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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Table of Contents
Cover
Title Page
Copyright
Preface
1 Kernel Density Estimation in Seismology
1.1. Introduction
1.2. Complexity of magnitude distribution
1.3. Kernel estimation of magnitude distribution
1.4. Implications for hazard assessments
1.5. Interval estimation of magnitude CDF and related hazard parameters
1.6. Transformation to equivalent dimensions
1.7. References
2 Earthquake Simulators Development and Application
2.1. Introduction
2.2. Development of earthquake simulators in the seismological literature
2.3. Conceptual evolution of a physics-based earthquake simulator
2.4. Application of the last version of the simulator to the Nankai mega-thrust fault system
2.5. Appendix 1: Relations among source parameters adopted in the simulation model
2.6. Appendix 2: Outline of the simulation program
2.7. References
3 Statistical Laws of Post-seismic Activity
3.1. Introduction
3.2. Earthquake productivity
3.3. Time-dependent distribution of the largest aftershock magnitude
3.4. The distribution of the hazardous period
3.5. Conclusion
3.6. References
4 Explaining Foreshock and the Båth Law Using a Generic Earthquake Clustering Model
4.1. Introduction
4.2. Theories related to foreshock probability and the Båth law under the assumptions of the ETAS model
4.3. Foreshock simulations based on the ETAS model
4.4. Simulation of the Båth law based on the ETAS model
4.5. Conclusion
4.6. Acknowledgments
4.7. References
5 The Genesis of Aftershocks in Spring Slider Models
5.1. Introduction
5.2. The rate-and-state equation
5.3. The Dieterich model
5.4. The mechanics of afterslip
5.5. The two-block model
5.6. Conclusion
5.7. References
6 Markov Regression Models for Time Series of Earthquake Counts
6.1. Introduction
6.2. Markov regression HMMs: definition and notation
6.3. Application
6.4. Conclusion
6.5. Acknowledgments
6.6. References
7 Scaling Properties, Multifractality and Range of Correlations in Earthquake Time Series: Are Earthquakes Random?
7.1. Introduction
7.2. The range of correlations in earthquake time series
7.3. Scaling properties of earthquake time series
7.4. Fractal and multifractal structures
7.5. Discussion and conclusions
7.6. References
8 Self-correcting Models in Seismology: Possible Coupling Among Seismic Areas
8.1. Introduction
8.2. Review of applications
8.3. Formulation of the models
8.4. Applications
8.5. Conclusion
8.6. References
9 Markovian Arrival Processes for Earthquake Clustering Analysis
9.1. Introduction
9.2. State of the art
9.3. Markovian Arrival Process
9.4. Methodology and results
9.5. Conclusion
9.6. References
10 Change Point Detection Techniques on Seismicity Models
10.1. Introduction
10.2. The change point framework
10.3. Changes in a Poisson process
10.4. Changes in the Epidemic Type Aftershock Sequence model
10.5. Changes in the Gutenberg–Richter law
10.6. ZMAP
10.7. Other statistical tests
10.8. Detection of changes without hypothesis testing
10.9. Discussion and conclusion
10.10. References
11 Semi-Markov Processes for Earthquake Forecast
11.1. Introduction
11.2. Semi-Markov processes – preliminaries
11.3. Transition probabilities and earthquake occurrence
11.4. Semi-Markov transition matrix
11.5. Illustrative example
11.6. References
List of Authors
Index
End User License Agreement
List of Table
Chapter 2
Table 2.1.
Statistical parameters of the synthetic catalog (based on Console
et ...
Table 2.2. List of observed or argued mega-earthquakes that ruptured two or more...
Table 2.3.
Features of the 2,000 years synthetic catalog
Table 2.4. Statistical parameters of the 2,000 years synthetic catalog of the Na...
Chapter 3
Table 3.1.
Estimates of
Λ2 for the original ANSS ComCat catalog for 1981–2019 an...
Table 3.2. Parameters and results in the estimation of mean earthquake productiv...
Table 3.3.
Estimating
Λ0 (the probability for an earthquake to initiate an event...
Table 3.4.
The parameters of the dynamic Båth law
[3.20] based on worldwide data...
Table 3.5. Average parameter values for estimating the duration of the hazardous...
Table 3.6. Results from retrospective testing of estimates for the duration of t...
Chapter 6
Table 6.1. Focal parameters of the strong earthquakes that occurred in the c-NAS...
Table 6.2. The values of the log-likelihood for the different models. The values...
Chapter 8
Table 8.1.
