Unified scaling law for earthquakes.

By P. Bak, K. Christensen, Leon Danon, T. Scanlon. Physical Review Letters, 2001

608 citations recorded by the source corpus.

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d(f) of earthquakes appear as critical indices.

Subfields: Condensed Matter Physics, Economics and Econometrics, Geophysics

View Paper: https://www.semanticscholar.org/paper/174f3d1f7c773a89213566aef19a71a7438f133c

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Citations in the corpus

Estimating Background Activity Based on Interevent-Time Distribution (2006, background): “Recently, the statistics of the waiting times between consecutive earthquakes (so-called interevent times) have also increasingly become the focus of research (Bak et al., 2002; Corral, 2004; Davidsen and Goltz, 2004).”
Power-Law Scaling in the Brain Surface Electric Potential (2009, background): “A popular example of this is the emergence of earthquakes of different sizes and the frequencies on which they occur [46], which have a power-law relationship.”
Global Catastrophic Risks (2008, background): “For example, the energy of earthquakes, asteroid impacts, and Pacific hurricanes all seem to be distributed with a power of about one (Christensen et al., 2002; Lay and Wallace, 1995; Morrison et al., 2003; Sanders, 2005).”
Grand minima and maxima of solar activity: new observational constraints (2007, background): “…been obtained for many solar and terrestrial indices on different time scales from minutes to 105 years: e.g., intervals between major earthquakes (Bak et al. 2002, Mega et al. 2003); intervals between successive solar flares (Pearce et al. 1993, Boffetta et al. 1999, Moon et al. 2001); waiting…”
On the probability of occurrence of extreme space weather events (2012, background): “throughout all areas of science, including earthquake magnitudes [Christensen et al., 2002] and solar flare size [Lu and Hamilton, 1991].”
Indicators for Complex Innovation Systems (2006, background): “Amongst other things a complex system • has a dynamic internal structure that evolves and interacts in a complex manner, • exhibits emergent behaviours and patterns that are not the result of rules or caused by a single entity in the system.”
Universal features of correlated bursty behaviour (2011, methodology): “Over the last few years different explanations have been proposed about the origin of inhomogeneous human dynamics [4, 22, 27], including the single event level [28], and about the impact of circadian and weekly fluctuations [7].”
Beyond Word Frequency: Bursts, Lulls, and Scaling in the Temporal Distributions of Words (2009, background): “Research on the distribution of time intervals between successive occurrences of events has revealed correspondences between natural phenomena on the one hand [1, 2] and social activities on the other hand [3, 4, 5].”
Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions (2012, background): “…waiting times, associated to a mixture of scales of waiting times due to the Omori law, and another for large waiting times, due to spatial heterogeneity arising from the mixture of different areas with different seismic rates (Bak et al., 2002; Corral, 2003, 2004b; Corral and Christensen, 2006).”
The Economics of Tail Events with an Application to Climate Change (2011, positive): “Figure 3 illustrates the power law for earthquakes based on data from the U.S. Geological Survey on the largest recorded earthquakes, but this is a typical result (see Christensen et al. 2002 as an example).”