Pure and Applied Geophysics

, Volume 174, Issue 6, pp 2279–2293 | Cite as

Spatial Evaluation and Verification of Earthquake Simulators

  • John Max Wilson
  • Mark R. Yoder
  • John B. Rundle
  • Donald L. Turcotte
  • Kasey W. Schultz


In this paper, we address the problem of verifying earthquake simulators with observed data. Earthquake simulators are a class of computational simulations which attempt to mirror the topological complexity of fault systems on which earthquakes occur. In addition, the physics of friction and elastic interactions between fault elements are included in these simulations. Simulation parameters are adjusted so that natural earthquake sequences are matched in their scaling properties. Physically based earthquake simulators can generate many thousands of years of simulated seismicity, allowing for a robust capture of the statistical properties of large, damaging earthquakes that have long recurrence time scales. Verification of simulations against current observed earthquake seismicity is necessary, and following past simulator and forecast model verification methods, we approach the challenges in spatial forecast verification to simulators; namely, that simulator outputs are confined to the modeled faults, while observed earthquake epicenters often occur off of known faults. We present two methods for addressing this discrepancy: a simplistic approach whereby observed earthquakes are shifted to the nearest fault element and a smoothing method based on the power laws of the epidemic-type aftershock (ETAS) model, which distributes the seismicity of each simulated earthquake over the entire test region at a decaying rate with epicentral distance. To test these methods, a receiver operating characteristic plot was produced by comparing the rate maps to observed \(m>6.0\) earthquakes in California since 1980. We found that the nearest-neighbor mapping produced poor forecasts, while the ETAS power-law method produced rate maps that agreed reasonably well with observations.


Earthquake simulators ETAS Earthquake forecasting RELM 



JMW and JBR would like to acknowledge support for this research from NASA Grant NNX12A22G and SCEC/USC Grant USC32774854-NSF FFT.


