Aftershock

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This article is about the geological event. For other uses of the term see Aftershock (disambiguation).

Aftershocks are earthquakes in the same region of the mainshock (generally within a few rupture length) but of smaller magnitude and which occur with a pattern that follows Omori's law. Omori's law, or more correctly the modified Omori's law, is an empirical relation for the temporal decay of aftershock rates. Omori published his work on the aftershocks of earthquakes, in which he stated that aftershock frequency decreases by roughly the reciprocal of time after the main shock, in 1894.

Aftershocks are smaller earthquakes formed as the displaced plate boundary tries to adjust itself.

$n(t) = \frac {K} {c+t}$

where:

n(t) is the number of earthquakes n measured in a certain time t
K is the decay rate; and
c is the "time offset" parameter

the modified version of the law, now commonly used was proposed by Utsu in 1961.

$n(t) = \frac {K} {(c+t)^p}$

where

p typically falls in the range 0.7–1.5.

what these equations describe is that the rate of aftershocks dies off quickly with time. The rate of aftershocks is proportional to the inverse of time since the mainshock. Thus whatever the odds of an aftershock are on the first day, the second day will have 1/2 the odds of the first day and the tenth day will have approximately 1/10th the odds of the first day (when p is equal to 1). These patterns describe only the mass behavior of aftershocks; the actual times, numbers and locations of the aftershocks are 'random', while tending to follow these patterns. As this is an empirical law values of the parameters are obtained by fitting to data after the mainshock occurred and they have no physical basis/meaning.

The other main law describing aftershocks is known as Bath's Law and this says that any mainshock typical has an aftershock approximately 1 magnitude (on average 1.2) less than its mainshock. Aftershock sequences also typical follow Guttenberg-Richter scaling.

Aftershocks are dangerous because they are usually unpredictable, can be of a large magnitude, and can collapse buildings that are damaged from the mainshock. Bigger earthquakes have more and larger aftershocks and the sequences can last for years or even longer especially when a large event occurs in a seismically quiet area, see New Madrid Seismic Zone where events still follow Omori's law from the mainshocks in 1811/1812. An Aftershock sequence is deemed to be over when the rate of seismicity drops back to a background level i.e. no further decay in the number of events with time can be detected.