LSRM’s applications in various areas worldwide
Table 8.2. Estimated parameters, standard errors and 90% confidence intervals re...
Table 8.3. Estimated parameters, standard errors and 90% confidence intervals re...
Table 8.4. SSRM’s estimated parameters using earthquakes that occurred in Greece...
Table 8.5. Degree of predictability for each of the alternative SSRMs over the b...
Table 8.6. Estimated parameters, standard errors and 90% confidence intervals of...
Table 8.7. Estimated parameters, standard errors and 90% confidence intervals re...
Chapter 9
Table 9.1. Details on the three datasets. D1, D2 and D3 correspond to the earthq...
Table 9.2. Log-likelihood (LL) and BIC values for the fitted models with two to ...
Table 9.3. Estimated seismicity rates of the fitted MAPs for the D1, D2 and D3 d...
Table 9.4. Details on the number of initial identified clusters, clusters with d...
Chapter 11
Table 11.1.
Earthquake prediction for 1 year ahead for the Weibull distribution
Table 11.2. Earthquake prediction for 1 year ahead for the exponential distribut...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
List of Authors
Index
End User License Agreement
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SCIENCES
Statistics, Field Director – Nikolaos Limnios and Kerrie MengersenGeostatistics
Statistical Methods and Modeling of Seismogenesis
Coordinated by
Nikolaos Limnios
Eleftheria Papadimitriou
George Tsaklidis
First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
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www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2021
The rights of Nikolaos Limnios, Eleftheria Papadimitriou and George Tsaklidis to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2020950512
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British LibraryISBN 978-1-78945-037-8
ERC code:
PE1 MathematicsPE1_13 ProbabilityPE1_14 StatisticsPE1_20 Application of mathematics in sciences
PE10 Earth System SciencePE10_7 Physics of earth’s interior, seismology, volcanology
Preface
Nikolaos LIMNIOS1, Eleftheria PAPADIMITRIOU2 and George TSAKLIDIS2
1Laboratoire de Mathématiques Appliquées de Compiègne, University of Technology of Compiègne, Sorbonne University, Compiègne, France2Aristotle University of Thessaloniki, Greece
The study of earthquakes is a multidisciplinary field where geodynamics meets mathematics, engineering, etc. In these approaches, the randomness is present in a natural way.
Stochastic studies (probabilistic modeling, stochastic processes and statistics) can have different types – black box (one state), white box (multi-state system), simulation of different aspects, etc.
One of the positive points of this multi-author volume is that it provides many of the previous aspects by authors from different institutions around the world, known for their earthquake-specific approaches.
Topics such as statistical non-parametric and parametric methods, multi-state systems approach, simulators of earthquake, post-seismic activity models, ETAS branching-type models, time series Markov models with regression, scaling properties and multifractal approaches, self-correcting models, linked stress release model, Markovian arrival models, Poisson models based detection techniques, change point detection techniques on seismicity models and, finally, semi-Markov models for earthquake forecast are presented in this volume.
The present volume is organized as follows.
Chapter 1, by Stanislaw Lasocki, deals with the non-parametric estimation of the density function, in particular the well-known kernel density estimation. The non-parametric approach is now a well-established method in statistical theory and, considering the fact that there are important collections of seismic data, it is important, and its applications in statistical seismology are natural. The kernel density estimation is a model-free estimation of the probability functions of continuous random variables. The estimation is carried out solely from sample data.
Chapter 2, by Rodolfo Console and Roberto Carluccio, deals with earthquake simulator development and applications. Especially, this chapter deals with the concepts which earthquake simulators have been built upon and gives examples of the applications of such simulators to real fault systems, comparing them with observed seismicity. An example is given of the application of a simulator to the Nankai mega-thrust fault system, with particular emphasis to the study of the stress evolution on the fault surface during numerous repeating earthquake cycles.
Chapter 3, by Peter Shebalin and Sergey Baranov, deals with the statistical laws of post-seismic activity. In particular, this chapter discusses the ETAS model (a branching-type model with two empirical exponential laws), which is widely used in seismology for describing the clustering features of the earthquake process, and to what degree this model can explain the foreshock generation and the Båth’s law. The authors comment further on research results that have already been published.
Chapter 4, by Jiancang Zhuang, deals with the ETAS model, which is a branching-type model, widely used in seismology for describing the clustering features of the earthquake process. Based on the ETAS model, this chapter shows that the magnitude distribution of the largest descendant from a given event determines the foreshock probabilities and deduces the Båth’s law from the asymptotic form of this magnitude distribution, both of which are close to the values of actual seismicity data. The author also comments on some results from previous works.
