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Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles,

Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, ykagan@ucla.edu , http://eq.ess.ucla.edu/~kagan.html. Leon Knopoff and the Development of Quantitative Statistical Earthquake Forecasts. http://moho.ess.ucla.edu/~kagan/Leon_SSA .ppt. Abstract.

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Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles,

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  1. Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, ykagan@ucla.edu, http://eq.ess.ucla.edu/~kagan.html Leon Knopoff and the Development of Quantitative Statistical Earthquake Forecasts http://moho.ess.ucla.edu/~kagan/Leon_SSA.ppt

  2. Abstract With Leon Knopoff we studied statistical seismicity patterns: earthquake size distribution, scale-invariant geometry of quake faulting, power-law time dependence for quake occurrence. We found that the size distribution should be limited (Knopoff and Kagan, JGR, 1977); large earthquakes are clustered in time and space (Kagan and Knopoff, PEPI, 1976); the spatial quake pattern is scale-invariant (Kagan and Knopoff, GJI, 1980); developed self-similar model of earthquake occurrence (Kagan and Knopoff, JGR, 1981). On the basis of these results, since 1987 (Kagan and Knopoff, Science, 1987) we have developed statistical short- and long-term earthquake forecasts to predict earthquake rate in California per unit area, time, and magnitude. Later these predictions were extended to many seismic regions and to global forecasts (Kagan and Jackson, GJI, 2000; 2011). The forecasts are based on smoothed maps of past seismicity and assume spatial and temporal clustering, and are being quantitatively and rigorously tested.

  3. Leon Knopoff (1925/7/1–2011/1/20) Photo -- June 1986 L. Knopoff was one of the founders of statistical seismology. 1975-1996: I published 15 papers with him on statistical analysis of seismicity and earthquake forecasting.

  4. Outline • Statistical study of seismicity patterns: earthquake size distribution, scale-invariant geometry of quake faulting, power-law time dependence for quake occurrence. • Quantitative earthquake prediction -- Leon Knopoff’s early efforts and later developments. • Current global earthquake forecasts and their testing.

  5. Stochastic Models of Earthquake Occurrence and Forecasting • Empirical branching models (Kagan, 1973a,b; Kagan and Knopoff, 1987; Ogata, 1988, 1998; Kagan, 2010). • Long-term models for earthquake occurrence, optimization and testing of smoothing procedure (Kagan and Jackson, 1994, 2000; 2010; 2011). • Physical branching models – simulated propagation of earthquake fault (Kagan and Knopoff, 1981; Kagan, 1982).

  6. The First Quantitative Model for Earthquake Forecast and Testing of its Effectiveness Information score: where L is the likelihood function, is the likelihood function for the Poisson process and N is events number. Predictive ratio or Probability gain:

  7. Branching Model for Dislocations (Kagan and Knopoff, JGR,1981; Kagan, GJRAS, 1982) • Predates use of self-exciting, ETAS models which also have branching structure. • A more complex model, exists on more fundamental level. • Continuum-state critical branching random walk in T x R^3 x SO(3). • Many unresolved claims, mathematical issues: is the synthetic earthquake set scale-invariant?

  8. Simulated source-time functions and seismograms for shallow earthquake sources. The upper trace is a synthetic source-time function. The middle plot is a theoretical seismogram, and the lower trace is a convolution of the derivative of source-time function with the theoretical seismogram. Kagan, Y. Y., and Knopoff, L., 1981. Stochastic synthesis of earthquake catalogs, J. Geophys. Res., 86, 2853-2862.

  9. Kagan and Knopoff, Science, 236, 1563-1567, 1987.

  10. Kagan, Y. Y., and Knopoff, L., 1987. Statistical short-term earthquake prediction, Science, 236, 1563-1567.

  11. Kagan, Y. Y., and D. D. Jackson, 1994. Long-term probabilistic forecasting of earthquakes, J. Geophys. Res., 99, 13,685-13,700.

  12. Kagan, Y. Y., and D. D. Jackson, 1995. New seismic gap hypothesis: Five years after, J. Geophys. Res., 100, 3943-3959. N test (events number) L test (events location likelihood) R test (likelihood comparison of models)

  13. Kagan, Y. Y., and D. D. Jackson, 2000. Probabilistic forecasting of earthquakes, (Leon Knopoff's Festschrift), Geophys. J. Int., 143, 438-453.

  14. Kagan, Y. Y., and D. D. Jackson, 2012. Whole Earth high-resolution earthquake forecasts, submitted to GJI 2011/12/16, GJI-11-0804

  15. Earthquake Forecast: Conclusions An earthquake forecast program quantitatively predicts both long- and short-term earthquake probabilities. The program is numerically and rigorously testable both retrospectively and prospectively as done by CSEP worldwide, as well as in California, Italy, Japan, New Zealand, etc. It is ready to be implemented as a technological solution for earthquake hazard forecasting and early warning.

  16. END Thank you

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