Earthquake Statistical Analysis through Multi-state Modeling

By Irene Votsi, Nikolaos Limnios, Eleftheria Papadimitriou and Georgios Tsaklidis

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.

• Language: English
• Publisher: Wiley
• Release date: Dec 31, 2018
• ISBN: 9781119579083

Book preview

List of Abbreviations

List of Symbols

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