How can the maximum strength of aftershocks after a major earthquake be calculated?

“Aftershocks differ from other earthquakes only in that we expect them. Unlike most earthquakes, aftershocks occur within predictable bounds of space, time, and magnitude. They are most common immediately after the mainshock and decay in time with approximately the reciprocal of time since the mainshock [Omori’s law, (Utsu, 1961)]. The magnitudes follow a Gutenberg-Richter relation, with the number of aftershocks proportional to ten to the power of the magnitude times a negative constant b. b is close to one so each unit decrease in magnitude leads to an order of magnitude decrease in number [Gutenberg and Richter, 1954]. This leads to a distribution of the largest aftershock that peaks at approximately one unit of magnitude below the mainshock (sometimes referred to as Bath’s law [Richter, 1958]).

The above properties of aftershock sequences allow for time-dependent prediction of aftershock probabilities [Reasenberg and Jones, 1989]. ”

Source

“This leads to a distribution of the largest aftershock that peaks at approximately one unit of magnitude below the mainshock.”

If I remember the math of the Richter scale correctly, one unit of magnitude below 9.0 is 8.0, and an 8.0 quake is 10% as strong as a 9.0
The units of magnitude (..7.0, 8.0, 9.0) are powers of 10, so that a 9.0 is 10 times as strong as an 8.0.

In 1994 we had a 6.7 quake and the strongest aftershock was 5.1.
That’s a logarithmic difference of 1.6, which means that the 6.7 quake was about 40 times as strong as the 5.1, i.e. the 5.1 was 2.5% as strong as the 6.7.

The truth is they can’t. You hear “experts” assure us that this and that can never happen, when in fact all they know is what characteristically has happened since seismographs were widely deployed around the Earth to record seismic events. The first instruments capable of accurately recording not just the occurrence of an earthquake but its intensity were developed in Japan between 1880 and 1895 by John Milne, James Alfred Ewing and Thomas Gray.

High accuracy deployment of instruments all around the world did not happen till after WWII. So we know quite accurately what has happened during the last 66 years and have a sketchy picture of what has happened for a little over 100 years. We have no idea what the 1,000 or 10,000 year earthquake might be like, or when the next one is likely due to strike. We know what is typical over the last 60 or 70 years in aftershocks, but that doesn’t mean nature is incapable of varying the formula.

So when spokespersons for some industry like nuclear power tell you that they have taken every seismic possibility into account, they are spouting nonsense to bolster their employer’s profits. Scientifically, there is no justification for such confidence. Their claims have little more validity than what a fortune teller might say about future earthquakes.

Thanks @marinelife !

Well an 8.0 would be devastating right now in Japan @Brian1946 – which means so far we’ve been lucky.

66 years do provide a lot of statistical data, @ETpro so despite the fact that accurate predictions seem impossible coming up with good quality likelihoods should be possible.

The Pasadena article points out the following:

“Aftershocks will obviously affect smaller regions than the mainshock, but, because of variations in location and radiation pattern and the cumulative nature of building damage, aftershocks can potentially be more damaging in some locations than their mainshock.”

What would more damaging mean for Fukushima? I guess the reactor cores would still be safe even if a 7.5 or 8.0 aftershock would occur within the next few days. But it might undo most of the repair efforts such as grid electricity restoration, cooling pump operation and so forth.

We are not out of the woods yet.