Aftershock
Aftershock
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Aftershock

In seismology, an aftershock is a smaller earthquake that follows a larger earthquake, in the same area of the main shock, caused as the displaced crust adjusts to the effects of the main shock. Large earthquakes can have hundreds to thousands of instrumentally detectable aftershocks, which steadily decrease in magnitude and frequency according to a consistent pattern. In some earthquakes the main rupture happens in two or more steps, resulting in multiple main shocks. These are known as doublet earthquakes, and in general can be distinguished from aftershocks in having similar magnitudes and nearly identical seismic waveforms.

Most aftershocks are located over the full area of fault rupture and either occur along the fault plane itself or along other faults within the volume affected by the strain associated with the main shock. Typically, aftershocks are found up to a distance equal to the rupture length away from the fault plane.

The pattern of aftershocks helps confirm the size of area that slipped during the main shock. In both the 2004 Indian Ocean earthquake and the 2008 Sichuan earthquake, the aftershock distribution in each case showed that the epicenter (where the rupture initiated) lay to one end of the final area of slip, implying strongly asymmetric rupture propagation.

Aftershock rates and magnitudes follow several well-established empirical laws.

The frequency of aftershocks decreases roughly with the reciprocal of time after the main shock. This empirical relation was first described by Fusakichi Omori in 1894 and is known as Omori's law. It is expressed as

where k and c are constants, which vary between earthquake sequences. A modified version of Omori's law, now commonly used, was proposed by Utsu in 1961.

where p is a third constant which modifies the decay rate and typically falls in the range 0.7–1.5.

According to these equations, the rate of aftershocks decreases quickly with time. The rate of aftershocks is proportional to the inverse of time since the mainshock and this relationship can be used to estimate the probability of future aftershock occurrence. Thus whatever the probability of an aftershock are on the first day, the second day will have 1/2 the probability of the first day and the tenth day will have approximately 1/10 the probability of the first day (when p is equal to 1). These patterns describe only the statistical behavior of aftershocks; the actual times, numbers and locations of the aftershocks are stochastic [citation needed], while tending to follow these patterns. As this is an empirical law, values of the parameters are obtained by fitting to data after a mainshock has occurred, and they imply no specific physical mechanism in any given case.

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