Y. Y. Kagan SEISMIC HAZARD AND PALEOSEISMIC INVESTIGATIONS 19-MAY-2007 In recent years earthquake faults have increasingly been studied by paleoseismic methods. The major impetus for such investigations is a hope that these results can be used to understand the long-term earthquake occurrence and by implication improve our estimates of the seismic hazard, i.e. the evaluation of the probability of major shaking at particular sites. Several difficulties can be identified: 1. Paleoseismic investigations have low time resolution, two or more events occurring closely in time are likely to be identified as one event. Measurements from instrumental earthquake catalogs indicate that short time intervals between large earthquakes are much more frequent than even the Poisson model would suggest (Kagan and Jackson, 1991; 1999, see also the update of their results at http://scec.ess.ucla.edu/~ykagan/pairs_index.html ). One could argue that the earthquakes studied by Kagan and Jackson are mostly thrust events in subduction zones, and that strike-slip earthquakes relevant to California seismic hazard analysis may display a different behavior. To provide an illustration, I created a table of M>=6.5 strike-slip earthquakes from the Harvard CMT catalog with centroids separated by less than 20 km (see the URL above). Several pairs, including two doublets at the Mendocino junction, off the California coast, are separated by very short time intervals. Even if these earthquakes did not produce a measurable displacement at the same fault site, their distance and magnitude suggest that their shaking area would significantly overlap. 2. Smaller earthquakes are not likely to rupture the Earth surface. Thus, some earthquakes which can cause significant damage, may not be part of the paleoseismic record (for example, the 1989 M7.1 Loma Prieta, California event, is unlikely to be identified by paleoseismic observations). These `missing' earthquakes make subsequent analysis problematic. 3. Similarly, earthquakes occurring close to a site, but not rupturing the fault would not be noticed. Since paleoseismic trenches are only a few tens of meters long, even earthquakes rupturing a close subsidiary fault may escape detection. 4. Lack of sediment deposits during particular periods may also inhibit observable rupture traces. 5. Generally, a major problem in the present paleoseismic investigations is lack of any discussion of accuracy and dependability of paleoseismic data. Such discussion would be of great importance since the results are used to formulate a public policy in earthquake hazard mitigation. Any analysis of data in a geophysical work must start with a discussion of accuracy of the input data, their systematic and random errors, and biases. Otherwise, the results of the analysis, even if sophisticated techniques were applied, would be meaningless. 6. I would suggest that statistical analysis of the paleoseismic data should take a different direction. The focus is presently on the earthquake recurrence interval and the coefficient of variation. Both of these variables strongly depend on small time interval statistics, where paleoseismic data are significantly deficient (see above). However, seismic hazard does not strongly depend on these variables. The probability of a large earthquake occurrence is usually evaluated for a fault site where a previous large event happened decades or centuries previously. By the present time all or most of the short-term clustering effects have already ended. Therefore, the main challenge in seismic hazard problem is to evaluate the long-term tail of the recurrence distribution. It would be interesting to see whether the tail behavior would be different, for instance, in slow vs fast deforming tectonic regions, such as the Eastern California Shear Zone vs the San-Andreas fault (see Biasi et al., 2002; Dawson et al., 2003; Rockwell et al. 2000; Weldon et al. 2004). On the other hand, if we need to estimate the probability of a major earthquake after a close event in time and space, the standard methods employed presently (Matthews et al., 2002; Working Group, 2003) would suggest a low probability. This prediction goes contrary to the behavior of strong earthquakes discussed above (see item 1). On a more intuitive level, the history of the 1811-12 New Madrid earthquakes as well as the 1992 Landers and the 1999 Hector Mine events imply that making such a prediction may be quite dangerous. 7. Finally, the seismic hazard problem can be handled by known statistical techniques such as the application of the inverse Gaussian distribution (Kagan and Knopoff, 1987; Matthews et al., 2002). This distribution can model both clustered and quasi-periodic earthquake occurrences. As I explained above (1), the former mode should be used in the hazard estimate. As Fig. 3b by Matthews et al. (2002) suggests, contrary to an almost universal belief by geoscientists, the hazard rate should decrease with time for the clustered earthquake occurrence (alpha>1). Such evaluations should be combined with estimates of the long-term earthquake occurrence rate based on the geodetic and plate-tectonic deformation rate (Bird and Kagan, 2004). REFERENCES: Biasi, G. P., R. J. Weldon, T. E. Fumal, and G. G. Seitz, 2002. Paleoseismic event dating and the conditional probability of large earthquakes on the southern San Andreas fault, California, Bull. Seismol. Soc. Amer., 92, 2761-2781. 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 (plus electronic supplement). Dawson, T. E., S. F. McGill, and T. K. Rockwell, 2003. Irregular recurrence of paleoearthquakes along the central Garlock fault near El Paso Peaks, California, J. Geophys. Res., 108(B7), 2356, doi:10.1029/2001JB001744. Kagan, Y. Y., and D. D. Jackson, 1991. Long-term earthquake clustering, Geophys. J. Int., 104, 117-133. Kagan, Y. Y. and D. D. Jackson, 1999. Worldwide doublets of large shallow earthquakes, Bull. Seismol. Soc. Amer., 89, 1147-1155. Kagan, Y. Y., and Knopoff, L., 1987. Random stress and earthquake statistics: Time dependence, Geophys. J. R. astr. Soc., 88, 723-731. Matthews, M. V., W. L. Ellsworth, and P. A. Reasenberg, 2002. A Brownian model for recurrent earthquakes, Bull. Seismol. Soc. Amer., 92, 2233-2250. Rockwell, T. K., Lindvall, S., Herzberg, M., Murbach, D., Dawson, T., and G. Berger, 2000. Paleoseismology of the Johnson Valley, Kickapoo, and Homestead Valley faults: clustering of earthquakes in the eastern California shear zone, Bull. Seismol. Soc. Amer., 90, 1200-1236. Weldon, R., K. Scharer, T. Fumal, and G. Biasi, 2004. Wrightwood and the earthquake cycle: what the long recurrence record tells us about how faults work, GSA Today, 14, 4-10, doi:10.1130/1052-5173(2004)014. Working Group on California Earthquake Probabilities (WGCEP), 2003. Earthquakes probabilities in the San Francisco Bay region: 2002 to 2031, USGS, Open-file Rept. 03-214.