Earthquakes models statistics testable forecasts First Edition by Yan K Kagan ISBN 1118637925 9781118637883

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ISBN 10: 1118637925

ISBN 13: 9781118637883 

Author: Yan K. Kagan 

This book is the first comprehensive and methodologically rigorous analysis of earthquake occurrence. Models based on the theory of the stochastic multidimensional point processes are employed to approximate the earthquake occurrence pattern and evaluate its parameters. The Author shows that most of these parameters have universal values. These results help explain the classical earthquake distributions: Omori’s law and the Gutenberg-Richter relation.

The Author derives a new negative-binomial distribution for earthquake numbers, instead of the Poisson distribution, and then determines a fractal correlation dimension for spatial distributions of earthquake hypocenters. The book also investigates the disorientation of earthquake focal mechanisms and shows that it follows the rotational Cauchy distribution. These statistical and mathematical advances make it possible to produce quantitative forecasts of earthquake occurrence. In these forecasts earthquake rate in time, space, and focal mechanism orientation is evaluated.

Table of contents:

PART I: MODELS
1: Motivation: Earthquake science challenges
2: Seismological background
 2.1: Earthquakes
 2.2: Earthquake catalogs
 2.3: Description of modern earthquake catalogs
 2.4: Earthquake temporal occurrence: quasi-periodic, Poisson, or clustered?
 2.5: Earthquake faults: one fault, several faults, or an infinite number of faults?
 2.6: Statistical and physical models of seismicity
 2.7: Laboratory and theoretical studies of fracture
3: Stochastic processes and earthquake occurrence models
 3.1: Earthquake clustering and branching processes
 3.2: Several problems and challenges
 3.3: Critical continuum-state branching model of earthquake rupture

PART II: STATISTICS
4: Statistical distributions of earthquake numbers: Consequence of branching process
 4.1: Theoretical considerations
 4.2: Observed earthquake numbers distribution
5: Earthquake size distribution
 5.1: Magnitude versus seismic moment
 5.2: Seismic moment distribution
 5.3: Is β ≡ 1¨M2?
 5.4: Seismic moment sum distribution
 5.5: Length of aftershock zone (earthquake spatial scaling)
 5.6: Maximum or corner magnitude: 2004 Sumatra and 2011 Tohoku mega-earthquakes
6: Temporal earthquake distribution
 6.1: Omori’s law
 6.2: Seismic moment release in earthquakes and aftershocks
 6.3: Random shear stress and Omori’s law
 6.4: Aftershock temporal distribution, theoretical analysis
 6.5: Temporal distribution of aftershocks: Observations
 6.6: Example: The New Madrid earthquake sequence of 1811–12
 6.7: Conclusion
7: Earthquake location distribution
 7.1: Multipoint spatial statistical moments
 7.2: Sources of error and bias in estimating the correlation dimension
 7.3: Correlation dimension for earthquake catalogs
 7.4: Conclusion
8: Focal mechanism orientation and source complexity
 8.1: Random stress tensor and seismic moment tensor
 8.2: Geometric complexity of earthquake focal zone and fault systems
 8.3: Rotation of double-couple (DC) earthquake moment tensor and quaternions
 8.4: Focal mechanism symmetry
 8.5: Earthquake focal mechanism and crystallographic texture statistics
 8.6: Rotation angle distributions
 8.7: Focal mechanisms statistics
 8.8: Models for complex earthquake sources

PART III: TESTABLE FORECASTS
9: Global earthquake patterns
 9.1: Earthquake time-space patterns
 9.2: Defining global tectonic zones
 9.3: Corner magnitudes in the tectonic zones
 9.4: Critical branching model (CBM) of earthquake occurrence
 9.5: Likelihood analysis of catalogs
 9.6: Results of the catalogs’ statistical analysis
10: Long- and short-term earthquake forecasting
 10.1: Phenomenological branching models and earthquake occurrence estimation
 10.2: Long-term rate density estimates
 10.3: Short-term forecasts
 10.4: Example: earthquake forecasts during the Tohoku sequence
 10.5: Forecast results and their discussion
 10.6: Earthquake fault propagation modeling and earthquake rate estimation
11: Testing long-term earthquake forecasts: Likelihood methods and error diagrams
 11.1: Preamble
 11.2: Log-likelihood and information score
 11.3: Error diagram (ED)
 11.4: Tests and optimization for global high-resolution forecasts
 11.5: Summary of testing results
12: Future prospects and problems
 12.1: Community efforts for statistical seismicity analysis and earthquake forecast testing
 12.2: Results and challenges
 12.3: Future developments

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Tags: Yan K Kagan, Earthquakes, Models, Statistics, Testable Forecasts