Tohoku earthquake: a surprise?

We consider three questions related to the 2011 Tohoku mega-earthquake: (1) Why was the event size so grossly under-estimated? (2) How should we evaluate the chances of giant earthquakes in subduction zones? and (3) What is the repeat time for magnitude 9 earthquakes off the Tohoku coast? The "maximum earthquake size" is often guessed from the available history of earthquakes, a method known for its significant downward bias. There are two quantitative methods for estimating the maximum magnitude in any region: a statistical analysis of the available earthquake record, and the moment conservation principle. However, for individual zones the statistical method is usually ineffective in estimating the maximum magnitude; only the lower limit can be evaluated. The moment conservation technique matches the tectonic deformation rate to that predicted by earthquakes. For subduction zones, the seismic or historical record is insufficient to constrain either the maximum or corner magnitude. However, the moment conservation principle yields consistent estimates: for all the subduction zones the maximum magnitude is of the order 9.0--9.7. Moreover, moment conservation indicates that variations in estimated maximum magnitude among subduction zones are not statistically significant. Another moment conservation method also suggests that magnitude 9 events are required to explain observed displacement rates. The global rate of magnitude 9 earthquakes in subduction zones, predicted from statistical analysis of seismicity as well as from moment conservation is about five per century -- five actually happened.