tohoku earthquake: a surprise?
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Tohoku Earthquake: A Surprise?
by Yan Y. Kagan and David D. Jackson
Abstract We consider three questions related to the 2011 Tohoku mega-earthquake:(1) Why was the event size so grossly underestimated by Japans national hazard map?(2) How should we evaluate the chances of giant earthquakes in subduction zones?(3) What is the repeat time for magnitude 9 earthquakes off the Tohoku coast? Themaximum earthquake size is often guessed from the available history of earthquakes, amethod known for its significant downward bias. We show that historical magnitudessystematically underestimate this maximum size of future events, but the discrepancyshrinks with time. There are two quantitative methods for estimating the corner mag-nitude in any region: a statistical analysis of the available earthquake record and themoment conservation principle. However, for individual zones the statistical method isusually ineffective in estimating the maximum magnitude; only the lower limit can beevaluated. The moment conservation technique, which we prefer, matches the tectonicdeformation rate to that predicted by earthquakes with a truncated or tapered magni-tudefrequency distribution. For subduction zones, the seismic or historical record isinsufficient to constrain either the maximum or corner magnitude. However, the mo-ment conservation principle yields consistent estimates: for all the subduction zonesthe corner magnitude is of the order 9.09.7. Moreover, moment conservation indi-cates that variations in estimated corner magnitude among subduction zones are notstatistically significant. Another moment conservation method, applied at a point ona major fault or plate boundary, also suggests that magnitude 9 events are requiredto explain observed displacement rates at least for the Tohoku area. The global rate ofmagnitude 9 earthquakes in subduction zones, predicted from statistical analysis ofseismicity as well as from moment conservation, is about five per century; fiveactually happened.
The magnitude 9.1 Tohoku, Japan, earthquake of11 March 2011 and the ensuing tsunami near the east coastof Honshu caused nearly 20,000 deaths and more than300 billion dollars in damage, ranking as one of the worstnatural disasters ever recorded (Geller, 2011; Hayes et al.,2011; Simons et al., 2011; Stein et al., 2011). The great dif-ference between the expected and observed earthquake mag-nitudes contributed to this enormous damage. The estimatedmaximum magnitude for the Tohoku area (around 7.7) wasproposed in the official hazard map (Headquarters for Earth-quake Research Promotion, 2005; Simons et al., 2011).
Several other estimates of the maximum size earthquakein the Tohoku area had been published before 2011. Ruff andKanamori (1980, fig. A1) suggested, basing their analysison historical data, age of subducting plate, and plate-ratesystematics, that the maximum magnitude is 8.28.35. Wes-nousky et al. (1984; their table 1, fig. 8) applied the charac-teristic earthquake hypothesis to estimate the maximumearthquake size and expected occurrence time for theseevents in three zones approximately covering the Tohoku
earthquake rupture area. Nishenko (1991, fig. 23 andpp. 234235) defines the magnitude of characteristic earth-quakes in northeast Japan, zones J4J6 as 7.17.7. However,he does mention anm 8:1 earthquake in 1611. Minoura et al.(2001) suggest that the 869 Jogan earthquake occurred on afault 240 85 km and was m 8:3. A similar estimate of theJogan earthquake magnitude is proposed by Sugawara et al.(2012). On the basis of the historical and instrumental cata-log analysis, Grunewald and Stein (2006) suggest the maxi-mum magnitude m 8:4 for the Tokyo area. Koravos et al.(2006) provide an estimate 7 < mmax < 8, based on histori-cal earthquakes since 599 A.D., again mentioning a fewearthquakes with magnitude slightly larger. Annaka et al.(2007) suggest mmax 8:5 based on historical earthquakessince 1611. Rikitake and Aida (1988; their table 1, fig. 5)did not expect the Tohoku area tsunami exceeding 7 metersand defined the maximum magnitude for zones IIIV to bewithin 7.47.9. The Evaluation of Major Subduction-zoneEarthquake(s) 2008 PDF file at the website (see Data andResources) defines probabilities of major earthquakes in
Bulletin of the Seismological Society of America, Vol. 103, No. 2B, pp. 11811194, May 2013, doi: 10.1785/0120120110
subduction zones. For the northeast part of Honshu Island,the maximum magnitudes are in the range of 6.88.2. Nanjoet al. (2011, p. 159) suggest that one should expect magni-tudes up to about 8 or larger for [Japan] offshore events.These opinions of the Japanese and international researchersconfirm that the maximum earthquake size in the Tohokuarea was dramatically underestimated before 11 March 2011.
