Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- List of Abbreviations -- List of Mathematical Symbols -- Part I Models -- Chapter 1 Motivation: Earthquake science challenges -- Chapter 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 -- Chapter 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 -- 3.3.1 Time-magnitude simulation -- 3.3.2 Space-focal mechanism simulation -- Part II Statistics -- Chapter 4 Statistical distributions of earthquake numbers: Consequence of branching process -- 4.1 Theoretical considerations -- 4.1.1 Generating function for the negative binomial distribution (NBD) -- 4.1.2 NBD distribution expressions -- 4.1.3 Statistical parameter estimation -- 4.2 Observed earthquake numbers distribution -- 4.2.1 Statistical analysis of earthquake catalogs -- 4.2.2 Observed earthquake numbers distributions -- 4.2.3 Likelihood analysis -- 4.2.4 Tables of parameters -- Chapter 5 Earthquake size distribution -- 5.1 Magnitude versus seismic moment -- 5.2 Seismic moment distribution -- 5.3 Is B ≡ 1/2? -- 5.3.1 Preamble -- 5.3.2 Catalog analysis and earthquake size distribution -- 5.3.3 Systematic and random effects in determining earthquake size -- 5.3.3.1 Scalar seismic moment errors -- 5.3.3.2 Earthquake sequences and their influence.

5.3.3.3 Seismic moment tensor and its complexity -- 5.3.3.4 Centroid depth influence -- 5.3.4 Dislocation avalanche statistics -- 5.3.5 What are B ≡ 1 /2 consequences? -- 5.4 Seismic moment sum distribution -- 5.4.1 Simulation and analytical results -- 5.4.2 Applications to seismicity analysis -- 5.5 Length of aftershock zone (earthquake spatial scaling) -- 5.6 Maximum or corner magnitude: 2004 Sumatra and 2011 Tohoku mega-earthquakes -- 5.6.1 Maximum moment for subduction zones -- 5.6.2 Seismic moment conservation principle -- Chapter 6 Temporal earthquake distribution -- 6.1 Omori's law -- 6.2 Seismic moment release in earthquakes and aftershocks -- 6.2.1 Temporal distribution of aftershocks -- 6.2.2 Southern California earthquakes and their aftershocks -- 6.2.3 Global shallow earthquakes -- 6.2.4 Comparison of source-time functions and aftershock moment release -- 6.3 Random shear stress and Omori's law -- 6.4 Aftershock temporal distribution, theoretical analysis -- 6.4.1 Lévy distribution -- 6.4.2 Inverse Gaussian distribution (IGD) -- 6.5 Temporal distribution of aftershocks: Observations -- 6.5.1 Aftershock sequences -- 6.5.2 Temporal distribution for earthquake pairs -- 6.6 Example: The New Madrid earthquake sequence of 1811-12 -- 6.7 Conclusion -- Chapter 7 Earthquake location distribution -- 7.1 Multipoint spatial statistical moments -- 7.2 Sources of error and bias in estimating the correlation dimension -- 7.2.1 The number of earthquakes in a sample -- 7.2.2 Earthquake location error -- 7.2.2.1 Earthquake location error: the 3-D case -- 7.2.2.2 Earthquake location error: the 2-D case -- 7.2.3 Projection effect for epicentral scaling dimension -- 7.2.4 Boundary effects -- 7.2.4.1 Boundary effects: a 2-D case -- 7.2.4.2 Boundary effects: 3-D case.

7.2.5 Inhomogeneity of earthquake depth distribution -- 7.2.6 Temporal influence -- 7.2.7 Randomness -- 7.3 Correlation dimension for earthquake catalogs -- 7.3.1 California catalogs -- 7.3.2 Global PDE catalog -- 7.4 Conclusion -- Chapter 8 Focal mechanism orientation and source complexity -- 8.1 Random stress tensor and seismic moment tensor -- 8.1.1 Challenges in stress studies -- 8.1.2 Cauchy stress distribution -- 8.1.3 Random stress tensors -- 8.2 Geometric complexity of earthquake focal zone and fault systems -- 8.2.1 Tensor invariants -- 8.2.2 CLVD sources and complexity -- 8.3 Rotation of double-couple (DC) earthquake moment tensor and quaternions -- 8.3.1 Quaternions -- 8.3.2 DC moment tensor and quaternions -- 8.4 Focal mechanism symmetry -- 8.4.1 Symmetry of DC source -- 8.4.2 DC symmetry and rotation angle -- 8.5 Earthquake focal mechanism and crystallographic texture statistics -- 8.6 Rotation angle distributions -- 8.6.1 Uniform random rotation of DC sources -- 8.6.2 Non-uniform distributions of random rotations -- 8.7 Focal mechanisms statistics -- 8.7.1 Disorientation angle statistics -- 8.7.2 Distributions of rotation axes -- 8.7.3 Rodrigues space statistics and display -- 8.7.4 Summary of results for DC orientation -- 8.8 Models for complex earthquake sources -- 8.8.1 Complex point source solutions -- 8.8.1.1 Point sources of elastic deformation in homogeneous infinite medium -- 8.8.1.2 Point sources of elastic deformation in homogeneous half-space -- 8.8.2 Higher-rank correlation tensors -- Part III Testable Forecasts -- Chapter 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 -- 9.4.1 Branching models.

9.4.2 Earthquake clusters-independent events -- 9.4.3 Dependent events -- 9.4.4 Stochastic branching processes and temporal dependence -- 9.5 Likelihood analysis of catalogs -- 9.5.1 Statistical analysis results -- 9.5.2 Comparison of results with the ETAS model -- 9.6 Results of the catalogs' statistical analysis -- Chapter 10 Long- and short-term earthquake forecasting -- 10.1 Phenomenological branching models and earthquake occurrence estimation -- 10.2 Long-term rate density estimates -- 10.2.1 Low-resolution forecasts -- 10.2.2 High-resolution global forecasts -- 10.2.3 Smoothing kernel selection -- 10.2.4 Comparing long-term forecasts -- 10.3 Short-term forecasts -- 10.4 Example: earthquake forecasts during the Tohoku sequence -- 10.4.1 Long- and short-term earthquake forecasts during the Tohoku sequence -- 10.4.2 Long-term earthquake rates for the Tokyo region -- 10.5 Forecast results and their discussion -- 10.6 Earthquake fault propagation modeling and earthquake rate estimation -- 10.6.1 Earthquake extended rupture representation and earthquake rate estimation -- 10.6.2 Earthquake fault propagation modeling -- Chapter 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) -- 11.3.1 Relation between the error diagram and information score -- 11.3.2 Two-segment error diagrams and information score -- 11.3.3 Information score for GCMT and PDE catalogs -- 11.4 Tests and optimization for global high-resolution forecasts -- 11.5 Summary of testing results -- Chapter 12 Future prospects and problems -- 12.1 Community efforts for statistical seismicity analysis and earthquake forecast testing.

12.1.1 Community Online Resource for Statistical Seismicity Analysis (CORSSA) -- 12.1.2 Collaboratory for the Study of Earthquake Predictability (CSEP): Global and regional forecast testing -- 12.2 Results and challenges -- 12.3 Future developments -- References -- Index.