Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA , Tohoku earthquake: A surprise?

Outline of the Talk Maximum size estimates for subduction zones relevant for Tohoku (Japan) M9 earthquake: 1.Statistical method. 2.Moment-conservation method (tectonic versus seismic rates) -- 2a. Area-specific, calculations for zones. 2b. Site-specific, calculations for fault site slip. Long- and short-term seismicity rate forecasts in Tohoku region.

GCMT catalog of shallow earthquakes

Gutenberg-Richter (G-R) law For the last 20 years a paper has been published every 10 days which substantially analyses b-values. Maximum or corner magnitude/moment needs to be introduced to take into account finite size of tectonic plates and moment flux. If we consider seismic moment instead of magnitude then the statistical distribution becomes the Pareto (power-law) one. Several approximations incorporating maximum moment have been proposed: Pareto truncated at cumulative or probability density function, or Pareto combined at the distribution tail with exponent – again either cumulative distribution (tapered G-R, TGR), or applied to a density, a GAMMA distribution.

threshold magnitude 95%-confidence lower limit 95%-confidence lower limit not to be taken literally! (“a large number”) 95%-confidence upper limit

Review of results on spectral slope,  Although there are variations, none is significant with 95%-confidence. Kagan’s [1999] hypothesis of uniform  still stands.

Tohoku M9 earthquake and tsunami

Losses from Tohoku earthquake Close to 20,000 dead and more than $300 billions (perhaps close to one trillion – $10^12) economic losses.

Flinn-Engdahl seismic regions: Why select them? Regions were defined before GCMT catalog started (no selection bias), and it is easier to replicate our results (programs and tables available).

A log- likelihood map for the distribution of the scalar seismic moment of earthquakes in the Flinn- Engdahl zone #19 (Japan-- Kurile- Kamchatka)

DETERMINATION OF MAXIMUM (CORNER) MAGNITUDE: AREA-SPECIFIC MOMENT CONCERVATION PRINCIPLE Seismic moment rate depends on 3 variables -- 1.The number of earthquakes in a region (N), 2.The beta-value (b-value) of G-R relation, 3.The value of maximum (corner) magnitude. Tectonic moment rate depends on 3 variables Width of seismogenic zone (W – km), 2. Seismic efficiency coefficient ( %), 3. Value of shear modulus (30GPa -- 49GPa).

Kagan, Seismic moment-frequency relation for shallow earthquakes: Regional comparison, J. Geophys. Res., 102, (1997). Tectonic rate for /6/30 period is calculated by using parameters: W=30 km, mu=30 GPa, chi=1.0.

Tectonic rate for /12/31 period is calculated by using Bird & Kagan (2004) parameters: W=104 km, mu=49 GPa, chi=0.5.

Global number of M9 events

DETERMINATION OF MAXIMUM (CORNER) MAGNITUDE: SITE-SPECIFIC MOMENT CONCERVATION PRINCIPLE 1. General (area-specific) distribution of the earthquake size, for the simplicity of calculations we take it as the truncated Pareto distribution. 2. Site-specific moment distribution – large earthquakes have a bigger chance to intersect a site, hence the moment distribution is different from area-specific. 3. Geometric scaling of earthquake rupture. Length-width-slip are scale-invariant, proportional to the cube root of scalar moment. 4. Earthquake depth distribution is different for small versus large shocks: at least for strike-slip earthquakes large events would penetrate below the seismogenic layer. 5. Most of the small earthquakes do not reach the Earth surface and therefore do not contribute to the surface fault slip.

McCaffrey, R., Global frequency of magnitude 9 earthquakes, Geology, 36(3),

Hauksson & Shearer (2005) catalog: Depth distribution

Simons, M. et al., The 2011 magnitude 9.0 Tohoku- Oki earthquake: mosaicking the megathrust from seconds to centuries, Science, 332(6036),

Calculation of Mmax for fault slip

Calculation of Mmax for fault slip (cont.)

Geller, R. J., Shake-up time for Japanese seismology, Nature, 472(7344),

M>=10.0 earthquakes

M>=10.0 earthquakes (cont.)

END Thank you

We consider three issues related to the 2011 Tohoku mega-earthquake: (1) how to evaluate the earthquake maximum size in subduction zones and why the event size was so grossly under-estimated for the Tohoku-Oki area, (2) what is the repeat time for the largest earthquakes in this area, and (3) what are the possibilities of numerical short-term forecasts during the 2011 earthquake sequence in the Tohoku area. The maximum earthquake size is usually guessed basing on the available history of earthquakes, the method known for its significant downward bias. We make an estimate of this bias: historical magnitudes underestimate the maximum/corner magnitude but discrepancy shrinks with time. There are two quantitative methods which can be applied to estimate the maximum earthquake size in any region: a statistical analysis of the available earthquake record and the moment conservation principle. The latter technique studies how much of the tectonic deformation rate in released by earthquakes. Both of these methods have been developed by the authors since For the subduction zones, the seismic or historical record is not sufficient to provide a reliable statistical measure of the maximum earthquake. However, the moment conservation principle yields consistent estimates: for all the subduction zones the maximum moment magnitude is of the order , this is the value suggested by various measurements. Abstract

Abstract (cont.) Moreover, the latter method indicates that for all major subduction zones the maximum earthquake size is statistically indistinguishable. Another moment conservation method -- comparing the site-specific deformation rate and its release by earthquakes rupturing the site, also suggests that the maximum earthquake size should be of the order m9. Since 1977 we have developed statistical short- and long-term earthquake forecasts to predict the earthquake rate per area, time, and magnitude unit. For worldwide seismicity as well as for several seismically active regions these forecasts are posted on our web sites. We have carried out long- and short-term forecasts for Japan and the surrounding areas using the GCMT catalog starting in For forecasts based on the GCMT catalog, the expected earthquake focal mechanisms are also evaluated. Long-term forecasts indicate that the repeat time for m9 earthquake in the Tohoku area is of the order of 350 years: this estimate is confirmed by the seismicity levels recorded by the GCMT catalog. We have archived several forecasts made before and after the Tohoku earthquake, they are displayed in diagrams and tables in this paper. The long-term rate estimates indicate that, as expected, the forecasted rate changed only by a few percent after the Tohoku earthquake, whereas due to the foreshocks, the short-term rate increased by a factor of more than 100 before the mainshock event as compared to the long-term rate.

After the Tohoku mega-earthquake the rate increased by a factor of more than These results suggest that an operational earthquake forecasting strategy needs to be developed to take the increase of the short-term rates into account. Abstract (cont.)

Gutenberg-Richter law For the last 20 years a paper has been published every 10 days which substantially analyses b-values. Theoretical analysis of earthquake occurrence (Vere- Jones, 1976, 1977) suggests that, given its branching nature, the exponent β of earthquake size distribution should be identical to 1/2. The same values of power- law exponents are derived for percolation and self- organized criticality (SOC) processes in a high- dimensional space (Kagan, 1991, p. 132). The best measurements of beta-value yields 0.63 (Kagan, 2002; Bird and Kagan, 2004), i.e. about 25% higher than 0.5.

The maximum-likelihood method is used to determine the parameters of these tapered G-R distributions (and their uncertainties): An ideal case (both parameters determined) A typical case (corner magnitude unbounded from above)