How a 70% Chance of a M7 Earthquake in 4 Years was Calculated
Are you wondering how a group at the Tokyo University Earthquake Research Institute (ERI) calculated a 70% chance of a Magnitude 7 quake occurring in the Tokyo area within the next four years? If so, take a look at the above plot of historical Japanese earthquake data that compares the number of quakes per year to the total energy released by each quake.
First of all, ERI didn’t do this from scratch. They started with a potentially flawed government calculation and suggested a new value based on recent observations. This new value is 98% chance within 30 years, which translates to 70% in 4.
Now to the plot. let’s consider the filled symbols, which represent data spanning as much as the past 55 years, up to 2010. The frequency of earthquakes rapidly and predictably decreases with magnitude, meaning larger quakes happen much less often than smaller ones. The relationship between frequency and magnitude is shown by the dashed lines. One line doesn’t fit the entire dataset. Rather, the occurrence of quakes in excess of M4 decreases more rapidly with size (and therefore plot along a different line).
Next, let’s look at the open blue circles, which are about 6 months worth of data, from March 11 to August 1, 2011. As you can see, these data exhibit a similar slope but plot significantly higher than the pre-3/11 data. This indicates that higher-magnitude earthquakes have occurred more frequently since 3/11, a fact of which anyone living in eastern Japan is keenly aware. There appear to be too few occurrences of quakes larger than M4 to calculate a robust fit, (i.e., no corresponding dashed line) though it appears that the slope for the larger quakes is also similar to the pre-3/11 data.
Finally, we come to the new prediction. In the bottom right of the plot, the government’s official prediction of a M6.7 – 7.2 quake occurring in Tokyo is overlain as a yellow star and horizontal solid line. The folks at ERI simply recalculated this based on the equation for the extrapolated fit between earthquake frequency and magnitude since 3/11.
There you have it. That’s how they did it. But is it correct?
I’d argue that this analysis, while interesting, contains several important flaws.
- The new prediction is based on extrapolation from a perturbed state. That is, the frequency of earthquakes is currently elevated but likely to drop to normal over time.
- It is based on very few observations.
- It is based on extrapolation beyond the limits of the data.
- It appears to be based on an inappropriate equation (the M4 and smaller frequency/magnitude relationship).
- It does not account for uncertainty.
Most importantly, the correlation between frequency and magnitude breaks down for large quakes in the pre-Tohoku dataset, and if calculated, would be significantly lower for the M4 and greater quakes since 3/11. Could this increased uncertainty yield a result that is statistically indistinguishable from the government’s prediction? Maybe, but without the raw data, I can’t say for sure.
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Contributor Bio: Steve has been splitting time between the US and Japan for the past 10 years or so and is now a researcher at a Japanese university.
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