We introduce a statistical methodology for clustering analysis of seismicity in the time-space-energy domain and use it to establish the existence of two statistically distinct populations of earthquakes: clustered and nonclustered. This result can be used, in particular, for nonparametric aftershock identification. The proposed approach expands the analysis of Baiesi and Paczuski [Phys. Rev. E 69, 066106 (2004)10.1103/PhysRevE.69.066106] based on the space-time-magnitude nearest-neighbor distance eta between earthquakes. We show that for a homogeneous Poisson marked point field with exponential marks, the distance eta has the Weibull distribution, which bridges our results with classical correlation analysis for point fields. The joint 2D distribution of spatial and temporal components of eta is used to identify the clustered part of a point field. The proposed technique is applied to several seismicity models and to the observed seismicity of southern California.

Abstract. We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

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Absirac•. We study the space-time relationships between strong earthquakes in California and the intermediate-magnitude earthquakes that both precede and follow them. All 11 earthquakes in California with nominal magnitudes greater than or equal to 6.8 from 1941 to 1993 were preceded by an increase in the rage of occurrence of earthquakes having magnitudes greater than 5.1. Ten of the 11 earthquakes occurred when or shortly after the intermediate magnitude activity was grea•er than its 75th percenttie. Three of these strong earthquakes are in a conventional space-time foreshock-aftershock relationship with others of the 11 strong events. The precursory activity is concentrated in regions having linear dimensions of the order of a few hundred kilometers; these dimensions are significantly larger than the estimated fracture lengths of the ensuing strong earthquakes. The correlations are ill defined for smaller earthquakes and are almost unidentifiable for earthquakes with magnitudes less than about 4.6. The precursors to the strong earthquakes appear over a time interval of the order of 5 to l0 years before the strong earthquake, although the onset was about 25 years before the San Francisco earthquake. In the case of the Loma Prieta and San Francisco earthquakes, the onset of increased activity appears to be relatively abrupt. The increased activity is either switched off abruptly to distances of the order of hundreds of kilometers shortly after the occurrence of a strong earthquake, or the strong events are themselves part of a precursory pattern of continuing high activity before a second strong earthquake that takes place soon thereafter, with subsequent extinction of activity after it. Thus the intermediate-magnitude precursors do not directly influence the time and location of the subsequent strong event, but •he strong event has a strong influence on the stress field in the vicinity of intermediate-magnitude earthquakes to distances of the order of many times the scale size of the strong earthquake.

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The lithosphere of the Earth can be viewed as a hierarchy of volumes, from tectonic plates to grains of rock. Their relative movement against the forces of friction and cohesion is realized to a large extent through earthquakes. The movement is controlled by a wide variety of independent processes, concentrated in the thin boundary zones between the volumes. A boundary zone has a similar hierarchical structure, consisting of volumes, separated by boundary zones, etc. Altogether, these processes transform the lithosphere into a large nonlinear system, featuring instability and deterministic chaos. From this background some integral grossly averaged empirical regularities emerge, indicating a wide range of similarity, collective behavior, and the possibility of intermediate‐term earthquake prediction.