
7.4.1 The Probability Density Function of the Order Parameter Fluctuations Before a Mainshock
7.4.2 The Variability of the Order Parameter Upon Gradually Approaching a Mainshock
7.5 Order Parameter Fluctuations Upon Sliding a Natural Time Window of Fixed Length: The Global Minimum of the Variability ...
7.6 Conclusions
Acknowledgements
References
8 Complexity in Laboratory Seismology: From Electrical and Acoustic Emissions to Fracture
8.1 Introduction
8.2 AE and PSC Experimental Studies: Laboratory and Field Observations
8.2.1 Fundamentals of Experimental Techniques
8.2.2 Characteristics of PSCs and AE During Stress-Induced Rock Fracturing
8.2.3 A Qualitative Correlation of AE and PSC Features
8.2.4 A Quantitative Correlation of AE and PSCs
8.3 Complexity of Rock Fracture and Similarity With Seismicity
8.3.1 Fundamentals of Tsallis Entropy: A Statistical Mechanics Approach to Laboratory Seismology
8.3.2 Applications to Laboratory Experiments
8.3.3 Natural Time Analysis
8.4 Summary and Open Questions
Acknowledgements
References
Further Reading
9 Complexity and Synchronization Analysis in Natural and Dynamically Forced Stick–Slip: A Review
9.1 Fracture or Friction
9.2 Natural Stick–Slip: Basics
9.2.1 From Static to Dynamic Friction
9.2.2 Laboratory Experiments
9.3 Forced Stick–Slip
9.3.1 Elementary Concepts and Geophysical Consequences
9.3.2 Laboratory Experiments on Forced Stick–Slip
9.4 Forced Stick–Slip Results: Mechanical Forcing
9.5 Measuring Complexity/Ordering of Natural Processes: Nonlinear Dynamics Tools
9.6 Complexity Analysis of Mechanically Forced Stick–Slip
9.6.1 On the Patterns of the Synchronization Area in the Phase Space Plot
9.6.2 Phase Space Plot of the Mechanical Synchronization Area (Arnold Tongue Plot)
9.6.3 Analysis of High-Order Synchronization in the High-Frequency Mode
9.6.4 Additional Tools for Complexity/Synchronization Analysis
9.7 Forced Stick–Slip Results: Electromagnetic Forcing
9.7.1 Experimental Set Up for Electromagnetic Forcing
9.7.2 Electromagnetic Synchronization: Results
9.8 Complexity Analysis of Electromagnetically Forced Stick–Slip
9.8.1 Phase Space Plot of the Electromagnetic Synchronization Area: Arnold Tongue Plot
9.9 Implications of the Forced Stick–Slip Model for Geophysical Phenomena
9.9.1 Tides
9.9.2 Reservoir Load–Unload
9.9.3 Nonvolcanic Tremors
9.10 Future Developments
9.11 Conclusions
Acknowledgements
References
Further Reading
10 Complexity and Time-Dependent Seismic Hazard Assessment: Should We Use Fuzzy, Approximate and Prone-to-Errors Prediction...
10.1 Intermediate-Term Earthquake Prediction Based on Seismicity Patterns
10.2 The Algorithms M8, Mendocino Scenario and California-Nevada
10.3 Accelerating (Accelerating Moment Release) and Decelerating Seismicity
10.4 Load/Unload Response Ratio
10.5 The Region–Time–Length Algorithm
10.6 Time-Dependent Probabilistic Seismic Hazard Assessment
10.7 Time-Dependent Probabilistic Seismic Hazard Assessment for a Generic Prediction Model
10.8 Conclusions
Acknowledgement
References
Further Reading
11 Are Seismogenetic Systems Random or Organized? A Treatise of Their Statistical Nature Based on the Seismicity of the Nor...
