Statistical Methods and Modeling of Seismogenesis

Nikolaos Limnios is Full Professor of Applied Mathematics at Université de Technologie de Compiègne, 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.

• Preface xiNikolaos LIMNIOS, Eleftheria PAPADIMITRIOU and George TSAKLIDISChapter 1. Kernel Density Estimation in Seismology 1Stanisław LASOCKI1.1. Introduction 11.2. Complexity of magnitude distribution 71.3. Kernel estimation of magnitude distribution 131.4. Implications for hazard assessments 141.5. Interval estimation of magnitude CDF and related hazard parameters 161.6. Transformation to equivalent dimensions 191.7. References 23Chapter 2. Earthquake Simulators Development and Application 27Rodolfo CONSOLE, Roberto CARLUCCIO2.1. Introduction 282.2. Development of earthquake simulators in the seismological literature 282.2.1. ALLCAL 282.2.2. Virtual quake 292.2.3. RSQSim 302.2.4. ViscoSim 302.2.5. Other simulation codes 302.2.6. Comparisons among simulators 312.3. Conceptual evolution of a physics-based earthquake simulator 322.3.1. A physics-based earthquake simulator (2015) 332.3.2. Frequency-magnitude distribution of the simulated catalog (2015) 362.3.3. Temporal features of the synthetic catalog (2015) 382.3.4. Improvements in the physics-based earthquake simulator (2017–2018) 412.3.5. Application to the seismicity of Central Italy 422.3.6. Further improvements of the simulator code (2019) 462.4. Application of the last version of the simulator to the Nankai mega-thrust fault system 492.5. Appendix 1: Relations among source parameters adopted in the simulation model 542.6. Appendix 2: Outline of the simulation program 562.7. References 58Chapter 3. Statistical Laws of Post-seismic Activity 63Peter SHEBALIN, Sergey BARANOV3.1. Introduction 633.2. Earthquake productivity 643.2.1. The proposed method to study productivity 653.2.2. Earthquake productivity at the global level 693.2.3. Independence of the proximity function 723.2.4. Earthquake productivity at the regional level 763.2.5. Productivity in relation to the threshold of the proximity function 783.2.6. Discussion 793.3. Time-dependent distribution of the largest aftershock magnitude 813.3.1. The distribution of the magnitude of the largest aftershock in relation to time 823.3.2. The agreement between the dynamic Båth law and observations 853.3.3. Discussion 863.4. The distribution of the hazardous period 883.4.1. A model for the duration of the hazardous period 893.4.2. Determining the model parameters 913.4.3. Using the early aftershocks 963.5. Conclusion 983.6. References 100Chapter 4. Explaining Foreshock and the Båth Law Using a Generic Earthquake Clustering Model 105Jiancang ZHUANG4.1. Introduction 1054.1.1. Issues related to foreshocks 1064.1.2. Issues related to the Båth law 1084.1.3. Study objectives 1084.2. Theories related to foreshock probability and the Båth law under the assumptions of the ETAS model 1094.2.1. Space–time ETAS model, stochastic declustering and classification of earthquakes 1094.2.2. Master equation 1104.2.3. Asymptotic property of F(m’) 1134.2.4. Foreshock probabilities and their magnitude distribution in the ETAS model 1174.2.5. Explanation of the Båth law by the ETAS model 1184.3. Foreshock simulations based on the ETAS model 1204.3.1. Works by Helmstetter and others 1204.3.2. Works by Zhuang and others 1204.3.3. Evidence of statistics between mainshocks and foreshocks 1214.3.4. Different simulation results 1214.4. Simulation of the Båth law based on the ETAS model 1234.4.1. On the simulation study by Helmstetter 1234.4.2. Observation on Båth’s law for volcanic earthquake swarms 1244.5. Conclusion 