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 known laws. 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.

Distribution of aftershocks



Aftershock size and frequency with time

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

Omori's law

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.[1] 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.[2][3]

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.[4] 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, 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. But the Utsu-Omori law has also been obtained theoretically, as the solution of a differential equation describing the evolution of the aftershock activity[5], where the interpretation of the evolution equation is based on the idea of deactivation of the faults in the vicinity of the main shock of the earthquake. Also, previously Utsu-Omori law was obtained from a nucleation process[6]. Results show that the spatial and temporal distribution of aftershocks is separable into a dependence on space and a dependence on time. And more recently, through the application of a fractional solution of the reactive differential equation[7], a double power law model shows the number density decay in several possible ways, among which is a particular case the Utsu-Omori Law.

Båth's law

The other main law describing aftershocks is known as Båth's Law[8][9] and this states that the difference in magnitude between a main shock and its largest aftershock is approximately constant, independent of the main shock magnitude, typically 1.1–1.2 on the Moment magnitude scale.

Gutenberg–Richter law



  • is the number of events greater or equal to
  • is magnitude
  • and are constants


Effect of aftershocks


Land movement around the New Madrid is reported to be no more than 0.2 mm (0.0079 in) a year,[10] in contrast to the San Andreas Fault which averages up to 37 mm (1.5 in) a year across California.[11] Aftershocks on the San Andreas are now believed to top out at 10 years while earthquakes in New Madrid are considered aftershocks nearly 200 years after the 1812 New Madrid earthquake.[12]






Following a large earthquake and aftershocks, many people have reported feeling "phantom earthquakes" when in fact no earthquake was taking place. This condition, known as "earthquake sickness" is thought to be related to motion sickness, and usually goes away as seismic activity tails off.[15][16]


  1. Omori, F. (1894). "On the aftershocks of earthquakes" (PDF). Journal of the College of Science, Imperial University of Tokyo. 7: 111–200. Archived from the original (PDF) on 2015-07-16. Retrieved 2015-07-15.
  2. Utsu, T. (1961). "A statistical study of the occurrence of aftershocks". Geophysical Magazine. 30: 521–605.
  3. Utsu, T.; Ogata, Y.; Matsu'ura, R.S. (1995). "The centenary of the Omori formula for a decay law of aftershock activity" (PDF). Journal of Physics of the Earth. 43: 1–33. doi:10.4294/jpe1952.43.1. Archived from the original (PDF) on 2015-07-16.
  4. Quigley, M. "New Science update on 2011 Christchurch Earthquake for press and public: Seismic fearmongering or time to jump ship". Christchurch Earthquake Journal. Archived from the original on 29 January 2012. Retrieved 25 January 2012.
  5. Guglielmi, A.V. (2016). "Interpretation of the Omori law". Izv., Phys. Solid Earth. 52 (5): 785–786. arXiv:1604.07017. doi:10.1134/S1069351316050165.
  6. Shaw, Bruce (1993). "Generalized Omori law for aftershocks and foreshocks from a simple dynamics". Geophysical Research Letters. 20 (10): 907–910. doi:10.1029/93GL01058.
  7. Sánchez, Ewin; Vega, Pedro (2018). "Modelling temporal decay of aftershocks by a solution of the fractional reactive equation". Applied Mathematics and Computation. 340: 24–49. doi:10.1016/j.amc.2018.08.022.
  9. Båth, Markus (1965). "Lateral inhomogeneities in the upper mantle". Tectonophysics. 2 (6): 483–514. Bibcode:1965Tectp...2..483B. doi:10.1016/0040-1951(65)90003-X.
  13. McGuire JJ, Boettcher MS, Jordan TH (2005). "Foreshock sequences and short-term earthquake predictability on East Pacific Rise transform faults". Nature. 434 (7032): 445–7. Bibcode:2005Natur.434..457M. doi:10.1038/nature03377. PMID 15791246.
  14. For example: Helmstetter, Agnès; Sornette, Didier (October 2003). "Predictability in the Epidemic-Type Aftershock Sequence model of interacting triggered seismicity". Journal of Geophysical Research: Solid Earth. 108 (B10): 2482ff. arXiv:cond-mat/0208597. Bibcode:2003JGRB..108.2482H. doi:10.1029/2003JB002485. As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, known as the Epidemic-Type Aftershock Sequence model (ETAS).
  15. Japanese researchers diagnose hundreds of cases of 'earthquake sickness', Daily Telegraph, 20 June 2016
  16. After the earthquake: why the brain gives phantom quakes, The Guardian, 6 November 2016