THE GUTENBERG-RICHTER OR CHARACTERISTIC EARTHQUAKE DISTRIBUTION, WHICH IS IT? (Wesnousky, 1994) The characteristic earthquake hypothesis (CH later) went through several stages of development. Initially it was proposed by Schwartz and Coppersmith (1984). This hypothesis, in its most basic form, assumes that faults are divided into segments, and that sequences of "characteristic" earthquakes, mostly contained within each segment, are responsible for most of the geologically observed slip there. The characteristic earthquakes are believed to be large enough to dominate the seismic moment release and substantially reduce the average stress. Two tests can be carried out to validate a model of earthquake occurrence, such as the CH: (1) Retrospective test -- we can test whether the model explains (a) available earthquake size distribution, and (b) seismic moment release. (2) Prospective (forward) test -- we explore whether the model correctly predicts the occurrence of future earthquakes and their distribution. It became obvious soon after the model was proposed that the CH failed both tests. Earthquake size distribution, determined on the basis of fault maps, cannot be fitted to historical and instrumental catalog data in California (Jackson et al., 1995). Nishenko (1989, 1991) made a testable prediction for the circum-Pacific seismic belt, using the CH model as the major component. Kagan and Jackson (1995) found that earthquakes after 1989 did not support Nishenko's gap model. Rong et al. (2003) concurred. About 10 years ago the old CH model was replaced by a new one in which the rupture of the neighboring fault segments (cascading) was allowed, and various adjustments for the magnitude distribution on a fault segment were proposed. The Working Group (WG02) report (2003) on earthquakes probabilities in the San Francisco Bay region discusses these changes. With all these adjustments, which introduce many additional degrees of freedom into the model, it is relatively easy to make the model predictions to agree with retrospective assessment. Thus, the only available test of the new CH model is the forward prediction (Jordan, 2006). However, this test may be difficult to perform and evaluate. In effect, the new CH model shifts almost all of the seismic moment release in seismically active fault zones with the maximum magnitude close to the estimate obtained using the Gutenberg-Richter (G-R) model (Bird and Kagan, 2004). The new CH hypothesis may differ from the G-R model only in a few less active fault segments. In these segments, the CH would predict maximum earthquakes which are significantly different (smaller) from the G-R predictions. Thus, to falsify the CH model one would need to show that the size distribution for future earthquakes in these zones is better described by the G-R law than by the CH model. In principle, we can make a rough estimate of the time necessary to test the new CH model. Assuming the Poisson occurrence of earthquakes, it is possible to simulate an earthquake occurrence according to both hypotheses (CH and G-R). Then we can use one of the standard statistical tests to estimate the "Forecast Time" necessary to reject one of the models with 95% confidence in 95% of the tests (Rong et al., 2003). If the "Forecast Time" exceeds 5-10 years, the model should be considered as practically non-falsifiable and consequently untestable. The new CH model is clearly untestable in the San Francisco Bay region (Stark and Freedman, 2003). It is unlikely to be testable, as proposed above, in California. The only testing possibility is to produce a forecast for a large seismic area similar to that proposed by Nishenko (1989, 1991). Nishenko's model was markedly different from the G-R law in many zones, so the statistically significant differences accumulated even in a 5-year interval. However, there is no clear evidence that the new CH model would be significantly different from the G-R distribution. If the preliminary simulation tests could show that the new CH model is not falsifiable in a reasonable time period, i.e., in practical terms its predictions are indistinguishable from the G-R law, then the only distinctive feature left in the CH model is its name. However, if the predictions are similar, the new CH model has a serious drawback because of its complexity. According to the Occam razor rule it should be rejected in favor of a simpler G-R hypothesis. REFERENCES: Bird, P., and 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. http://scec.ess.ucla.edu/~ykagan/plates_index.html Jackson, D. D., Aki, K., Cornell, C. A., Dieterich, J. H., Henyey, T. L., Mahdyiar, M., Schwartz, D., Ward, S. N., (Working Group on California Earthquake Probabilities), 1995. Seismic hazards in southern California: Probable earthquakes, 1994-2024, Bull. Seism. Soc. Am., 85, 379-439. Jordan, T. H., 2006. Earthquake predictability, brick by brick, Seismol. Res. Lett., 77(1), 3-6. Kagan, Y. Y., and D. D. Jackson, 1995. New seismic gap hypothesis: Five years after, J. Geophys. Res., 100, 3943-3959. http://scec.ess.ucla.edu/~ykagan/nish_index.html Nishenko, S. P., 1989. Circum-Pacific earthquake potential: 1989-1999, USGS, Open-file report 89-86, 126 pp. Nishenko, S. P., 1991. Circum-Pacific seismic potential -- 1989-1999, Pure Appl. Geophys. (pageoph), 135, 169-259. 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, doi:10.1029/2002JB002334. http://scec.ess.ucla.edu/~ykagan/gap_index.html Schwartz, D. P., and K. J. Coppersmith, 1984. Fault behavior and characteristic earthquakes: Examples from Wasatch and San Andreas fault zones, J. Geophys. Res., 89, 5681-5698. Stark, P. B., and Freedman, D. A., 2003. What is the chance of an earthquake?, Chapter 5.3 in "EARTHQUAKE SCIENCE AND SEISMIC RISK REDUCTION", eds. F. Mulargia and R. J. Geller, pp. 201-213, Kluwer, Dordrecht; preliminary draft of the document is available at http://oz.berkeley.edu/~stark/Preprints/611.pdf . Wesnousky, S. G., 1994. The Gutenberg-Richter or characteristic earthquake distribution, Which is it?, Bull. Seismol. Soc. Amer., 84, 1940-1959. Working Group on California Earthquake Probabilities (WG02), 2003. Earthquakes probabilities in the San Francisco Bay region: 2002 to 2031, USGS, Open-file Rept. 03-214; http://pubs.usgs.gov/of/2003/of03-214 .