1254.5.1. Back to the starting point 1254.5.2. On the comparison between foreshock probability in the ETAS model and real catalogs 1254.5.3. Impracticality of the foreshock concept 1264.5.4. What should we do? 1264.6. Acknowledgments 1274.7. References 127Chapter 5. The Genesis of Aftershocks in Spring Slider Models 131Eugenio LIPPIELLO, Giuseppe PETRILLO, François LANDES and Alberto ROSSO5.1. Introduction 1315.2. The rate-and-state equation 1335.3. The Dieterich model 1345.3.1. Time to instability 1355.3.2. Initial conditions during stationary seismicity 1375.3.3. Effect of a constant stress increase Δτ 1375.4. The mechanics of afterslip 1385.5. The two-block model 1405.5.1. Synthetic catalogs 1425.6. Conclusion 1465.7. References 148Chapter 6. Markov Regression Models for Time Series of Earthquake Counts 153Dimitris KARLIS, Katerina ORFANOGIANNAKI6.1. Introduction 1536.2. Markov regression HMMs: definition and notation 1566.3. Application 1576.3.1. Data 1576.3.2. Results 1606.4. Conclusion 1636.5. Acknowledgments 1666.6. References 166Chapter 7. Scaling Properties, Multifractality and Range of Correlations in Earthquake Time Series: Are Earthquakes Random? 171Georgios MICHAS, Filippos VALLIANATOS7.1. Introduction 1717.2. The range of correlations in earthquake time series 1737.2.1. Short-range correlations 1737.2.2. Long-range correlations 1777.3. Scaling properties of earthquake time series 1837.3.1. The probability distribution function 1847.3.2. A stochastic dynamic mechanism with memory effects 1927.3.3. The cumulative distribution function 1957.4. Fractal and multifractal structures 1977.5. Discussion and conclusion 2017.6. References 204Chapter 8. Self-correcting Models in Seismology: Possible Coupling Among Seismic Areas 211Ourania MANGIRA, Eleftheria PAPADIMITRIOU, Georgios VASILIADIS and George TSAKLIDIS8.1. Introduction 2118.2. Review of applications 2128.3. Formulation of the models 2188.3.1. Simple Stress Release Model 2188.3.2. Independent Stress Release Model 2208.3.3. Linked Stress Release Model 2208.4. Applications 2228.4.1. Greece and the surrounding area 2228.4.2. Gulf of Corinth 2298.5. Conclusion 2358.6. References 236Chapter 9. Markovian Arrival Processes for Earthquake Clustering Analysis 241Polyzois BOUNTZIS, Eleftheria PAPADIMITRIOU and George TSAKLIDIS9.1. Introduction 2419.2. State of the art 2439.2.1. Earthquake clustering methods and applications 2439.2.2. Hidden Markov models and applications in seismology 2449.3. Markovian Arrival Process 2479.3.1. Definition and basic results 2489.3.2. Parameter fitting 2509.3.3. Inference of the latent states 2529.4. Methodology and results 2549.4.1. Motivation 2549.4.2. Clustering detection procedure 2549.5. Conclusion 2649.6. References 265Chapter 10. Change Point Detection Techniques on Seismicity Models 271Rodi LYKOU, George TSAKLIDIS10.1. Introduction 27110.2. The change point framework 27210.3. Changes in a Poisson process 27610.4. Changes in the Epidemic Type Aftershock Sequence model 27910.5. Changes in the Gutenberg–Richter law 28210.6. ZMAP 28610.7. Other statistical tests 28710.8. Detection of changes without hypothesis testing 28910.9. Discussion and conclusion 29010.10. References 291Chapter 11. Semi-Markov Processes for Earthquake Forecast 299Vlad Stefan BARBU, Alex KARAGRIGORIOU and Andreas MAKRIDES11.1. Introduction 29911.2. Semi-Markov processes – preliminaries 30011.2.1. Special class of distributions 30311.3. Transition probabilities and earthquake occurrence 30411.3.1. Likelihood and estimation 30411.4. Semi-Markov transition matrix 30511.5. Illustrative example 30711.6. References 308List of Authors 309Index 311