Table of Contents
1 Distributions of Characteristics of Natural Disasters: Data and Classification 1
1.1 The Problem of Parameterization and Classification of Disasters 1
1.2 Empirical Distributions of Physical Parameters of Natural Disasters 4
1.3 Distributions of Death Tolls and Losses Due to Disasters 14
1.4 The Classification and Parameterization of Disasters 17
1.5 The Main Results 21
2 Models for the Generation of Distributions of Different Types 23
2.1 Why Are the Characteristic Types of Distribution Prevalent? 23
2.2 The Multiplicative Model of Disasters 33
2.3 The Mixed Models 34
2.4 The Main Results 36
3 Nonparametric Methods in the Study of Distributions 39
3.1 Application to Earthquake Catalogs 39
3.2 Estimates of the Lower and Upper Bounds for the Tail of a Distribution Function 41
3.3 Confidence Intervals for the Intensity of a Poisson Process 44
3.4 Probability of Exceeding a Past Record in a Future Time Interval 47
3.5 Distribution of the time to the Nearest Event Exceeding the Past Maximum 49
3.6 Main Results 52
4 Nonlinear and Linear Growth of Cumulative Effects of Natural Disasters 55
4.1 Nonlinear Growth of Cumulative Effects in a Stationary Model with the Power (Pareto) Distribution 55
4.1.1 The Existence of a Nonlinear Growth of Cumulative Effects in a Stationary Model with the Pareto Distribution 55
4.1.2 The Evaluation of the Maximum Individual Loss 57
4.1.3 The Relation Between the Total Loss and the Maximum Individual Loss for the Pareto Law 59
4.2 The Growth of Total Earthquake Loss 63
4.2.1 The Raw Data on Seismic Disasters 63
4.2.2 The Nature of Nonlinear Growth of Cumulative Earthquake Loss 66
4.2.3 The Limits of Applicability of the Pareto Law to the Estimation of Earthquake Losses 75
4.3 Main Results 82
5 The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment 85
5.1 Nonlinear Mode of Growth of Cumulative Seismic Moment 85
5.2 Change in the Rate at which the Cumulative Seismic Moment Increases with Time 94
5.3 Characteristic Maximum Earthquake: Definition and Properties 97
5.4 The Characteristic Maximum Earthquake: Estimation and Application 102
5.5 The Seismic Moment-Frequency Relation: Universal? 107
5.6 Nonlinear Mode of Growth of Cumulative Seismotectonic Deformation 110
5.7 Main Results 112
6 Estimating the Uppermost Tail of a Distribution 115
6.1 The Problem of Evaluation of the "Maximum Possible" Earthquake Mmax 115
6.2 Estimation of Quantiles Qq(τ) with the Help of Theorem 1 (Fitting the GEV Distribution) 122
6.3 Estimation of Quantiles Qq(τ) with the Help of Theorem 2 (Fitting the GPD Distribution) 123
6.4 Application of the GEV and GPD to the Estimation of Quantiles Qq(τ). The Global Harvard Catalog of Scalar Seismic Moments 126
6.5 Application of the GEV and GPD to the Estimation of Quantiles Qq(τ) for Catalogs of Binned Magnitudes 134
6.5.1 Catalog of the Japan Meteorological Agency (JMA) 136
6.5.2 Fennoscandia Catalog 144
6.5.3 Main Results 152
Appendix A Application of the Kolmogorov Test to the Densities That Depending on a Parameter 154
Appendix B Estimation of the Parameters (μ,σ, ξ) of the GEV Distribution Function: The Method of Moments (MM) 155
Appendix C Estimation of Parameters (s,ξ) of the GPD by Maximum Likelihood (ML) Method 156
7 Relationship Between Earthquake Losses and Social and Economic Situation 159
7.1 Variation in the Number of Casualties and Economic Loss from Natural Disasters 159
7.2 Dependence of Losses on Per Capita National Product Values 165
7.3 Damage Values and Social Cataclysms 167
7.4 The Natural Disasters and the Concept of Sustainable Development 170
7.5 Main Results 171
Summary and a Review 173
References 181
Index 189
