Earthquake occurrence : short- and long-term models and their validation / Rodolfo Console, Maura Murru, Giuseppe Falcone.

Format:

Book

Author/Creator:

Console, Rodolfo, author.

Murru, Maura, author.

Falcone, G. (Giuseppe), author.

Series:

Mathematics and statistics series (ISTE) ; Volume 1.

Mathematics and Statistics Series ; Volume 1

Language:

English

Subjects (All):

Earthquake prediction.

Seismology.

Physical Description:

1 online resource (170 pages) : illustrations (some color), tables, graphs.

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2017.

Summary:

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.

Contents:

Cover

Half-Title Page

Title Page

Copyright Page

Contents

Foreword

Preface: Short- and Long-term Models of Earthquake Occurrence and their Validation

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

4.2.1. The ROC diagrams

4.2.2. Molchan's error diagram

4.2.3. Probability gain

4.2.4. R-score

4.3. Statistical tests implemented within CSEP

4.3.1. Number test or N-test

4.3.2. Data-consistency test or L-test

4.3.3. S(pace)-test or S-test

4.3.4. M(agnitude)- test or M-test

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.

6.4.1. Exponential distribution (under the time-dependent hypothesis)

6.4.2. Log-normal distribution

6.4.3. Gamma distribution

6.4.4. Weibull distribution

6.4.5. Double-exponential distribution

6.4.6. BPT distribution

6.5. Validation and comparison of renewal time-dependent models

6.5.1. The likelihood ratio

6.5.2. Long-term earthquake records

6.5.3. Application of a Monte Carlo procedure

6.5.4. Concluding remarks

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

Other titles from iSTE in Mathematics and Statistics

EULA.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-119-37221-6

1-119-37230-5

OCLC:

994221173