Several quantitative estimates of the maximum possibleearthquakes in the subduction zones had been published be-fore the Tohoku event (Kagan, 1997; Kagan and Jackson,2000; Bird and Kagan, 2004; McCaffrey, 2007, 2008; Kaganet al., 2010). In these publications, the upper magnitudeparameter was determined to be within a wide rangefrom 8.5 to 9.6.
Two quantitative methods have been deployed to esti-mate the upper magnitude limit: a statistical determinationof the magnitudemoment-frequency parameters from earth-quake data alone, and a moment conservation principle inwhich the total moment rate is estimated from geologic orgeodetic deformation rates (Kagan, 1997).
The distinction between maximum and corner magnitudesrefers to different approaches in modeling the magnitudefrequency relationship for large earthquakes. In one approach,the classical GutenbergRichter magnitude distribution ismodified by truncating it at an upper limit called the maxi-mummagnitude. In another approach, an exponential taper isapplied to the moment distribution derived from the classicalmagnitude distribution. For the tapered GutenbergRichter(TGR) distribution, the corner moment is the value at whichthe modeled cumulative rate is reduced to 1=e of the classicalrate, and the corner magnitude is that which correspondsto the corner moment. In either approach, the rate of earth-quakes of any magnitude and the total seismic moment ratecan be computed from three observable parameters: the rateof earthquakes at the lower magnitude threshold, the b-valueor asymptotic slope of the magnitude distribution, and themaximum or corner magnitude. Conversely, the maximumor corner magnitude may be determined if the threshold rate,b-value, and total moment rate are known.
We generally shun the use of maximum magnitude be-cause there is no scientific evidence that it really represents amaximum possible magnitude, although it is frequently in-terpreted that way. Where the two approaches lead to similarconclusions, we will generalize the discussion by referring tothe upper magnitude parameter.
In the following text we use the term mmax to signifythe upper limit of the magnitude variable in a likelihoodmap or the limit of integration in an equation to compute atheoretical tectonic moment arising from earthquakes. As wewill see next, in different approximations of earthquake sizedistribution, mmax may have various forms, though theirestimated numerical values are usually close. We do not treatmmax as a firm limit, but we use it as a convenient generalreference because many other researchers do so.
The statistical estimate of the maximum magnitude forglobal earthquakes, including subduction zones and other
tectonic regions, yielded the values mmax 8:3 (Kagan andJackson, 2000). The moment conservation provided an esti-mate for subduction zones mmax 8:5 8:7 0:3 (Kagan,1997, 2002b). Moreover, the maximum earthquake size wasshown to be indistinguishable, at least statistically, for all thesubduction zones studied. Applying a combined statisticalestimate and moment conservation principle, Bird and Kagan(2004) estimated the corner magnitude to be about 9.6. Aswe explain next, the difference between the previously pre-sented estimates (8.6 versus 9.6) is caused mainly by variousassumptions about the tectonic motion parameters. Thesemmax determinations, combined with the observation of verylarge (m 9:0) events in the other subduction zones (McCaf-frey, 2007, 2008; Stein and Okal, 2007, 2011), should havewarned of such a possible earthquake in any major subduc-tion zone, including the Sumatra and Tohoku areas.
In the Evaluation of Earthquake Size Distribution sectionwe consider two statistical distributions for the earthquakescalar seismic moment and statistical methods for evaluatingtheir parameters. The Seismic Moment Conservation Princi-ple section discusses the seismic moment conservation prin-ciple and its implementation for determining the uppermagnitude parameter. We then demonstrate how these tech-niques for size evaluation work in subduction zones, showingthat m 9:09:7 earthquakes can be expected in all majorzones, including the Tohoku area. For the Tohoku area, theapproximate recurrence interval for m 9:0 earthquakes ison the order of 350 years (Kagan and Jackson, 2012; seethe Discussion section in this paper). By the term recurrenceinterval we do not imply that large earthquakes occur cycli-cally or quasi-periodically; contrary to that, we presentedevidence that all earthquakes, including the large ones, areclustered in time and space (Kagan and Jackson, 1999; seethe Discussion section in this paper).
Evaluation of Earthquake Size Distributionfor Subduction Zones
We studied earthquake distributions and clustering forthe global CMT catalog of moment tensor inversions com-piled by the GCMT group (Ekstrm et al., 2005; Ekstrm,2007; Nettles et al., 2011). The present catalog containsmore than 33,000 earthquake entries for the period 1 January1977 to 31 December 2010. The event size is character