  1. Anagnos, T., & Kiremidjian, A. S. (1988). A review of earthquake occurrence models for seismic hazard analysis. Probabilistic Engineering Mechanics, 3(1), 3–11.CrossRefGoogle Scholar
  2. Båth, M. (1965). Lateral inhomogeneities of the upper mantle. Tectonophysics, 2(6), 483–514.CrossRefGoogle Scholar
  3. Chernick, M. R. (2011). Bootstrap methods: A guide for practitioners and researchers (vol. 619). Hoboken, New jersey: Wiley.Google Scholar
  4. Davison, A. C., & Hinkley, D. (1997). Bootstrap methods and their applications. Cambridge: Cambridge Series in Statistical and Probabilistic Mathematics.CrossRefGoogle Scholar
  5. Felzer, K. R., & Brodsky, E. E. (2006). Decay of aftershock density with distance indicates triggering by dynamic stress. Nature, 441(7094), 735–738.CrossRefGoogle Scholar
  6. Field, E. H. (2007a). Overview of the working group for the development of regional earthquake likelihood models (relm). Seismological Research Letters, 78(1), 7–16.CrossRefGoogle Scholar
  7. Field, E. H. (2007b). A summary of previous working groups on california earthquake probabilities. Bulletin of the Seismological Society of America, 97(4), 1033–1053.CrossRefGoogle Scholar
  8. Field, E. H., Arrowsmith, R. J., Biasi, G. P., Bird, P., Dawson, T. E., Felzer, K. R., et al. (2014). Uniform california earthquake rupture forecast, version 3 (ucerf3)the time-independent model. Bulletin of the Seismological Society of America, 104(3), 1122–1180.CrossRefGoogle Scholar
  9. Field, E. H., Dawson, T. E., Felzer, K. R., Frankel, A. D., Gupta, V., Jordan, T. H., et al. (2009). Uniform california earthquake rupture forecast, version 2 (ucerf 2). Bulletin of the Seismological Society of America, 99(4), 2053–2107.CrossRefGoogle Scholar
  10. Glasscoe, M., Rosinski, A., Vaughan, D., & Morentz, J. (2014). Disaster response and decision support in partnership with the california earthquake clearinghouse. In AGU Fall Meeting Abstracts (vol. 1, p. 07).Google Scholar
  11. Gutenberg, B. & Richter, C. (1954). Seismicity of the earth and associated phenomena. Princeton, New Jersey: Princeton University Press.Google Scholar
  12. Jolliffe, I. (2014). Principal Component Analysis. Wiley StatsRef: Statistics Reference Online.Google Scholar
  13. Jolliffe, I. T., & Stephenson, D. B. (2003). Forecast verification: a practitioner’s guide in atmospheric science. Chichester, West Sussex, England: WileyGoogle Scholar
  14. Kagan, Y. Y. (2002). Aftershock zone scaling. Bulletin of the Seismological Society of America, 92(2), 641–655.CrossRefGoogle Scholar
  15. Kajitani, Y., Chang, S. E., & Tatano, H. (2013). Economic impacts of the 2011 tohoku-oki earthquake and tsunami. Earthquake Spectra, 29(s1), S457–S478.CrossRefGoogle Scholar
  16. Lee, T.-T., Turcotte, D. L., Holliday, J. R., Sachs, M. K., Rundle, J. B., Chen, C.-C., et al. (2011). Results of the regional earthquake likelihood (relm) test of earthquake forecasts in california. Proceedings of the National Academy of Sciences, 108(40), 16533–16538.CrossRefGoogle Scholar
  17. Molchan, G. M. (1997). Earthquake prediction as a decision-making problem. Pure and Applied Geophysics, 149(1), 233–247.CrossRefGoogle Scholar
  18. Nanjo, K., Holliday, J., Chen, C.-C., Rundle, J., & Turcotte, D. (2006). Application of a modified pattern informatics method to forecasting the locations of future large earthquakes in the central japan. Tectonophysics, 424(3), 351–366.CrossRefGoogle Scholar
  19. Nanjo, K. Z. (2010). Earthquake forecast models for italy based on the ri algorithm. Annals of Geophysics, 53(3), 117–127.Google Scholar
  20. Ogata, Y. (1989). Statistical model for standard seismicity and detection of anomalies by residual analysis. Tectonophysics, 169(1), 159–174.CrossRefGoogle Scholar
  21. Ogata, Y., & Zhuang, J. (2006). Space-time etas models and an improved extension. Tectonophysics, 413(1), 13–23.CrossRefGoogle Scholar
  22. Parsons, T. (2008). Appendix c: Monte carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: Example calculations for california. US Geological Survey Open File Report, 1437-C, 32.Google Scholar
  23. Petersen, M. D., Moschetti, M. P., Powers, P. M., Mueller, C. S., Haller, K. M., Frankel, A. D., et al. (2014). Documentation for the 2014 update of the united states national seismic hazard maps. Technical report, US Geological Survey.Google Scholar
  24. Pollitz, F. F. (2012). Viscosim earthquake simulator. Seismological Research Letters, 83(6), 979–982.CrossRefGoogle Scholar
  25. Richards-Dinger, K., & Dieterich, J. H. (2012). Rsqsim earthquake simulator. Seismological Research Letters, 83(6), 983–990.CrossRefGoogle Scholar
