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Aftershocks are earthquakes that are triggered by a previous, larger earthquake mainshock.  Today we know that aftershocks are a result of the transfer of stress from the region of the mainshock to surrounding, smaller faults.   About 5%-10% of mainshocks have foreshocks, which can be regarded as instances when the aftershock is larger than the mainshock.

Following the Nobi earthquake in 1891, the Japanese seismologist Fusakichi Omori proposed the first of the earthquake statistical laws.  This relation, included in a paper published in 1894,  is called the Omori law of aftershock decay.  It states that the rate of occurrence of aftershocks is inversely proportional to the time since the earthquake mainshock.  In 1961, another Japanese seismologist, Tokuji Utsu, proposed a modified version of the Omori law to account for subtleties that were not explained by the original 1894 paper.  

Another of the earthquake statistical laws is Bath's law, proposed by Markus Bath in 1965.  This law states that the largest aftershock is typically about 1 magnitude smaller than the mainshock magnitude.  The third of the common statistical laws that aftershocks obey is the Gutenberg-Richter law relating frequency of occurrence of earthquakes to their magnitudes.  The Gutenberg-Richter law was proposed in 1942 by the seismologists  Beno Gutenberg and Charles Richter at the California Institute of Technology.

The Omori law and the Gutenberg-Richter law are examples of what are often called "scaling laws" or power laws.  There are many examples of power laws in other physical systems. Examples can be found in the physics of phase transitions, in which liquids are transformed into gases, or when a bar of iron acquires a magnetic field.  It is for these reasons that scientists believe that earthquakes are a kind of phase transition also.  From this perspective, the clustering of earthquakes in space and time is believed to arise from the interaction of one earthquake fault with another, and is to be expected from the underlying physics.

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