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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications.
The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.
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Seitenzahl: 189
Veröffentlichungsjahr: 2018
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Table of Contents
Cover
List of Abbreviations
List of Symbols
Preface
Introduction
I.1. Motivation and objectives
I.2. Seismic hazard assessment
I.3. Earthquake occurrence models
1 Fundamentals on Stress Changes
1.1. Introduction
1.2. Stress interaction
1.3. Stress changes calculation
1.4. Modeling of Coulomb stress changes for different faulting types
1.5. Seismicity triggered by stress transfer
1.6. Discussion on stress interaction
2 Hidden Markov Models
2.1. Introduction
2.2. Hidden Markov framework
2.3. Seismotectonic regime and seismicity data
2.4. Application to earthquake occurrences
2.5. Conclusion
3 Hidden Markov Renewal Models
3.1. Introduction
3.2. Semi-Markov framework
3.3. Hidden Markov renewal framework
3.4. Modeling earthquakes in Greece
3.5. Conclusion
4 Hitting Time Intensity
4.1. Introduction
4.2. DTIHT for semi-Markov chains
4.3. DTIHT for hidden Markov renewal chains
4.4. Conclusion
5 Models Comparison
5.1. Introduction
5.2. Markov framework
5.3. Markov renewal framework
5.4. Conclusion
Discussion & Concluding Remarks
Appendices
Appendix 1: Markov Models
Appendix 2: Hidden Markov Models
A2.1. Scoring or evaluation problem
Appendix 3: Dataset
References
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1. Confidence intervals for the transition probabilities of the underlyi...
Table 2.2. Confidence intervals for the emission probabilities at 5% significanc...
Chapter 3
Table 3.1. Estimated mean recurrence times and stationary distribution of the un...
Table 3.2. Estimated instantaneous rate of earthquake occurrences
Table 3.3. Estimated instantaneous rate of earthquake occurrences – starting sta...
Table 3.4. Estimated instantaneous rate of earthquake occurrences – starting sta...
Appendix 3
Table A3.1. Dataset of earthquakes with M ≥ 6.5 that occurred in the study area ...
Guide
Cover
Table of Contents
Begin Reading
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“We Athenians in our persons take our decisions on policy and submit them to proper discussion. The worst thing is to rush into action before the consequences have been properly debated. And this is another point where we differ from other people. We are capable at the same time of taking risks and estimating them beforehand. Others are brave out of ignorance; and when they stop to think, they begin to fear. But the man who can most truly be accounted brave is he who best knows the meaning of what is sweet in life, and what is terrible, and he then goes out undeterred to meet what is to come.”
– Abstract from Pericle’s Funeral Oration in Thucydides’ “History of the Peloponnesian War” (started in 431 B.C.)
Statistical Methods for Earthquakes Set
coordinated by
Nikolaos Limnios, Eleftheria Papadimitriou, George Tsaklidis
Volume 2
Earthquake Statistical Analysis through Multi-state Modeling
Irene Votsi
Nikolaos Limnios
Eleftheria Papadimitriou
George Tsaklidis
First published 2019 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
27-37 St George’s Road
London SW19 4EU
UK
www.iste.co.uk
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.wiley.com
© ISTE Ltd 2019
The rights of Irene Votsi, Nikolaos Limnios, Eleftheria Papadimitriou, 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: 2018957211
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-150-5
List of Abbreviations
Δ
CFF
Coulomb failure function
AIC
Akaike’s information criterion
a.s.
almost surely
BIC
Bayesian information criterion
EM
expectation-maximization
EMC
embedded Markov chain
HMC
hidden Markov chain
HMRC
hidden Markov renewal chain
HMM
hidden Markov model
HMRM
hidden Markov renewal model
HSMM
hidden semi-Markov model
HSMC
hidden semi-Markov chain
MC
Markov chain
MLE
maximum likelihood estimator
MRC
Markov renewal chain
PHMM
Poisson hidden Markov model
SMC
semi-Markov chain
SMM
semi-Markov model
SMK
semi-Markov kernel
Preface
Statistical seismology attracts the attention of seismologists, statisticians, geologists, engineers, government officials and insurers among others, since it serves as a powerful tool for seismic hazard assessment and, consequently, for risk mitigation. This field aims to connect physical and statistical models and to provide a conceptual basis for the earthquake generation process. To date, purely deterministic models have inadequately described earthquake dynamics. This is mainly due to the restricted knowledge concerning fundamental state parameters related to the causative process, such as stress state and properties of the medium. Comparing the deterministic approaches with the stochastic ones, we should note that, today, the latter are the most favorable. Stochastic processes allow for the efficient modeling of real-life random phenomena and the quantification of associated indicators.
