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An aftershock is a smaller earthquake which comes after a large earthquake (called the main shock) in the same area. An aftershock is the opposite of a foreshock, which a small earthquake comes before the large earthquake.

Omori's Law

There are many laws which refer to aftershocks, but the most famous is Omori's Law. In 1894, Fusakichi Omori did some works on aftershocks, and firstly he came up with this rule:

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

"t" is time.
"n(t)" is the rate of earthquakes in a time after the main shock
"c" is a constant
"K" is the size of the earthquake.

^[1]

By 1961, Utsu wanted to change the rule.^[2]^[3] His rule looked like this:

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

where "p" changes the rate, this mainly has a number between 0.7 and 1.5.

References

↑ F. Omori (1894) "On the aftershocks of earthquakes," Journal of the College of Science, Imperial University of Tokyo, vol. 7, pages 111–200.
↑ Utsu, T. (1961) "A statistical study of the occurrence of aftershocks," Geophysical Magazine, vol. 30, pages 521–605.
↑ Utsu, T., Ogata, Y. ,and Matsu'ura, R.S. (1995) "The centenary of the Omori formula for a decay law of aftershock activity," Journal of Physics of the Earth, vol. 43, pages 1–33.