Aftershocks: what follows a big earthquake

A large earthquake is rarely a single event. It is usually the opening of a sequence that can run for weeks, months or years, and the question people actually want answered in the hours afterwards is whether the worst has already happened. The honest answer is that it probably has, but not certainly - and seismologists can put a number on that.

What an aftershock is

Most large earthquakes are followed by additional earthquakes in the same area, and together these make up an aftershock sequence. The great majority are smaller than the earthquake that started the sequence - the mainshock - but smaller does not mean harmless. An aftershock can still be damaging or deadly, particularly when it strikes buildings that the mainshock has already weakened.

Sometimes the first quake was not the main one

A small fraction of earthquakes are followed by a larger one. When that happens, the labels change retroactively: the first earthquake is reclassified as a foreshock, and the later, larger event becomes the mainshock.

The 2011 Japan earthquake is the clearest example. A magnitude 7.3 struck two days before the magnitude 9.1. At the time it occurred, the 7.3 was the mainshock. It only became a foreshock when the far larger earthquake followed.

How the rate behaves over time

Aftershock rates generally decrease with time. The decay is not smooth, though: the rate can temporarily increase again after a significant aftershock, because a large aftershock triggers aftershocks of its own.

The USGS models this with a statistical relationship developed by Reasenberg and Jones, which expresses the rate of aftershocks above a given magnitude in terms of four parameters: the productivity of the region, how aftershock rate scales with mainshock magnitude, how quickly the rate decays with time, and the timescale of the earliest part of the sequence before decay sets in. Page and colleagues extended the method worldwide by grouping tectonically similar regions and fitting parameters for each, and Hardebeck and colleagues updated the California parameters with more modern data.

What an official forecast actually says

A USGS aftershock forecast is a set of probabilities and expected counts, not a prediction of specific earthquakes. For a given mainshock it gives:

• the expected number of smaller aftershocks likely to be felt, at magnitude 3 and above and magnitude 4 and above;
• the probability of aftershocks large enough to potentially do damage, at magnitude 5 and above;
• the probability of future moderate to large earthquakes, at magnitude 6 and above and magnitude 7 and above.

Each of these is given over four time windows - a day, a week, a month and a year - and the forecast is updated as the sequence progresses, so that it reflects the behaviour of that specific sequence rather than just the regional average.

Forecasts are not produced for every earthquake. The USGS posts them for magnitude 4 and above in the contiguous United States and magnitude 5 and above in other US states and territories, plus some smaller earthquakes of particular public interest, such as those in densely populated areas. They are usually not computed for earthquakes that are themselves aftershocks of a prior larger event, or for earthquakes that are part of known volcanic activity. Significant international earthquakes requiring a humanitarian response are sometimes included.

Where the model is weak

The model assumes every aftershock was triggered by the mainshock, which is not always true. It works well when a mainshock is followed only by smaller aftershocks, and less well for sequences containing large aftershocks that trigger substantial sequences of their own. It can also perform poorly for swarms - clusters of similar-sized earthquakes with no clear mainshock, which may be driven by fluid movement or slow slip rather than by a single rupture.

There is also irreducible uncertainty in the numbers themselves. Where a forecast has to fall back on generic regional parameters, it inherits the full variability of every past sequence in that tectonic setting, so the ranges are wide. The USGS publishes those ranges rather than a single number for exactly that reason.