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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models.
In short-term models, known by the term ETAS, the occurrence space and time rate density of earthquakes is modeled as the sum of two terms, one representing the independent or spontaneous events, and the other representing the activity triggered by previous earthquakes. Examples of the application of such algorithms in real cases are also reported.
Dealing with long-term recurrence models, renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what has occurred in the past.
The book also introduces a number of computer codes developed by the authors over decades of seismological research.
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Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title
Copyright
Foreword
Preface
Introduction
1 Seismicity and Earthquake Catalogues Described as Point Processes
1.1. The Gutenberg–Richter law
1.2. The time-independent Poisson model
1.3. Occurrence rate density as a space–time continuous variable
1.4. Time-independent spatial distribution
1.5. Clustered seismicity
1.6. Epidemic models
2 The Likelihood of a Hypothesis
2.1. The Bayes theorem
2.2. Likelihood function
2.3. Alternative formulations
2.4. Likelihood ratio
3 The Likelihood for a Model of Continuous Rate Density Distribution
3.1. The limit case of regions of infinitesimal dimensions
3.2. The case of discrete regions
3.3. The case of time independence
3.4. The likelihood of an epidemic model in a 4-D space of parameters
4 Forecast Verification Procedures
4.1. Scoring procedures
4.2. The binary diagrams
4.3. Statistical tests implemented within CSEP
5 Applications of Epidemic Models
5.1. Declustering a catalogue through an epidemic model
5.2. Earthquake forecasting
5.3. Seismic hazard maps for short-term forecast
6 Long-term Earthquake Occurrence Models
6.1. The empirical Gutenberg–Richter law and the time-independent model under the Poisson hypothesis
6.2. Statistics of inter-event times
6.3. The truncated magnitude distribution
6.4. Earthquake rate assessment under a renewal time-dependent model
6.5. Validation and comparison of renewal time-dependent models
6.6. The Cornell method for time-independent seismic hazard assessment
6.7. Acknowledgments
7 Computer Programs and Examples of their Use
7.1. PDE2REC, ZMAP2REC
7.2. REC2PDE
7.3. SMOOTH
7.4. LIKELAQP
7.5. LIKSTAQP
7.6. BPT
Bibliography
Index
End User License Agreement
List of Tables
4 Forecast Verification Procedures
Table 4.1.
Contingency table
Table 4.2.
Contingency tables for the ETAS model applied to the Italian catalogue from 1 January 2006 to 11 October 2007 as a function of a threshold occurrence rate value (r), expressed as events/day/100 km
2
5 Applications of Epidemic Models
Table 5.1.
Probability of an earthquake of magnitude ≥ 5 in 24 h in the area of L’Aquila. The red arrows point to the occurrence of the main observed earthquakes
6 Long-term Earthquake Occurrence Models
Table 6.1.
Statistical parameters of the inter-event times distribution obtained from a Monte Carlo procedure on 19 earthquake datasets for each of six renewal models (from [CON 12])
Table 6.2.
Confidence levels by which the Poisson distribution can be rejected, with their uncertainties. These values refer to different renewal models and to any of the 19 sites considered in this study (from [CON 12])
Table 6.3.
Estimated effects on the city of Messina for the nine earthquakes of the first 100 years of a 100 ky synthetic catalogue (from [CON 17a])
Guide
Cover
Table of Contents
Begin Reading
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e1
Statistical Methods for Earthquakes Set
coordinated byNikolaos Limnios, Eleftheria Papadimitriou and Georgios Tsaklidis
Volume 1
Earthquake Occurrence
Short- and Long-term Models and their Validation
Rodolfo Console
Maura Murru
Giuseppe Falcone
First published 2017 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 Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2017The rights of Rodolfo Console, Maura Murru and Giuseppe Falcone 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: 2017937771
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78630-124-6
Foreword
This volume presents models of earthquake occurrence that are of incredible importance in earthquake forecasting. The authors of this text are among the first to systematically study and utilize these models for assessing seismic hazard in diverse seismically active regions. Within this book an integrated view of earthquakes catalogs, their detailed descriptions and analysis related to short- and long-term earthquake occurrence models and their validation is given.
One of the most important insights in earthquake forecasting is the development of statistical models, because a deterministic approach in determining the occurrence of an anticipated strong earthquake is perhaps the most difficult problem to be solved, since earthquake occurrence is characterized by clustering in space and time, at different scales, reflecting the complexity of the geodynamic processes.
Earthquake forecasting necessitates the development of stochastic models for earthquake occurrence, which observations have revealed is far from exhibiting regular recurrence, and which constitutes a critically important problem whose solution requires fundamental research. At the same time, earthquake forecasting is a major tool for testing hypotheses and theories.