  26. Rundle, J. B., Holliday, J. R., Yoder, M., Sachs, M. K., Donnellan, A., Turcotte, D. L., et al. (2011). Earthquake precursors: activation or quiescence? Geophysical Journal International, 187(1), 225–236.CrossRefGoogle Scholar
  27. Rundle, J. B., Turcotte D. L., Shcherbakov R., Klein W., & Sammis C. (2003). Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems. Reviews of Geophysics, 41, 1019. doi: 10.1029/2003RG000135.CrossRefGoogle Scholar
  28. Sachs, M., Turcotte, D. L., Holliday, J. R., & Rundle, J. (2012a). Forecasting earthquakes: The relm test. Computing in Science & Engineering, 14(5), 43–48.CrossRefGoogle Scholar
  29. Sachs, M., Yoder, M., Turcotte, D., Rundle, J., & Malamud, B. (2012b). Black swans, power laws, and dragon-kings: Earthquakes, volcanic eruptions, landslides, wildfires, floods, and soc models. The European Physical Journal-Special Topics, 205(1), 167–182.CrossRefGoogle Scholar
  30. Sachs, M. K., Heien, E. M., Turcotte, D. L., Yikilmaz, M. B., Rundle, J. B., & Kellogg, L. H. (2012c). Virtual california earthquake simulator. Seismological Research Letters, 83(6), 973–978.CrossRefGoogle Scholar
  31. Schorlemmer, D., Gerstenberger, M., Wiemer, S., Jackson, D., & Rhoades, D. (2007). Earthquake likelihood model testing. Seismological Research Letters, 78(1), 17–29.CrossRefGoogle Scholar
  32. Schorlemmer, D., & Gerstenberger, M. C. (2007). Relm testing center. Seismological Research Letters, 78(1), 30–36.CrossRefGoogle Scholar
  33. Schultz, K. W., Sachs, M. K., Heien, E. M., Yoder, M. R., Rundle, J. B., Turcotte, D. L., & Donnellan, A. (2015). Virtual quake: Statistics, co-seismic deformations and gravity changes for driven earthquake fault systems. In International Association of Geodesy Symposia (pp. 1–9). doi: 10.1007/1345_2015_134.
  34. Shcherbakov, R., & Turcotte, D. L. (2004). A modified form of båth’s law. Bulletin of the Seismological Society of America, 94(5), 1968–1975.CrossRefGoogle Scholar
  35. Shcherbakov, R., Turcotte D. L., & Rundle J. B. (2004). A generalized Omori’s law for earthquake aftershock decay. Geophysical Research Letters, 31, L11613. doi: 10.1029/2004GL019808.CrossRefGoogle Scholar
  36. Shcherbakov, R., Turcotte, D. L., & Rundle, J. B. (2006). Scaling properties of the parkfield aftershock sequence. Bulletin of the Seismological Society of America, 96(4B), S376–S384.CrossRefGoogle Scholar
  37. Tullis, T. E., Richards-Dinger, K., Barall, M., Dieterich, J. H., Field, E. H., Heien, E. M., et al. (2012). A comparison among observations and earthquake simulator results for the allcal2 california fault model. Seismological Research Letters, 83(6), 994–1006.CrossRefGoogle Scholar
  38. Turcotte, D. L., Holliday J. R., & Rundle J. B. (2007). BASS, an alternative to ETAS. Geophysical Research Letters, 34, L12303. doi: 10.1029/2007GL029696.CrossRefGoogle Scholar
  39. Ward, S. N. (2012). Allcal earthquake simulator. Seismological Research Letters, 83(6), 964–972.CrossRefGoogle Scholar
  40. Ward, S. N., & Goes, S. D. (1993). How regularly do earthquakes recur? a synthetic seismicity model for the san andreas fault. Geophysical Research Letters, 20(19), 2131–2134.CrossRefGoogle Scholar
  41. Yoder, M. R., Rundle, J. B., & Glasscoe, M. T. (2015a). Near-field ETAS constraints and applications to seismic hazard assessment. Pure and Applied Geophysics, 172(8), 2277–2293.CrossRefGoogle Scholar
  42. Yoder, M. R., Schultz, K. W., Heien, E. M., Rundle, J. B., Turcotte, D. L., Parker, J. W., & Donnellan, A. (2015b). The Virtual Quake earthquake simulator: a simulation-based forecast of the El Mayor-Cucapah region and evidence of predictability in simulated earthquake sequences. Geophysical Journal International, 203(3), 1587–1604.  CrossRefGoogle Scholar
  43. Yoder, M. R., Turcotte, D. L., & Rundle, J. (2011). Record-breaking earthquake precursors. PhD thesis.Google Scholar
  44. Zechar, J. D., Schorlemmer, D., Liukis, M., Yu, J., Euchner, F., Maechling, P. J., et al. (2010). The collaboratory for the study of earthquake predictability perspective on computational earthquake science. Concurrency and Computation: Practice and Experience, 22(12), 1836–1847.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • John Max Wilson
    • 1
  • Mark R. Yoder
    • 1
  • John B. Rundle
    • 1
    • 2
  • Donald L. Turcotte
    • 1
  • Kasey W. Schultz
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaDavisUSA
  2. 2.Department of Earth and Planetary SciencesUniversity of CaliforniaDavisUSA

Personalised recommendations