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Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where slow buildup of energy is punctuated by an abrupt release of energy through avalanche events which usually follow scale invariant statistics. From the simulations of these systems it is possible to extract sequences of record-breaking avalanches, where each subsequent record-breaking event is larger in magnitude than all previous events. In the present work, several cellular automata are analyzed among them the sandpile model, Manna model, Olami-Feder-Christensen (OFC) model, and the forest-fire model to investigate the record-breaking statistics of model avalanches which exhibit temporal and spatial correlations. Several statistical measures of record-breaking events are derived analytically and confirmed through numerical simulations. The statistics of record-breaking avalanches for the four models are compared to that of record-breaking events extracted from the sequences of independent identically distributed (\emph{i.i.d.}) random variables. It is found that the statistics of record-breaking avalanches for the above cellular automata exhibit behavior different from that observed for \emph{i.i.d.} random variables which in turn can be used to characterize complex spatio-temporal dynamics. The most pronounced deviations are observed in the case of the OFC model with a strong dependence on the conservation parameter of the model. This indicates that avalanches in the OFC model are not independent and exhibit spatio-temporal correlations., Comment: 18 pages, 7 figures, accepted in Phys Rev E (2013)

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering., Comment: 5 pages, 3 figures. Submitted to PRL

We present a RELM forecast of future earthquakes in California that is primarily based on the pattern informatics (PI) method. This method identifies regions that have systematic fluctuations in seismicity, and it has been demonstrated to be successful. A PI forecast map originally published on 19 February 2002 for southern California successfully forecast the locations of sixteen of eighteen M>5 earthquakes during the past three years. The method has also been successfully applied to Japan and on a worldwide basis. An alternative approach to earthquake forecasting is the relative intensity (RI) method. The RI forecast map is based on recent levels of seismic activity of small earthquakes. Recent advances in the PI method show considerable improvement, particularly when compared with the RI method using relative operating characteristic (ROC) diagrams for binary forecasts. The RELM application requires a probability for each location for a number of magnitude bins over a five year period. We have therefore constructed a hybrid forecast in which we combine the PI method with the RI method to compute a map of probabilities for events occurring at any location, rather than just the most probable locations. These probabilities are further converted, using Gutenberg-Richter scaling laws, to anticipated rates of future earthquakes that can be evaluated using the RELM test., Comment: 6 pages, 4 figures (color), 1 table

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain., Comment: 13 pages, 1 figure. Submitted to Tectonophysics on 30 August 2004

Recent studies in the literature have introduced a new approach to earthquake forecasting based on representing the space-time patterns of localized seismicity by a time-dependent system state vector in a real-valued Hilbert space and deducing information about future space-time fluctuations from the phase angle of the state vector. While the success rate of this Pattern Informatics (PI) method has been encouraging, the method is still in its infancy. Procedural analysis, statistical testing, parameter sensitivity investigation and optimization all still need to be performed. In this paper, we attempt to optimize the PI approach by developing quantitative values for "predictive goodness" and analyzing possible variations in the proposed procedure. In addition, we attempt to quantify the systematic dependence on the quality of the input catalog of historic data and develop methods for combining catalogs from regions of different seismic rates., Comment: 39 pages, 4 tables, 9 figures. Submitted to Pure and Applied Geophysics on 30 November 2004

No proven method is currently available for the reliable short time prediction of earthquakes (minutes to months). However, it is possible to make probabilistic hazard assessments for earthquake risk. These are primarily based on the association of small earthquakes with future large earthquakes. In this paper we discuss a new approach to earthquake forecasting. This approach is based on a pattern informatics (PI) method which quantifies temporal variations in seismicity. The output is a map of areas in a seismogenic region (``hotspots'') where earthquakes are forecast to occur in a future 10-year time span. This approach has been successfully applied to California, to Japan, and on a worldwide basis. These forecasts are binary--an earthquake is forecast either to occur or to not occur. The standard approach to the evaluation of a binary forecast is the use of the relative operating characteristic (ROC) diagram, which is a more restrictive test and less subject to bias than maximum likelihood tests. To test our PI method, we made two types of retrospective forecasts for California. The first is the PI method and the second is a relative intensity (RI) forecast based on the hypothesis that future earthquakes will occur where earthquakes have occurred in the recent past. While both retrospective forecasts are for the ten year period 1 January 2000 to 31 December 2009, we performed an interim analysis 5 years into the forecast. The PI method out performs the RI method under most circumstances., Comment: 10(+1) pages, 5 figures, 2 tables. Submitted to Nonlinearl Processes in Geophysics on 5 August 2005

We analyze the space-time patterns of earthquake occurrence in southern California using a new method that treats earthquakes as a phase dynamical system. The system state vector is used to obtain a probability measure for current and future earthquake occurrence. Thousands of statistical tests indicate the method has considerable forecast skill. We emphasize that the method is not a model, and there are no unconstrained or free parameters to be determined by fits to training data sets., Comment: email: kristy@fractal.colorado.edu

Earthquake faults occur in networks that have dynamical modes not displayed by single isolated faults. Using simulations of the network of strike-slip faults in southern California, we find that the physics depends critically on both the interactions among the faults, which are determined by the geometry of the fault network, as well as on the stress dissipation properties of the nonlinear frictional physics, similar to the dynamics of integrate-and-fire neural networks., Comment: 12 pages, 4 figures