Abstract We consider three issues related to the 2011 Tohoku mega-earthquake:

1. TOHOKU EARTHQUAKE: A SURPRISE?Yan Y. Kagan and David D. JacksonDepartment of Earth and Space Sciences, University of California Los Angeles AbstractWe consider three issues related to the 2011 Tohoku mega-earthquake: (1) Why was the magnitude limit for the Tohoku region so badly underestimated, and how can we estimate realistic limits for subduction zones in general? (2) How frequently can such large events occur off Tohoku? (3) Could short-term forecasts have offered effective guidance for emergency preparation? Two methods can be applied to estimate the maximum earthquake size in any region: statistical analysis of available earthquake records, and the moment conservation principle -- how earthquakes release tectonic deformation. We have developed both methods since 1991. For subduction zones, the seismic record is usually insufficient, and failed badly for Tohoku, because the largest earthquakes are so rare. However, the moment conservation principle yields consistent estimates for all subduction zones. Various measurements imply maximum moment magnitudes of the order 9.0--9.7. Comparison of inter-earthquake secular strain accumulation and its release by coseismic slip implies a similar maximum earthquake size estimate. Since 1977 we have developed statistical short- and long-term earthquake forecasts (earthquake rate per unit area, time, and magnitude). Beginning in 1999 we have made such forecasts for the northwest Pacific, including Japan, based on the GCMT catalog. We have posted them on the web and included expected focal mechanisms as well. Long-term forecasts indicate that the average frequency for magnitude 9 earthquakes in the Tohoku area is about 1/400 years. This rate is consistent with that of moderate earthquakes recorded in the GCMT catalog. We have archived several forecasts made before and after the Tohoku earthquake. As expected, the Tohoku mega-earthquake changed the forecasted long-term rate by just a few percent. However, the magnitude 7.5 foreshock increased the short term rate to more than 100 times the long-term rate, and the magnitude 9 event increased it briefly to more than 1000 times the long-term rate. These results could well justify development of an operational earthquake forecasting plan. URL: http://eq.ess.ucla.edu/~kagan/tohoku_index.html • References • 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), • Ekstrom, G., 2007. Global seismicity: results from systematic waveform analyses, 1976-2005, in Treatise on Geophysics, 4(4.16), ed. H. Kanamori, pp. 473-481, Elsevier, Amsterdam. • Engdahl, E.R. & Villasenor, A., 2002. Global seismicity: 1900-1999, in IASPEI Handbook of Earthquake and Engineering Seismology, W. H. K. Lee, H. Kanamori et al., Eds., part A, pp.665-690. • Flinn, E. A., E. R. Engdahl, and A. R. Hill, 1974. Seismic and • geographical regionalization, Bull. Seismol. Soc. Amer., 64, 771-992. • Jackson, D. D., and Y. Y. Kagan, 2011. Characteristic earthquakes and seismic gaps, In Encyclopedia of Solid Earth Geophysics, Gupta, H. K. (Ed.), Springer, pp. 37-40, DOI 10.1007/978-90-481-8702-7. • Jordan, T. H., & L. M. Jones, 2010. Operational earthquake forecasting: some thoughts on why and how, SRL, 81(4), 571-574. • Kagan, Y. Y., 1997. Seismic moment-frequency relation for shallow • earthquakes: Regional comparison, J. Geophys. Res., 102, 2835-2852. • Kagan, Y. Y., and D. D. Jackson (2000), Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438-453. • McCaffrey, R., 2008. Global frequency of magnitude 9 earthquakes, • Geology, 36(3), 263-266. • Ozawa, S., et al., 2011. Coseismic and postseismic slip of the 2011 magnitude-9 Tohoku-Oki earthquake, Nature, 475, 373-376. • Ruff, L., and H. Kanamori, 1980. Seismicity and the subduction process, Phys. Earth Planet. Inter., 23, 240-252. • Stein, S., and E. A. Okal, 2011. The size of the 2011 Tohoku earthquake need not have been a surprise, Eos Trans. AGU, 92(27). • Zhuang, J., 2011. Next-day earthquake forecasts for the Japan region • generated by the ETAS model, Earth Planets Space, 63, 207-216. Figs. 4-5. Corner moment magnitude M_c distribution in Flinn-Engdahl subduction zones, GCMT catalog (1977-1995/6/30 and 1977-2010, respectively). Figs. 6. Centennial catalog (1900-1976). Region's M_c and +/-1.96 standard deviations are shown, the black line -- average <M_c> for all subduction zones. Red circles show earthquakes with historical maximum magnitude M_x which occurred in the regions during the catalog time interval. The red line -- average <M_x> for all subduction zones. Magenta diamond shows the Tohoku earthquake magnitude. 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. Earthquake forecast rates around the epicenter of the M7.5 foreshock. Long-term rates do not change significantly even after an occurrence of the M9.1 mainshock. Forecasted focal mechanisms are also essentially the same. The ratio of the short- to long-term rates (the last column) rises sharply both after the foreshock and after the mainshock. Flinn-Engdahl Seismic Regions Why select them? Regions were defined before GCMT catalog started (no bias), and easier to replicate our results. Fig. 8. Long-term forecast rate for north-west NW Pacific calculated March 8, 2011, before M7.5 Tohoku foreshock. Fig. 9. Long-term forecast rate for NW Pacific calculated March 17, 2011, after Tohoku M9.1 mainshock. Little change compared to Fig. 8. Fig. 7. Ratio of seismic to tectonic rate in Flinn-Engdahl subduction zones for GCMT catalog 1977-1995/6/30 (blue) and 1977-2010 (red). Vertical lines show average ratio for all regions the black line -- ratio of 1.0. Figs. 2, 3.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 Fig, 2 (1977-1995/6/30) <beta>=0.633 and <beta>= 0.654 in Fig. 3 (1977-2010) for all subduction zones. GCMT catalog of shallow earthquakes 1976-2005 Fig. 1.Number of earthquakes in the Flinn-Engdahl zone 19 (Japan-Kamchatka) with moment magnitude (M) for the shallow earthquakes in the GCMT catalog during 1977--2010. Magnitude threshold M=5.8, the total number of events 425. The unrestricted Gutenberg-Richter law is shown by dotted line. Dashed lines show two tapered G-R distributions: the G-R law restricted at large magnitudes by an exponential taper with the corner magnitude. One corner magnitude Ms=8.7 is evaluated by the maximum likelihood method using earthquake statistical record (with no upper limit), another estimate Mm=9.4 is based on the moment conservation. • Conclusions • The maximum earthquake size offshore Japan should not be a surprise: the moment conservation principle as well as a comparison of inter-earthquake secular strain accumulation and its release by coseismic slip suggest the maximum magnitude of 9.0--9.7. • The recurrence time of these earthquakes in the Tohoku area is of the order of 400 years. • The short-term earthquake forecasts produced since 1999 for the western Pacific area can in principle be used for the development of an operational earthquake forecasting plan.