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Probabilities for large events in driven threshold systems

John B. Rundle1,2,3,*, James R. Holliday1,†, William R. Graves4,‡, Donald L. Turcotte2,§, Kristy F. Tiampo5,∥, and William Klein6,¶

  • 1Department of Physics, University of California, Davis, California 95616
  • 2Department of Geology, University of California, Davis, California 95616
  • 3The Santa Fe Institute, Santa Fe, New Mexico 87501
  • 4Open Hazards Group, Davis, California 95616
  • 5Department of Earth Sciences, University of Western Ontario, London, ON, Canada N6A 3K7
  • 6Department of Physics, Boston University, Boston, Massachusetts 02215

  • *jbrundle@ucdavis.edu
  • †jrholliday@ucdavis.edu
  • ‡wrgraves@openhazards.com
  • §turcotte@geology.ucdavis.edu
  • ∥ktiampo@seis.es.uwo.ca
  • klein@physics.bu.edu
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Phys. Rev. E 86, 021106 – Published 7 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.021106

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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Phys. Rev. E 86, 021106– Published 7 August, 2012
  • Received 22 August 2011

©2012 American Physical Society

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