The study of earthquakes is a multidisciplinary field, an amalgam of
geodynamics, mathematics, engineering and more. The overriding
commonality between them all is the presence of natural randomness.
Stochastic studies (probability, stochastic processes and statistics) can
be of different types, for example, the black box approach (one state),
the white box approach (multi-state), the simulation of different aspects,
and so on. This book has the advantage of bringing together a group of
international authors, known for their earthquake-specific approaches,
to cover a wide array of these myriad aspects.
A variety of topics are presented, including statistical nonparametric and
parametric methods, a multi-state system approach, earthquake
simulators, post-seismic activity models, time series Markov models
with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival
models, Poisson-based detection techniques, change point detection
techniques on seismicity models, and, finally, semi-Markov models for
earthquake forecasting.
Autorentext
Nikolaos Limnios is Full Professor of Applied Mathematics at Universite de Technologie de Compiegne, Sorbonne University, France. His research interests include stochastic processes and statistics, Markov and semi-Markov processes and random evolutions with varied applications.
Eleftheria Papadimitriou is Professor of Seismology at the Aristotle University of Thessaloniki, Greece. Her research interests are related to Earthquake Seismology and she engages in scientific exchange and collaboration with several international institutions.
George Tsaklidis is Professor of Probability and Statistics at the Aristotle University of Thessaloniki, Greece. His research interests include stochastic processes and computational statistics with applications in seismology, finance and continuum mechanics, and state-space modeling.
Klappentext
The study of earthquakes is a multidisciplinary field, an amalgam ofgeodynamics, mathematics, engineering and more. The overridingcommonality between them all is the presence of natural randomness.
Stochastic studies (probability, stochastic processes and statistics) canbe of different types, for example, the black box approach (one state),the white box approach (multi-state), the simulation of different aspects,and so on. This book has the advantage of bringing together a group ofinternational authors, known for their earthquake-specific approaches,to cover a wide array of these myriad aspects.A variety of topics are presented, including statistical nonparametric andparametric methods, a multi-state system approach, earthquakesimulators, post-seismic activity models, time series Markov modelswith regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrivalmodels, Poisson-based detection techniques, change point detectiontechniques on seismicity models, and, finally, semi-Markov models forearthquake forecasting.
Zusammenfassung
The study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness.
Stochastic studies (probability, stochastic processes and statistics) can be of different types, for example, the black box approach (one state), the white box approach (multi-state), the simulation of different aspects, and so on. This book has the advantage of bringing together a group of international authors, known for their earthquake-specific approaches, to cover a wide array of these myriad aspects. A variety of topics are presented, including statistical nonparametric and parametric methods, a multi-state system approach, earthquake simulators, post-seismic activity models, time series Markov models with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival models, Poisson-based detection techniques, change point detection techniques on seismicity models, and, finally, semi-Markov models for earthquake forecasting.
Inhalt
Preface xi
Nikolaos LIMNIOS, Eleftheria PAPADIMITRIOU and George TSAKLIDIS
Chapter 1. Kernel Density Estimation in Seismology 1
Stanisaw LASOCKI
1.1. Introduction 1
1.2. Complexity of magnitude distribution 7
1.3. Kernel estimation of magnitude distribution 13
1.4. Implications for hazard assessments 14
1.5. Interval estimation of magnitude CDF and related hazard parameters 16
1.6. Transformation to equivalent dimensions 19
1.7. References 23
Chapter 2. Earthquake Simulators Development and Application 27
Rodolfo CONSOLE, Roberto CARLUCCIO
2.1. Introduction 28
2.2. Development of earthquake simulators in the seismological literature 28
2.2.1. ALLCAL 28
2.2.2. Virtual quake 29
2.2.3. RSQSim 30
2.2.4. ViscoSim 30
2.2.5. Other simulation codes 30
2.2.6. Comparisons among simulators 31
2.3. Conceptual evolution of a physics-based earthquake simulator 32
2.3.1. A physics-based earthquake simulator (2015) 33
2.3.2. Frequency-magnitude distribution of the simulated catalog (2015) 36
2.3.3. Temporal features of the synthetic catalog (2015) 38
2.3.4. Improvements in the physics-based earthquake simulator (20172018) 41
2.3.5. Application to the seismicity of Central Italy 42
2.3.6. Further improvements of the simulator code (2019) 46
2.4. Application of the last version of the simulator to the Nankai mega-thrust fault system 49
2.5. Appendix 1: Relations among source parameters adopted in the simulation model 54
2.6. Appendix 2: Outline of the simulation program 56
2.7. References 58
Chapter 3. Statistical Laws of Post-seismic Activity 63
Peter SHEBALIN, Sergey BARANOV
3.1. Introduction 63
3.2. Earthquake productivity 64
3.2.1. The proposed method to study productivity 65
3.2.2. Earthquake productivity at the global level 69
3.2.3. Independence of the proximity function 72
3.2.4. Earthquake productivity at the regional level 76
3.2.5. Productivity in relation to the threshold of the proximity function 78
3.2.6. Discussion 79
3.3. Time-dependent distribution of the largest aftershock magnitude 81
3.3.1. The distribution of the magnitude of the largest aftershock in relation to time 82
3.3.2. The agreement between the dynamic Båth law and observations 85
3.3.3. Discussion 86
3.4. The distribution of the hazardous period 88
3.4.1. A model for the duration of the hazardous period 89
3.4.2. Determining the model parameters 91
3.4.3. Using the early aftershocks 96
3.5. Conclusion 98
3.6. References 100
Chapter 4. Explaining Foreshock and the Båth Law Using a Generic Earthquake Clustering Model 105
Jiancang ZHUANG
4.1. Introduction 105
4.1.1. Issues related to foreshocks 106
4.1.2. Issues related to the Båth law 108
4.1.3. Study objectives 108
4.2. Theories related to foreshock probability and the Båth law under the assumptions of the ETAS model 109
4.2.1. Spacetime ETAS model, stochastic declustering and classification of earthquakes 109
4.2.2. Master equation 110
4.2.3. Asymptotic property of F(m') 113
4.2.4. Foreshock probabilities and their magnitude distribution in the ETAS model 117
4.2.5. Explanation of the Båth law by the ETAS model 1…