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Ergodicity and Earthquake Catalogs: Forecast Testing and Resulting Implications


Recently the equilibrium property of ergodicity was identified in an earthquake fault system (Tiampo et al., Phys. Rev. Lett. 91, 238501, 2003; Phys. Rev. E 75, 066107, 2007). Ergodicity in this context not only requires that the system is stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages when studying their behavior in space and time. In this work we show that this property can be used to identify those regions of parameter space which are stationary when applied to the seismicity of two naturally-occurring earthquake fault networks. We apply this measure to one particular seismicity-based forecasting tool, the Pattern Informatics index (Tiampo et al., Europhys. Lett. 60, 481–487, 2002; Rundle et al., Proc. National Acad. Sci., U.S.A., Suppl. 1, 99, 2463, 2002), in order to test the hypothesis that the identification of ergodic regions can be used to improve and optimize forecasts that rely on historic seismicity catalogs. We also apply the same measure to synthetic catalogs in order to better understand the physical process that affects this accuracy. We show that, in particular, ergodic regions defined by magnitude and time period provide more reliable forecasts of future events in both natural and synthetic catalogs, and that these improvements can be directly related to specific features or properties of the catalogs that impact the behavior of their spatial and temporal statistics.

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The work of KFT and YT was supported by the NSERC and Aon Benfield/ICLR Industrial Research Chair in Earthquake Hazard Assessment. This research also was supported by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008. The SCEC contribution number for this paper is 1213. The research of SZLK-K was funded by the Institute of Catastrophic Loss Reduction. We would like to thank Dr. J. Adams and Dr. S. Halchuck for supplying the SHEEF catalog. HCL is grateful for the effort of CWB to maintain the CWBSN and the support from the National Science Council (ROC), the Institute of Geophysics (NCU, ROC) and the Department of Earth Science (UWO, Canada). Research by HCL is funded by NSC grant 096-2917-1-008-005. The work of CCC was supported by the National Science Council (ROC) and the Department of Earth Sciences (NCU, ROC). Several figures in this presentation are generated by a tool package “MAPI (Mapping and Analysis via Pattern Informatics)” developed by YT ( Other images were plotted with the help of GMT software developed and supported by Paul Wessel and Walter H.F. Smith. Other geographical maps in this manuscript were generated using M_Map Toolbox developed by R. Pawlowicz ( This paper was significantly improved by the comments of two anonymous reviewers.

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Tiampo, K.F., Klein, W., Li, HC. et al. Ergodicity and Earthquake Catalogs: Forecast Testing and Resulting Implications. Pure Appl. Geophys. 167, 763–782 (2010).

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  • Earthquake forecasting
  • ergodic behavior
  • PI method
  • Thirumalai–Mountain metric
  • Canadian seismicity
  • Taiwanese seismicity