The book aims to introduce the reader to current understanding of algorithms applicable for modelling seismicity, it presents statistical analysis of seismicity as a point process in space, time and magnitude without presupposing that the reader possesses profound experience in research on these topics, but at the same time, without lessening the rigor of the reasoning or the variety of the chosen material.
It summarizes the state-of-the-art of the models’ application, explicitly focuses on the related verification procedures and appropriate tests, and finally provides the computer tools and examples of their use which are given for the reader’s ease in the application of the described models, written by scientists who have participated and contributed to the development of this research sector.
Although there are books on earthquake occurrence models worth reading by researchers and students, there is a gap in summarizing the most relevant statistical approaches from completely random earthquake occurrence up to renewal time–dependent models.
As can be seen from the contents list, statistical approaches and research results are presented in a logical and meaningful order, starting from examining the properties of an earthquake catalog up to seismic hazard assessment.
The book summarizes certain streams of seismological efforts that lead to a level of understanding of the seismicity and its processes.
It will be useful to scientists and researchers, students and lecturers dealing with statistical seismology. It can also be used to “teach yourself” by those who have little knowledge on the topics.
It is blatantly obvious that the stochastic approach brings optimism concerning efficiency in earthquake forecasting to those investigators dealing with relevant topics to strengthen their efforts, and the conviction that if they do so they can strongly contribute to its accomplishment.
Eleftheria PapadimitriouProfessor of SeismologyGeophysics DepartmentAristotle University of Thessaloniki
PrefaceShort- and Long-term Models of Earthquake Occurrence and their Validation
This book includes a review of the algorithms applicable for modeling seismicity, such as earthquake clustering, as in the ETAS short-term models, and pseudo-periodic behavior of major earthquakes. Examples of the application of such algorithms to real seismicity are also given.
In short-term models, earthquakes are regarded as the realization of a point process modeled by a generalized Poisson distribution. No hypothesis is inferred on the physical model of such a process. The occurrence of a seismic event within an infinitesimal volume of the space of its characterizing parameters is supposed to be completely random, while the behavior in a reasonably large volume of the same space may exhibit some average non-random features.
In the application of the statistical algorithms to seismicity, the Gutenberg–Richter law is assumed to describe the magnitude distribution of all the earthquakes in a sample, with a constant b value. The occurrence rate density of earthquakes in space and time is modeled as the sum of two terms, one representing the independent, or spontaneous, activity and the other representing the activity triggered by previous earthquakes. The first term depends only on space and is modeled by a continuous function of the geometrical coordinates, obtained by smoothing the discrete distribution of the past instrumental seismicity. The second term depends on both space and time, and it is factorized in two terms that depend on the space distance (according to an assigned spatial kernel) and on the time difference (according to the generalized Omori law), respectively, from the past earthquakes.
The description of seismicity as a point process in space, time and magnitude is suitable for the application of statistical tools for comparing the performance of different models. Here, the Bayes theorem is introduced, aiming at its application in computing the probability that a given model is true in light of the results of experimental observations. The use of the Bayes theorem requires the computation of the likelihood ratio for the two models to be compared. It follows that both hypotheses must be fully and quantitatively described.
Dealing with long-term recurrence models, the renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what had occurred in the past. In addition, in this case, the comparison is carried out through the concept of likelihood ratio of a set of observations under different models.
Chapter 1 deals with the application of the statistical tools to the seismicity of a region described by a seismic catalogue, starting with the extension to the continuum of the concepts suitable for earthquakes modeled as a continuous rate density function. The model introduced in this book (commonly known as the epidemic model) contains both a time-independent term, function of the space coordinates, and a time-dependent term, conditioned by the previous events in order to model the mutual interaction among earthquakes (short-term earthquake clustering).
Chapter 2 is devoted to a statistical background presented in an elementary way. It introduces the concept of the Bayes theorem, followed by the concepts of likelihood and likelihood ratio that are the tools for estimating and comparing the reliability of different hypotheses.
Chapter 3 develops the concepts introduced in Chapter 2 in the specific case of epidemic models.
Chapter 4 introduces a variety of verification procedures that have recently become popular to test the validity of forecasting models.
Chapter 5 reports examples of the application of epidemic models to real catalogues of recent seismic activity, namely the de-clustering of earthquakes catalogues and earthquake forecasting.
Chapter 6 is devoted to the problem of long-term earthquake occurrence, addressing the question of the validity of renewal models with memory when they are applied to seismicity, which has important implications with earthquake hazard assessment.
Chapter 7 contains a short description of a set of computer programs, each of which performs one of the steps necessary for processing a seismic catalogue. In this respect, most of the programs are linked together by their input and output making the whole set a sort of dedicated software package.
Rodolfo CONSOLE
Maura MURRU
Giuseppe FALCONEMay 2017
