2012
DOI: 10.1103/physreve.86.021106
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Probabilities for large events in driven threshold systems

Abstract: Many driven threshold systems display a spectrum of avalanche event sizes, often characterized by power-law scaling. An important problem is to compute probabilities of the largest events ("Black Swans"). We develop a data-driven approach to the problem by transforming to the event index frame, and relating this to Shannon information. For earthquakes, we find the 12-month probability for magnitude m>6 earthquakes in California increases from about 30% after the last event, to 40%-50% prior to the next one.

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Cited by 45 publications
(26 citation statements)
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“…Seismicity is a typical example of complex time series, and earthquakes exhibit complex correlations in time, space and magnitude (M) which have been studied by several authors (for example see Huang 2008Huang , 2011Lennartz et al 2008Lennartz et al , 2011Rundle et al 2012Rundle et al , 2016. The observed earthquake scaling laws (e.g., Turcotte 1997) indicate the existence of phenomena closely associated with the proximity of the system to a critical point (e.g., Holliday et al 2006;Varotsos et al 2011c).…”
Section: Pðxþmentioning
confidence: 99%
“…Seismicity is a typical example of complex time series, and earthquakes exhibit complex correlations in time, space and magnitude (M) which have been studied by several authors (for example see Huang 2008Huang , 2011Lennartz et al 2008Lennartz et al , 2011Rundle et al 2012Rundle et al , 2016. The observed earthquake scaling laws (e.g., Turcotte 1997) indicate the existence of phenomena closely associated with the proximity of the system to a critical point (e.g., Holliday et al 2006;Varotsos et al 2011c).…”
Section: Pðxþmentioning
confidence: 99%
“…Earthquakes (EQs) exhibit complex correlations in time, space and magnitude (Telesca et al, 2002;Eichner et al, 2007;Huang, 2008Huang, , 2011Telesca, 2010;Lippiello et al, 2009Lippiello et al, , 2012Lennartz et al, 2008Lennartz et al, , 2011Sarlis, 2011;Rundle et al, 2012;Tenenbaum et al, 2012;Sarlis and Christopoulos, 2012). The EQ scaling laws (Turcotte, 1997) point to the view (e.g., Holliday et al, 2006) that a mainshock occurrence may be considered as an approach to a critical point.…”
Section: Introductionmentioning
confidence: 99%
“…Criticality has earlier been suggested as an EQ precursory sign (Chelidze, 1982;Chelidze and Kolesnikov, 1982;Chelidze et al, 2006;Rundle et al, 2012;Wanliss et al, 2015). Critical phenomena have been proposed as the likely framework to study the origins of EQ-related EM fluctuations, suggesting that the theory of phase transitions and critical phenomena may be useful in gaining insight into the mechanism of their complex dynamics (Bowman et al, 1998;Contoyiannis et al, 2004aContoyiannis et al, , 2005Contoyiannis et al, , 2015Varotsos et al, 2011a, b).…”
Section: Critical Dynamics Analysis Methodsmentioning
confidence: 99%