This book is intended as a first, but at the same time, a systematic approach for earthquake multi-state modeling by means of hidden (semi-)Markov models. It provides a presentation of bibliography sources, methodological studies and the development of stochastic models in order to reveal the mechanism and assessment of future seismogenesis. This book aims to ease the reader in getting and exploiting conceivable tools for the application of multi-state models to concrete physical problems encountered in seismology. It also aims to encourage discussions and future modeling efforts in the domain of statistical seismology, by tackling from, theoretical advances to very practical applications.
This book is concerned with several central themes in a rapidly developing field: earthquake occurrence modeling. It contains seven chapters and three appendices and begins with two lists containing abbreviations and symbols used throughout the book.
Next is an introduction that describes the state-of-the-art earthquake modeling approaches that focus on multi-state models.
Chapter 1 introduces the reader to the crustal stress state, stress changes and evolution and the association with earthquake generation. The complexity of this process is then investigated by using advanced stochastic models in the chapters that follow.
Chapter 2 presents a multi-state modeling approach that enables the description of strong seismicity in the broader Aegean area from 1865 to 2008. This chapter aims to help the reader to acquaint with the application of hidden Markov models and it presents a detailed example of multi-state modeling in seismology. In particular, hidden Markov models are used to shed some new light on the “hidden” component that controls the generation of earthquakes: the stress field. Our purpose is to assess the evolution of the stress field and its inherently causative role in both the number and size of earthquakes.
Chapter 3 presents (hidden) semi-Markov models and their associated stochastic processes. It contains all statistical estimation tools that enable the reader to estimate indicators of interest associated with the occurrence of strong earthquakes.
Chapter 4 presents theoretical results for the statistics of stochastic processes that can have direct applications in seismology. It aims to teach how the study of a real-life phenomenon could lead to the development of the statistics of stochastic processes and thereafter how these theoretical results could be further used to answer open questions regarding the phenomenon under study.
Chapter 5 gives some guidelines for the comparison of multi-state models and provides specific numerical examples. This last chapter is a collection of concluding remarks, open questions and perspectives in the field.
At the end of the book, three appendices are provided. Appendix 1 presents some main definitions of Markov models. Appendix 2 presents how the three problems regarding hidden Markov models could be solved. Appendix 3 presents the dataset used throughout the book.
The authors express their gratitude to M. Hamdaoui for his technical help and assistance. The changes and evolution of the stress field were calculated using the program written by J. Deng [DEN 97a] based on the DIS3D code by S. Dunbar and Erikson (1986) and the expressions of G. Converse.
Some of the figures were plotted using the Generic Mapping Tools algorithm [WES 98]. This book will be useful to applied statisticians and geophysicists interested in the theory of multi-state modeling. It can also be useful to students, teachers and professional researchers who are interested in statistical modeling for earthquakes.
Irene VOTSI
Nikolaos LIMNIOS
Eleftheria PAPADIMITRIOU
George TSAKLIDIS
October 2018
Introduction
“Act with awareness”
— Pittacus of Mytilene
I.1. Motivation and objectives
Earthquakes constitute one of the most lethal natural hazards resulting in more than 200.000 casualties worldwide each decade. They can become vastly devastating and life-threatening, as in the cases of the recent 2011 M8.9 Japan, the 2008 M8.0 Sichuan China and the 2004 M9.3 Sumatra earthquakes. Earthquake forecasting is therefore a social demand, and scientific efforts have to be intensified for this scope. The quest for earthquake prediction dates back to times when superstition prevailed, and prediction was the domain of occultism and this search is still ever-present. Despite more than a century of research, research on earthquake prediction has undergone broad criticism and skepticism, is continuously debatable and continuously remains as an insolvable but highly attractive scientific problem.
At the outset, clarification is needed regarding the usage of the term “prediction” in seismology. Reliable earthquake predictions are considered the ones that provide a space–time–magnitude range, including the magnitude scale (i.e. local magnitude, moment magnitude, etc.) and the number of earthquakes expected in this range (i.e. zero, one, at least one, etc.). The forecast or prediction of an earthquake is a statement about time, hypocenter location, magnitude and the probability of occurrence of an individual future event within reasonable error ranges [ZÖL 09].
