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Pure and Applied Geophysics

, Volume 167, Issue 8–9, pp 907–917 | Cite as

Space–Time Earthquake Prediction: The Error Diagrams

  • G. Molchan
Article

Abstract

The quality of earthquake prediction is usually characterized by a two-dimensional diagram n versus τ, where n is the rate of failures-to-predict and τ is a characteristic of space–time alarm. Unlike the time prediction case, the quantity τ is not defined uniquely. We start from the case in which τ is a vector with components related to the local alarm times and find a simple structure of the space–time diagram in terms of local time diagrams. This key result is used to analyze the usual 2-d error sets {n, τ w } in which τ w is a weighted mean of the τ components and w is the weight vector. We suggest a simple algorithm to find the (n, τ w ) representation of all random guess strategies, the set D, and prove that there exists the unique case of w when D degenerates to the diagonal n + τ w  = 1. We find also a confidence zone of D on the (n, τ w ) plane when the local target rates are known roughly. These facts are important for correct interpretation of (n, τ w ) diagrams when we discuss the prediction capability of the data or prediction methods.

Keywords

Prediction earthquake dynamics statistical seismology 

Notes

Acknowledgements

This work was supported by the Russian Foundation for Basic Research through grant 08-05-00215. I thank D.L. Turcotte for useful discussions, which have stimulated the writing of the present paper.

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsRussian Academy of SciencesMoscowRussia
  2. 2.The Abdus Salam International Centre for Theoretical Physics, SAND GroupTriesteItaly

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