Eleftheria Papadimitriou - Statistical Methods and Modeling of Seismogenesis

4 Chapter 4Figure 4.1. Illustration of the condition that equation [4.13] has a non-zero so...Figure 4.2. Illustration of the coefficient ξ in F ( m ) when the process is criti...Figure 4.3. Illustration of F ( m ) for different cases. (a) β = 2.30 , α = 1.40 (β...Figure 4.4. Illustration of ξ ( m , m′ ) for different cases. (a) Sub-critical: A = ...Figure 4.5. Illustration of H ( m ) for different cases Figure 4.6. Comparison between the theoretical ζ ( m, m′ ) and reconstructed ζ ˆ(m, ...Figure 4.7. (see Marzocchi and Zhuang 2011) Cumulative curves of mainshock, pre-...Figure 4.8. Plots of different Δ against initiating magnitude for the central vo...

5 Chapter 5Figure 5.1. Schematic description of the slider models considered in the chapter...Figure 5.2. The behavior of the seismic rate before, during and after a stress s...Figure 5.3. (Upper panel) We plot the seismic moment n Δh as a function of the oc...Figure 5.4. The aftershock rate λ ( t ) is a function of t/ts (left), with t the ti...

6 Chapter 6Figure 6.1. Map of the central North Aegean Sea showing the epicenters of large ...Figure 6.2. Magnitude-frequency distribution for the c-NAS regional catalog for ...Figure 6.3. Monthly counts of ML = 3 earthquakes observed in the c-NAS region fo...Figure 6.4. Maximum magnitude distribution with time Figure 6.5. Probability of remaining in the “low” state (left) and in the “high”...Figure 6.6. Time variations of the probability of remaining in a state of low se...Figure 6.7. Time variations of the probability of remaining in a state of high s...Figure 6.8. The probability of remaining in a high state of seismicity around th...

7 Chapter 7Figure 7.1. Seismicity rate per day for Southern California (top) and Japan (bot...Figure 7.2. The occurrence rate of aftershocks (filled symbols) (top) and the cu...Figure 7.3. Detrended fluctuation analysis for the waiting time series for two p...Figure 7.4. Detrended fluctuation analysis for the waiting time series in the Co...Figure 7.5. Normalized probability densities Pm,L(τ) of the rescaled waiting tim...Figure 7.6. Normalized probability densities Pm,L(τ) of the rescaled waiting tim...Figure 7.7. Normalized probability densities Pm,L(τ) of the rescaled waiting tim...Figure 7.8. The cumulative distribution function P (> τ′) of the rescaled waitin...Figure 7.9. The range of generalized Hurst exponents h(q) for various values of ...

8 Chapter 8Figure 8.1. Conditional intensity function of the LSRM (a) in North China (1 + 2...Figure 8.2. Epicentral distribution of crustal earthquakes with M ≥ 6.5 that occ...Figure 8.3. (a) Conditional intensity function versus time fitted to the catalog...Figure 8.4. Conditional intensity function versus time fitted to the catalog of ...Figure 8.5. Seismicity map showing earthquakes with M ≥ 5.2 that occurred in the...Figure 8.6. Conditional intensity functions versus time fitted to the catalog of...Figure 8.7. Coulomb stress changes due to the coseismic slip of the characterist...Figure 8.8. Conditional intensity functions versus time fitted to the catalog of...

9 Chapter 9Figure 9.1. Earthquakes with M ≥ 3.5 that occurred in the area of Greece from Ja...Figure 9.2. An illustration of a MAP with two states for a period (0,8.2). For a...Figure 9.3. The MAP is fitted to simulated samples of a four-state MAP with Nst=...Figure 9.4. The main active boundaries of the broader area of Greece and the thr...Figure 9.5. Decoded path for the D1 dataset along with the magnitude distributio...Figure 9.6. Same as Figure 9.5 for dataset D2. For a color version of this figur...Figure 9.7. Same as Figure 9.5 for dataset D3. For a color version of this figur...Figure 9.8. Left: epicentral distribution of the Mw6.5 Lefkada aftershock sequen...Figure 9.9. Left: epicentral distribution of the events that occurred from Febru...Figure 9.10. Left: epicentral distribution of the events that occurred from May ...

1 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...

2 Chapter 3Table 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...

3 Chapter 6Table 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...

4 Chapter 8Table 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...

5 Chapter 9Table 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...

6 Chapter 11Table 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...

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2 Table of Contents

3 Title Page SCIENCES Statistics , Field Director – Nikolaos Limnios and Kerrie Mengersen Geostatistics

4 Copyright 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 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 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 Library ISBN 978-1-78945-037-8 ERC code: PE1 Mathematics PE1_13 ProbabilityPE1_14 Statistics PE1_20 Application of mathematics in sciences PE10 Earth System Science PE10_7 Physics of earth’s interior, seismology, volcanology