Chapter 5, by Eugenio Lippiello, Giuseppe Petrillo, François Landes and Alberto Rosso, deals with the genesis of aftershocks in spring slider models. The main purpose of this chapter is to review the main assumptions and analytical steps proposed to explain the temporal behavior of aftershocks, in terms of both a time-dependent friction and afterslip dynamics. As a final step, we present how the two approaches can be combined. The two models are schematically presented in the figures of the chapter. The mathematical analogies between the two interpretations, and at the same time their very different physical implications, are stressed. The two descriptions are illustrated in a model with two blocks, with a different rheology interacting between each other.
Chapter 6, by Dimitris Karlis and Katerina Orfanogiannaki, deals with Markov regression models for time series of earthquake counts. Markov modems and HMMs offer a very elegant interpretation. Each state represents a different seismicity level, hence one may consider the transition probabilities as estimates of moving from one state to another, with the relevant increase/decrease of seismicity. In the Markov regression models, the transition probabilities change with time depending on additional variables. Different variables have a different effect on the transition probabilities. So, this property of the Markov regression model gives an insight into the mechanism behind state changes. This mechanism has physical interpretations, since the transition probabilities are directly linked, through regression, to physical quantities like earthquake magnitudes.
Chapter 7, by Georgios Michas and Filippos Vallianatos, deals with scaling properties, multifractality and a range of correlations in earthquake time series. The authors provide a mini-review on some of the collective properties of earthquake populations in the time domain, and based on these properties, we discuss whether earthquakes occur randomly in time or not. This topic is quite important for earthquake physics and ultimately for earthquake predictability. Their approach is based on the statistical physics of earthquakes that aims to elucidate the general physical mechanisms of seismogenesis, which produce the collective properties of earthquake populations that are empirically observed in nature. The earthquake occurrence is modeled by a point process in space and time, marked by the magnitude of the event and investigating the correlation properties of the waiting time (or interevent time) series between successive events.
Chapter 8, by Ourania Mangira, Eleftheria Papadimitriou and Georgios Vasiliadis, deals with self-correcting probabilistic models in seismology. The Stress Release Model (SRM) that belongs to this category considers elastic strain being accumulated due to slow tectonic loading, which is suddenly released when it overpasses the strength of a fault, during an earthquake. The real situation is more complicated, and for this reason, improved versions of the model have been developed, like the Linked Stress Release Model (LSRM), where interaction between different sub-areas is allowed by stress transfer, and the Independent Stress Release Model (ISRM), where the study area is divided into smaller independent parts without interaction. Results of the model applications in areas of Greece are presented, discussed and interpreted.
Chapter 9, by Polyzois Bountzis, Eleftheria Papadimitriou and George Tsaklidis, deals with Markovian arrival processes for earthquake clustering analysis. The temporal variations of the seismicity rate in certain areas are considered as the manifestation of the physical mechanism behind the seismicity behavior, which exhibits periods of excitation (clustering) and periods of relative quiescence (background seismicity). The method used for this purpose is based on the application of a bivariate stochastic point process, the Markovian arrival process (MAP), (Nt, Jt)t∈R+, whose intensity function, λt, is modulated by the latent Markov process, Jt. The hidden states of the latter correspond to distinct occurrence rates of the counting process, Nt, which enables the modeling of changes in the seismicity rate.
Chapter 10, by Rodi Lykou and George Tsaklidis, deals with change point detection techniques on seismicity models. They present the detection techniques of the Poisson process, ETAS model and G–R law, and suggested approaches for seismicity rate changes, covering parametric and non-parametric tests and approaches lacking statistical hypothesis testing. Change detection in seismicity rates has been combined with the use of probabilistic forecasting models and simultaneous studies in the stress field and space domain. It constitutes a powerful tool for solving non-stationarity problems leading to promising results for the underlying mechanism of seismogenesis.
Chapter 11, by Vlad Stefan Barbu, Alex Karagrigoriou and Andreas Makrides, deals with semi-Markov processes for earthquake forecasts. In particular, the authors provide a different approach of earthquake forecasting using a special type of semi-Markov processes. The seismic zones are considered as the states of a semi-Markov process and a methodology is employed for estimating the transition probabilities of seismic events transit, from one specific seismic zone to another. The sojourn times in a certain state belong to a general class of distributions presenting the advantage that it is closed under minima and includes various continuous distributions like the exponential, Weibull, Pareto, Rayleigh and Erlang truncated exponential distribution.
The authors of this preface are grateful to all authors for their excellent collaboration.
December 2020