The prediction was continuously expressed as the occurrence probability of an earthquake, in a given time, space and magnitude range. The definition of this range constitutes a scientific target by itself. The techniques developed for this scope were diverse, and thus, earthquake prediction was discriminated in a short term, when the referred time interval concerned a day to a few hundred days before a strong earthquake, an intermediate term covering the interval from about one year to one decade and a long term for intervals longer than a decade [KNO 96].
I.2. Seismic hazard assessment
For the evaluation of seismic hazard, a set of parameters are used that express the intensity of ground motion. Thus, the probability of exceedance of predefined parameter values in a specified exposure time needs to be calculated. For the seismic hazard assessment at a specific site, either the deterministic approach or the stochastic approach is followed. In the deterministic approach, the ground shaking at the site is estimated from one or more earthquakes of a specified location and magnitude. Deterministic earthquake scenarios may be based on the actual occurrences of past events, or they may be postulated scenarios backed by analysis of seismological and geological data. The other approach is the probabilistic method, in which the contributions from all possible earthquakes around the site are integrated to find the shaking to not overpass a certain probability estimate at that place in some time period.
Both approaches exhibit strong and weak points. “The deterministic approach provides a clear and trackable method of computing seismic hazard, whose assumptions are easily discerned. It provides understandable scenarios that can be related to the problem at hand. However, it has no way for accounting for uncertainty. Conclusions based on deterministic analysis can be easily upset by the occurrence of new earthquakes”. The probabilistic approach to seismic hazard calculations originally proposed by Cornell [COR 68] uses an integration of the anticipated ground motion produced by all earthquake sources and magnitudes comprised in a specific area around the site of interest, for calculating the probabilities of certain levels of the ground motion there. In this way, the probabilistic method provides the potential of the specific ground motion exceedance during some time period. “The probabilistic approach is capable of integrating a wide range of information and uncertainties into a flexible framework. Unfortunately, its highly integrated framework can obscure those elements that drive the results and its highly quantitative nature can lead to false impressions of accuracy”.
I.3. Earthquake occurrence models
Comparing the deterministic approach for seismic hazard assessment with the probabilistic one, we should note that the latter is the most favorable today, relying on stochastic models for estimating the probabilities of generation of strong earthquakes. Deterministic earthquake prediction is still far from becoming feasible for practical applications, whereas the probabilistic one is realistic.
Besides data analysis, the modeling of the earthquake process is essential for a deep understanding and potential forecasts of the earthquake process. Progress in earthquake modeling can be assessed by examining different model classes. The two main classes are stochastic models and physics-based models [HAI 09]. Here, we focus on stochastic models serving as a tool for probabilistic seismic hazard assessment. Let us first provide the fundamental difference between a stochastic model and a physical model. The main difference between a stochastic model and a physical model is that the former, in contrast to the latter, considers that the physical process depends on some random aspects and therefore could not be fully understood. These random aspects are taken into account in the stochastic modeling and are expressed by means of parameters or associated stochastic processes. The stochastic models could enable us to quantify the parts of the physical process that are accessible to direct measurement, the parts that are due to its randomness and the associated uncertainties. On the other hand, the physical models aim to achieve full understanding and prediction of the physical process. The strict discrimination between the stochastic and physical models, however, cannot be unambiguously performed, since a large percentage of the models comprise physical, stochastic and empirical components.
Stochastic models play two main roles in their diverse fields of application [VER 10b, VER 10a]. First, in statistical mechanics, stochastic models aim to understand the associated physical process itself. Second, they aim to achieve planification, decision-making and/or prediction. Earthquake occurrence models are further divided into time-dependent and time-independent ones. The main assumption of the time-independent earthquake occurrence models is that the number of earthquake occurrences follows the Poisson distribution. In this case, the only information that is needed in order to calculate the associated probabilities is the mean recurrence times. The most common time-independent stochastic model of earthquake occurrences is the Poisson model, which assumes that earthquake occurrence does not depend on time. This model considers that the epicenters and times of earthquakes that exceed a certain threshold magnitude correspond to the realization of a temporally homogeneous Poisson process and serve as a test bed for comparisons with more complicated models.
