Variations of trends of indicators describing complex systems: change of scaling precursory to extreme events.

Socioeconomic and natural complex systems persistently generate extreme events also known as disasters, crises, or critical transitions. Here we analyze patterns of background activity preceding extreme events in four complex systems: economic recessions, surges in homicides in a megacity, magnetic storms, and strong earthquakes. We use as a starting point the indicators describing the system's behavior and identify changes in an indicator's trend. Those changes constitute our background events (BEs). We demonstrate a premonitory pattern common to all four systems considered: relatively large magnitude BEs become more frequent before extreme event. A premonitory change of scaling has been found in various models and observations. Here we demonstrate this change in scaling of uniformly defined BEs in four real complex systems, their enormous differences notwithstanding.

Premonitory patterns of seismicity months before a large earthquake: five case histories in Southern California.

This article explores the problem of short-term earthquake prediction based on spatio-temporal variations of seismicity. Previous approaches to this problem have used precursory seismicity patterns that precede large earthquakes with "intermediate" lead times of years. Examples include increases of earthquake correlation range and increases of seismic activity. Here, we look for a renormalization of these patterns that would reduce the predictive lead time from years to months. We demonstrate a combination of renormalized patterns that preceded within 1-7 months five large (M > or = 6.4) strike-slip earthquakes in southeastern California since 1960. An algorithm for short-term prediction is formulated. The algorithm is self-adapting to the level of seismicity: it can be transferred without readaptation from earthquake to earthquake and from area to area. Exhaustive retrospective tests show that the algorithm is stable to variations of its adjustable elements. This finding encourages further tests in other regions. The final test, as always, should be advance prediction. The suggested algorithm has a simple qualitative interpretation in terms of deformations around a soon-to-break fault: the blocks surrounding that fault began to move as a whole. A more general interpretation comes from the phenomenon of self-similarity since our premonitory patterns retain their predictive power after renormalization to smaller spatial and temporal scales. The suggested algorithm is designed to provide a short-term approximation to an intermediate-term prediction. It remains unclear whether it could be used independently. It seems worthwhile to explore similar renormalizations for other premonitory seismicity patterns.

Similarities of multiple fracturing on a neutron star and on the Earth.

In this paper the similarities of multiple fracturing on a neutron star and on the Earth are explored, including power-law energy distributions, clustering, and the symptoms of transition to a major rupture. These similarities may reflect a scenario of a critical transition, common for a broader class of nonlinear systems.

Critical transitions in colliding cascades

We consider here the interaction of direct and inverse cascades in a hierarchical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarchy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail (i. e., break down) under the load. The smallest elements fail first. The failures gradually expand up the hierarchy to the larger elements, thus forming an inverse cascade. Eventually the failures heal, ensuring that the system will function indefinitely. The direct and inverse cascades collide and interact. Loading triggers the failures, while failures release and redistribute the load. Notwithstanding its relative simplicity, this model reproduces the major dynamical features observed in seismicity, including the seismic cycle, intermittence of seismic regime, power-law energy distribution, clustering in space and time, long-range correlations, and a set of seismicity patterns premonitory to a strong earthquake. In this context, the hierarchical structure of the model crudely imitates a system of tectonic blocks spread by a network of faults (note that the behavior of such a network is different from that of a single fault). Loading mimics the impact of tectonic forces, and failures simulate earthquakes. The model exhibits three basic types of premonitory pattern reflecting seismic activity, clustering of earthquakes in space and time, and the range of correlation between the earthquakes. The colliding-cascade model seemingly exhibits regularities that are common in a wide class of complex hierarchical systems, not necessarily Earth specific.

Intermediate-term earthquake prediction.

An earthquake of magnitude M and linear source dimension L(M) is preceded within a few years by certain patterns of seismicity in the magnitude range down to about (M - 3) in an area of linear dimension about 5L-10L. Prediction algorithms based on such patterns may allow one to predict approximately 80% of strong earthquakes with alarms occupying altogether 20-30% of the time-space considered. An area of alarm can be narrowed down to 2L-3L when observations include lower magnitudes, down to about (M - 4). In spite of their limited accuracy, such predictions open a possibility to prevent considerable damage. The following findings may provide for further development of prediction methods: (i) long-range correlations in fault system dynamics and accordingly large size of the areas over which different observed fields could be averaged and analyzed jointly, (ii) specific symptoms of an approaching strong earthquake, (iii) the partial similarity of these symptoms worldwide, (iv) the fact that some of them are not Earth specific: we probably encountered in seismicity the symptoms of instability common for a wide class of nonlinear systems.

Geometric incompatibility in a fault system.

Interdependence between geometry of a fault system, its kinematics, and seismicity is investigated. Quantitative measure is introduced for inconsistency between a fixed configuration of faults and the slip rates on each fault. This measure, named geometric incompatibility (G), depicts summarily the instability near the fault junctions: their divergence or convergence ("unlocking" or "locking up") and accumulation of stress and deformations. Accordingly, the changes in G are connected with dynamics of seismicity. Apart from geometric incompatibility, we consider deviation K from well-known Saint Venant condition of kinematic compatibility. This deviation depicts summarily unaccounted stress and strain accumulation in the region and/or internal inconsistencies in a reconstruction of block- and fault system (its geometry and movements). The estimates of G and K provide a useful tool for bringing together the data on different types of movement in a fault system. An analog of Stokes formula is found that allows determination of the total values of G and K in a region from the data on its boundary. The phenomenon of geometric incompatibility implies that nucleation of strong earthquakes is to large extent controlled by processes near fault junctions. The junctions that have been locked up may act as transient asperities, and unlocked junctions may act as transient weakest links. Tentative estimates of K and G are made for each end of the Big Bend of the San Andreas fault system in Southern California. Recent strong earthquakes Landers (1992, M = 7.3) and Northridge (1994, M = 6.7) both reduced K but had opposite impact on G: Landers unlocked the area, whereas Northridge locked it up again.

Aggregate-level analysis and prediction of midterm senatorial elections in the United States, 1974-1986.

Pattern recognition study demonstrates that the outcomes of American midterm senatorial elections follow the dynamics of simple integral parameters that depict preelectoral situations aggregated to the state as a whole. A set of "commonsense" parameters is identified that is sufficient to predict such elections state-by-state and year-by-year. The analysis rejects many similar commonsense parameters. The existence and nature of integral collective behavior in U.S. elections at the level of the individual states is investigated. Implications for understanding the American electoral process are discussed.

Pattern recognition applied to presidential elections in the United States, 1860-1980: Role of integral social, economic, and political traits.

The outcome of American presidential elections in 1860-1980 follows certain regular patterns which can be described phenomenologically by simple integral parameters of "common sense" type.

Model of clustering of earthquakes.

A two-dimensional model of the expansion of a crack in an elastic medium is considered in which friction depends on the slip rate and the modulus of cohesion depends on the speed of expansion of the crack. Elastic waves are neglected (quasi-static model). Under some conditions, the expansion of the crack is realized by the alternation of slow and fast episodes ("shocks") of slip. This offers a possible qualitative explanation of several forms of earthquake clustering, including clustering that is premonitory to strong earthquakes.