11.1 Introduction
11.2 Nonextensive Approach to the Statistical Physics of Earthquakes
11.2.1 Brief Exposé of NESP
11.2.2 Seismicity and NESP: An Overview
11.2.3 Multivariate Earthquake Frequency Distributions: Construction and NESP-Based Modelling
11.3 Earthquake Data and Analysis
11.3.1 Earthquake Source Areas and Catalogues
11.3.2 California
11.3.2.1 Alaska and the Alaskan–Aleutian Arc and Trench System
11.3.3 Declustering
11.4 Results
11.4.1 Determination of Randomness Thresholds
11.4.2 Entropic Indices
11.4.2.1 California Full Catalogues
11.4.2.2 California Declustered Catalogues
11.4.2.3 North Pacific Rim
11.5 Discussion
Acknowledgements
References
12 Phase Space Portraits of Earthquake Time Series of Caucasus: Signatures of Strong Earthquake Preparation
12.1 Introduction
12.2 Methodology for ETS Analysis
12.3 Study Area
12.4 Results and Discussion
12.4.1 Batumi Area
12.4.2 Spitak Earthquake Area
12.4.3 Racha EQ Area
12.5 Discussion and Conclusions
Acknowledgements
References
Further Reading
13 Four-Stage Model of Earthquake Generation in Terms of Fracture-Induced Electromagnetic Emissions: A Review
13.1 Introduction (The State of the Art at the Beginning of the Investigation)
13.2 A Proposed Strategy for the Study of MHz and kHz EM Precursors
13.2.1 Our Proposal: The Four-Stage Model of Earthquake Generation by Means of Fracture-Induced EM Activities
13.3 Focus on the First Stage Reflected in the Observed Preseismic MHz EM Field
13.3.1 The MHz EM Phenomenon in Terms of Criticality
13.3.2 The Fracture Control Mechanism is Characterized by a Negative Feedback
13.3.3 The Analysis of MHz EME by Means of the Method of Critical Fluctuations
13.3.4 Is an Earthquake Unavoidable After the Appearance of an MHz EM Anomaly?
13.3.5 On the Physical Mechanism that Organizes the Heterogeneous System in its Critical State
13.3.6 The MHz EM Anomaly by Means of Percolation Theory
13.3.7 On the Compatibility of the MHz EM Anomaly with the Corresponding Foreshock Activity
13.3.8 On the Compatibility of the MHz EM Anomaly With the Corresponding Geodetic Precursors
13.3.9 Is the Observed MHz EM Anomaly in Accordance With Different Precursors?
13.4 Focus on the Second Stage Reflected in the Observed Preseismic EM Fracto-Emission With Tricritical Crossover Dynamics
13.5 Focus on the Third Stage Reflected in the Observed Preseismic Strong Avalanche-Like kHz EME
13.5.1 Arguments in Terms of Statistical Analysis
13.5.2 Arguments in Terms of Universal Structural Patterns of the Fracture Process
13.5.2.1 The Activation of a Single Fault is a Reduced Self-Affine Image of Regional Seismicity and a Magnified Image of La...
13.5.2.2 Arguments in Terms of Universal Characteristics of Rock Surfaces: The kHz EME Includes the Signature that Rock Sur...
13.5.2.3 The kHz EME is Consistent with the Interpretation that Surface Roughness is a Universal Indicator of Surface Fracture
13.5.3 On the Morphology of the Observed KHz EME Precursors
13.5.4 On the Consistency of the kHz EME Precursor With Other Precursors
13.5.4.1 Focus on the Existence of Simultaneous kHz EME and Seismological Precursors
13.5.4.2 Focus on the Existence of Simultaneous kHz EM and Geodetic Precursors
13.6 Focus on the Fourth Stage Reflected in the Observed Quiescence in all EM Frequency Bands Following the Strong Avalanch...
13.6.1 Focus on the EM Silence in Terms of Numerical Experiments
13.6.2 Focus on the EM Silence by Means of AE and EME Laboratory Experiments
13.6.3 Focus on EM Silence in Terms of Elastic Moduli
13.6.4 The Heat-Flow Paradox and the EM Silence Paradox: Two Sides of the Same Coin
13.6.5 EM Silence in Light of the Notion of Granular Packings
13.6.6 Focus on the Duration of the Observed EM Silence
13.7 On the Paradox of the Association of EME Signals with Small Precursory Strain Changes but not with much Larger Coseism...
13.8 On the Paradox of the Systematically Observed EM Silence During the Aftershock Period
13.9 On the Traceability of the EM Precursors
13.10 The Earth as a Living Planet by Means of Precursory EM Activities
13.10.1 The Earth’s Crust and Human Heart Undergo Similar Second-Order Phase Transitions from the Healthy State to a Pathol...
13.10.2 Earthquakes Can Be Considered as Epileptic Seizures of the Earth’s Crust in Terms of Complexity
13.11 Αn Open Issue of the Materials Science Community: Do the Scaling Laws Associated with the Fracture and Faulting Proce...
13.12 Conclusions
References
Further Reading
Index