[1] We use recent results on statistical analysis of seismicity to present a robust method for comprehensive detection and analysis of earthquake clusters. The method is based on nearest-neighbor distances of events in space-time-energy domain. The method is applied to a 1981-2011 relocated seismicity catalog of southern California having 111,981 events with magnitudes m ≥ 2 and corresponding synthetic catalogs produced by the Epidemic Type Aftershock Sequence (ETAS) model. Analysis of the ETAS model demonstrates that the cluster detection results are accurate and stable with respect to (1) three numerical parameters of the method, (2) variations of the minimal reported magnitude, (3) catalog incompleteness, and (4) location errors. Application of the method to the observed catalog separates the 111,981 examined earthquakes into 41,393 statistically significant clusters comprised of foreshocks, mainshocks, and aftershocks. The results reproduce the essential known statistical properties of earthquake clusters, which provide overall support for the proposed technique. In addition, systematic analysis with our method allows us to detect several new features of seismicity that include (1) existence of a significant population of single-event clusters, (2) existence of foreshock activity in natural seismicity that exceeds expectation based on the ETAS model, and (3) dependence of all cluster properties, except area, on the magnitude difference of events from mainshocks but not on their absolute values. The classification of detected clusters into several major types, generally corresponding to singles, burst-like and swarm-like sequences, and correlations between different cluster types and geographic locations is addressed in a companion paper.

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.

[1] This is a second paper in a study of statistical identification and classification of earthquake clusters using a relocated catalog of 1981-2011 seismicity in southern California and synthetic catalogs produced by the Epidemic Type Aftershock Sequence model. Here we focus on classification of event families-statistically significant clusters composed of foreshocks, mainshocks, and aftershocks-that are detected with the methodology discussed in part I of the study. The families are analyzed using their representation as time oriented tree graphs. The results (1) demonstrate that the clustering associated with the largest earthquakes, m > 7, is statistically different from that of small-to-medium earthquakes; (2) establish the existence of two dominant types of small-to-medium magnitude earthquake families-burst-like and swarm-like sequences-and a variety of intermediate cluster forms obtained as a mixture of the two dominant types; (3) suggest a simple new quantitative measure for identifying the cluster type based on its topological structure; (4) demonstrate systematic spatial variability of the cluster characteristics on a scale of tens of kilometers in relation to heat flow and other properties governing the effective viscosity of a region; and (5) establish correlation between the family topological structure and a dozen of metric properties traditionally considered in the literature (number of aftershocks, duration, spatial properties, b-value, parameters of Omori-Utsu and Båth law, etc.). The burst-like clusters likely reflect highly brittle failures in relatively cold regions, while the swarm-like clusters are likely associated with mixed brittle-ductile failures in regions with relatively high temperature and/or fluid content. The results of this and paper I may be used to develop improved region-specific hazard estimates and earthquake forecasts.Citation: Zaliapin, I., and Y. Ben-Zion (2013), Earthquake clusters in southern California II: Classification and relation to physical properties of the crust,

River deltas are intricate landscapes with complex channel networks that self-organize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of material and energy fluxes, which maintains a stable hydrologic, geomorphologic, and ecological state of a river delta, is often disrupted by external perturbations causing topological and dynamical changes in the delta structure and function. A formal quantitative framework for studying delta channel network connectivity and transport dynamics and their response to change is lacking. Here we present such a framework based on spectral graph theory and demonstrate its value in computing delta's steady state fluxes and identifying upstream (contributing) and downstream (nourishment) areas and fluxes from any point in the network. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. The framework is applied to the Wax Lake delta in the Louisiana coast of the U.S. and the Niger delta in West Africa. In a companion paper, we present a comprehensive suite of metrics that quantify topologic and dynamic complexity of delta channel networks and, via application to seven deltas in diverse environments, demonstrate their potential to reveal delta morphodynamics and relate to notions of vulnerability and robustness.