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Characteristic earthquake model, 1884 – 2011, R.I.P. Y.Y. Kagan, D.D. Jackson, and R.J. Geller ESS/UCLA and University of Tokyo Abstract Unfortunately, working scientists sometimes reflexively continue to use “buzz phrases” grounded in once prevalent paradigms that have been subsequently refuted. This can impede both earthquake research and hazard mitigation. Well-worn seismological buzz phrases include “earthquake cycle,” “seismic cycle,” “seismic gap,” and “characteristic earthquake,”. They all assume that there are sequences of earthquakes that are nearly identical except for the times of their occurrence. If so, the complex process of earthquake occurrence could be reduced to a description of one “characteristic” earthquake plus the times of the others in the sequence. A common additional assumption is that characteristic earthquakes dominate the displacement on fault or plate boundary “segments.” The “seismic gap” (or the effectively equivalent “seismic cycle”) model depends entirely on the “characteristic” assumption, with the added assumption that characteristic earthquakes are quasi-periodic. However, since the 1990s numerous statistical tests have failed to support characteristic earthquake and seismic gap models, and the 2004 Sumatra earthquake and 2011 Tohoku earthquake both ripped through several supposed segment boundaries. Earthquake scientists should scrap ideas that have been rejected by objective testing or are too vague to be testable. URL: http://eq.ess.ucla.edu/~kagan/kjg_srl_index.html Recommendations: Since the 1990s numerous statistical tests showed that characteristic earthquake and seismic gap hypotheses perform worse than the Poisson (random) model. Buzz phrases used by many in seismological community include “earthquake cycle,” “seismic cycle,” “seismic gap,” and “characteristic earthquake.” Their baggage of implicit assumptions often arrives undeclared and goes unquestioned. What can be done to overcome this intellectual inertia? First, reviewers, editors, and funding agency officials must recognize that there is a problem. The buzzwords discussed above, like the words ‘forecast’ and ‘prediction,’ have been used quite loosely. Terms in publications and proposals should be defined clearly, evidence for assumed segmentation and characteristic behavior should be critically examined, dependence on and rules for selected data should be made explicit, and full prospective tests for unproven assumptions should be described. Second, those responsible for hazard estimates should emphasize models that deal with the whole spectrum of earthquake occurrence, not characteristic and other models based on small subsets of arbitrarily selected data. Statistical studies based on all earthquakes within given time, space, and size limits–not just those which fit the investigator’s preconceptions—are advancing rapidly and should become our new standard. All of us in earthquake science must wake up to the problems caused by relying on selected data. Arbitrarily chosen datasets are fine for formulating hypotheses, but not for validating them. Third, characteristic advocates and statistical hypothesis testers should collaborate to develop appropriate tests. Collaboratory for the Study of Earthquake Predictability (CSEP) centers are prospectively testing hundreds of regional and global earthquake models. True believers should now either throw in the towel or reformulate the characteristic model for another explicit prospective test. A problem for such testing is that modern models often address limited regions in which definitive earthquakes may not occur for centuries. In summary, the time for case studies, anecdotes, speculation, and band-aids for failed models has passed. We must take a rigorous look at characteristic earthquake models and their implicit assumptions. Let’s begin by scrapping merely long-standing ideas that have been rejected by objective testing or are too vague to be testable. References Bakun, W. H., et al. (2005). Implications for prediction and hazard assessment from the 2004 Parkfield earthquake. Nature 437, 969-974. Bird, P., & Y. Y. Kagan, 2004. Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, and coupling in seven tectonic settings, Bull. Seismol. Soc. Amer., 94(6), 2380-2399, (plus electronic supplement), Fedotov, S. A. (1965). Regularities of the distribution of strong earthquakes in Kamchatka, the Kurile Islands and northeastern Japan (in Russian). Tr. Inst. Fiz. Zemli Akad. Nauk SSSR 36(203), 66-93. Gilbert, G. K. (1884). A theory of the earthquakes of the Great Basin, with a practical application. American Journal of Science, ser. 3 27(157), 49-54. Jackson, D. D., and Y. Y. Kagan, 2006. The 2004 Parkfield earthquake, the 1985 prediction, and characteristic earthquakes: lessons for the future, Bull. Seismol. Soc. Amer., 96(4B), S397-S409. Kagan, Y. Y., and D. D. Jackson, 1991. Seismic gap hypothesis: Ten years after, J. Geophys. Res., 96, 21,419-21,431. Kagan, Y. Y., and D. D. Jackson, 1995. New seismic gap hypothesis: Five years after, J. Geophys. Res., 100, 3943-3959. Reid, H. F. (1911). The elastic-rebound theory of earthquakes. Univ. Calif. Publ. Bull. Dept. Geol. Sci. 6, 413-444. Rong, Y.-F., D. D. Jackson and Y. Y. Kagan, 2003. Seismic gaps and earthquakes, J. Geophys. Res., 108(B10), 2471, ESE-6, pp. 1-14. Flinn-Engdahl Seismic Regions Why select them? Regions were defined before GCMT catalog started (no bias), and easier to replicate our results.. Corner moment magnitude M_c distribution in Flinn-Engdahl subduction zones, GCMT catalog (1977-2010). Region's M_c and +/-1.96 standard deviations are shown, the black line -- average for all subduction zones, dashed lines display 95% limits for all zones. Green and magenta circles show earthquakes with historical maximum magnitude M_x which occurred in the regions during the catalog time interval for periods 1977-95 and 1977-2010, respectively. The green and magenta lines -- average for all subduction zones. Red squares show mega-earthquakes which occur during recent years. No statistically significant difference is found between different subduction zones in beta value and corner magnitude. Historical magnitudes underestimate corner magnitude but discrepancy shrinks with time. Figure 1. Magnitude–frequency relation for the Parkfield earthquakes (Jackson and Kagan, 2006). Solid line is the G–R approximation. Dotted and dashed lines are 95% confidence limits; former are conditioned by the total number of earthquakes observed, and latter are estimates based on the Poisson assumption for earthquake occurrence. (a) Time period 1967–2003 (before the 2004 Parkfield earthquake); (b) time period 1967–2005 (including time after the 2004 Parkfield earthquake). Figure 3. Distribution of PDE magnitude differences for two time periods: 1 July 1968–1 January 1989 and 1 January 1989–1 January 2003, calculated relative to the characteristic magnitude (Nishenko, 1991). Circles, 1 July 1968–1 January 1989; crosses, 1 January 1989–1 January 2003; dash-dot line, the G-R relation; dashed line, the predicted distribution of characteristic magnitudes (Jackson and Kagan, 2006). Smoothed seismicity for Northwest Pacific region. Nishenko [1989a] zones are shown, as well as four earthquakes with Mw ~ 7.0 (black circles) which occurred in the zones during January 1, 1989 - January 1, 1994. None of these events qualify as characteristic or generic earthquakes. Three additional earthquakes Mw ~ 7.0 which occur during October-December 1994 in zones KK-9 and J-3 are displayed as white circles (Kagan and Jackson, 1995). Cross-likelihood test for the new seismic gap and null hypotheses, using the characteristic magnitude as a threshold. Small dots show the scores for synthetic records generated using the gap probabilities, and small crosses of ‘‘plusses’’ show the scores for synthetic null- hypothesis records. The diagonal line shows the locus of points corresponding to the critical values for the PDE and the CMT catalogs. The probability of falsely rejecting the null hypothesis is large (>80% for the PDE catalog and >97% for the CMT catalog), and the probability of falsely rejecting the gap hypothesis is less than 1% for both catalogs (Rong et al., 2003). Seismicity map of the northern Pacific region for 1979-1988 All of the earthquake with M s > 7.0 are shown in the map: R indicates red zone (high seismic potential); O -- orange zone; G -- green zone (lowest seismic potential), see Kagan and Jackson (1991). Bird and Kagan, BSSA, 2004 Rong et al,, JGR, 2003 Parameter beta distribution in Flinn-Engdahl subduction zones. GCMT catalog is used. Average region's beta and +/-1.96 standard deviations are shown, the black line corresponds to the average in 1977-1995/6/30, =0.633 and = 0.654 in 1977-2010 for all subduction zones. From a scientific point of view there are two relevant points in this work: 1. Only falsifiable, testable hypotheses are accepted. 2. Results of their test are final, unless a new hypothesis is proposed and tested. In 1989 there was Nishenko's testable characteristic earthquake model. Its prospective test turned out to be clearly negative. Since no new testable hypothesis has been proposed and tested, this makes it the end of the story.

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