Aftershock

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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.

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Distribution of aftershocks

Sichuan 2008 Aftershocks.jpg
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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 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 [ 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.

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

Gutenberg-Richter law for b = 1 GR law b=1.svg
Gutenberg–Richter law for b = 1
Magnitude of the Central Italy earthquake of August 2016 (red dot) and aftershocks (which continued to occur after the period shown here) 2016 Central Italy earthquake (magnitude).svg
Magnitude of the Central Italy earthquake of August 2016 (red dot) and aftershocks (which continued to occur after the period shown here)

Aftershock sequences also typically follow the Gutenberg–Richter law of size scaling, which refers to the relationship between the magnitude and total number of earthquakes in a region in a given time period.

Where:

In summary, there are more small aftershocks and fewer large aftershocks.

Effect of aftershocks

Aftershocks are dangerous because they are usually unpredictable, can be of a large magnitude, and can collapse buildings that are damaged from the main shock. 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, for example, the New Madrid Seismic Zone, where events still follow Omori's law from the main shocks of 1811–1812. An aftershock sequence is deemed to have ended 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.

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 were considered aftershocks nearly 200 years after the 1812 New Madrid earthquake. [12]

Foreshocks

Some scientists have tried to use foreshocks to help predict upcoming earthquakes, having one of their few successes with the 1975 Haicheng earthquake in China. On the East Pacific Rise however, transform faults show quite predictable foreshock behaviour before the main seismic event. Reviews of data of past events and their foreshocks showed that they have a low number of aftershocks and high foreshock rates compared to continental strike-slip faults. [13]

Modeling

Seismologists use tools such as the Epidemic-Type Aftershock Sequence model (ETAS) to study cascading aftershocks and foreshocks. [14] [15]

Psychology

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. [16] [17]

Related Research Articles

A foreshock is an earthquake that occurs before a larger seismic event – the mainshock – and is related to it in both time and space. The designation of an earthquake as foreshock, mainshock or aftershock is only possible after the full sequence of events has happened.

The 1857 Fort Tejon earthquake occurred at about 8:20 a.m. on January 9 in central and Southern California. One of the largest recorded earthquakes in the United States, with an estimated moment magnitude of 7.9, it ruptured the southern part of the San Andreas Fault for a length of about 225 miles, between Parkfield and Wrightwood.

Coulomb stress transfer is a seismic-related geological process of stress changes to surrounding material caused by local discrete deformation events. Using mapped displacements of the Earth's surface during earthquakes, the computed Coulomb stress changes suggest that the stress relieved during an earthquake not only dissipates but can also move up and down fault segments, concentrating and promoting subsequent tremors. Importantly, Coulomb stress changes have been applied to earthquake-forecasting models that have been used to assess potential hazards related to earthquake activity.

The 1999 Hector Mine earthquake occurred in Southern California, United States, on October 16 at 02:46:50 PDT. Its moment magnitude was 7.1 and the earthquake was preceded by 12 foreshocks, the largest of which had a magnitude of 3.8. The event is thought to have been triggered by the 1992 Landers earthquake which occurred seven years earlier. It also deformed nearby faults vertically and horizontally. The earthquake's hypocenter was at a depth of 20 kilometers and its epicenter at 34.603° N 116.265° W.

The Dasht-e Bayaz and Ferdows earthquakes occurred in Dashte Bayaz, Kakhk and Ferdows, Iran in late August and early September 1968. The mainshock measured 7.4 on the moment magnitude scale and had a maximum perceived intensity of X (Extreme) on the Mercalli intensity scale. Damage was heavy in the affected areas with thousands of lives lost in the first event and many hundreds more in the second strong event.

<span class="mw-page-title-main">2002 Denali earthquake</span> 7.9 magnitude; November 3, 2002

The 2002 Denali earthquake occurred at 22:12:41 UTC November 3 with an epicenter 66 km ESE of Denali National Park, Alaska, United States. This 7.9 Mw earthquake was the largest recorded in the United States in 37 years. The shock was the strongest ever recorded in the interior of Alaska. Due to the remote location, there were no fatalities and only one injury.

<span class="mw-page-title-main">San Jacinto Fault Zone</span> Southern Californian fault zone

The San Jacinto Fault Zone (SJFZ) is a major strike-slip fault zone that runs through San Bernardino, Riverside, San Diego, and Imperial Counties in Southern California. The SJFZ is a component of the larger San Andreas transform system and is considered to be the most seismically active fault zone in the area. Together they relieve the majority of the stress between the Pacific and North American tectonic plates.

The 1991 Uttarkashi earthquake occurred at 02:53:16 Indian Standard Time (UTC+05:30) on 20 October with a moment magnitude of 6.8 and a maximum Mercalli intensity of IX (Violent). This thrust event was instrumentally recorded and occurred along the Main Central Thrust in the Uttarkashi and Gharwal regions of the Indian state of Uttarakhand. High intensity shaking resulted in the deaths of at least 768 people and the destruction of thousands of homes.

<span class="mw-page-title-main">1997 Umbria and Marche earthquake</span> Mw5.7 and Mw6.0 earthquakes in central Italy

The 1997 Umbria and Marche earthquake occurred in the regions of Umbria and Marche, central Italy on the morning of 26 September. It was preceded by a foreshock almost as strong as the main quake. The foreshock occurred at 02:33 CEST, rated Mw5.7, and the second – the main shock – occurred at 11:40 CEST, rated Mw 6.0. Their epicentre was in Annifo. The mainshock was assigned X (Extreme) and foreshock VIII (Severe) on the Mercalli intensity scale.

In seismology, doublet earthquakes – and more generally, multiplet earthquakes – were originally identified as multiple earthquakes with nearly identical waveforms originating from the same location. They are now characterized as distinct earthquake sequences having two main shocks of similar magnitude, sometimes occurring within tens of seconds, but sometimes separated by years. The similarity of magnitude – often within 0.4 magnitude – distinguishes multiplet events from aftershocks, which start at about 1.2 magnitude less than the parent shock and decrease in magnitude and frequency according to known laws.

The 1986 Chalfant Valley earthquake struck southern Mono County near Bishop and Chalfant, California at 07:42:28 Pacific Daylight Time on July 21. With a moment magnitude of 6.2 and a maximum Mercalli intensity of VI (Strong), the shock injured two people and caused property damage estimated at $2.7 million in the affected areas. There was a significant foreshock and aftershock sequence that included a few moderate events, and was the last in a series of three earthquakes that affected southern California and the northern Owens Valley in July 1986.

<span class="mw-page-title-main">1978 Miyagi earthquake</span>

The 1978 Miyagi earthquake occurred at 17:14 local time on 12 June. The epicentre was offshore of Miyagi Prefecture, Japan. It had a surface wave magnitude of 7.7, JMA magnitude 7.4, and triggered a small tsunami. The earthquake reached a maximum intensity of Shindo 5 in Sendai and caused 28 deaths and 1,325 injuries.

<span class="mw-page-title-main">Sagaing Fault</span> Seismic fault in Myanmar

The Sagaing Fault is a major fault in Myanmar, a mainly continental right-lateral transform fault between the Indian Plate and Sunda Plate. It links the divergent boundary in the Andaman Sea with the zone of active continental collision along the Himalayan front. It passes through the populated cities of Mandalay, Yamethin, Pyinmana, the capital Naypyidaw, Toungoo and Pegu before dropping off into the Gulf of Martaban, running for a total length of over 1200 kilometers.

This is a list of different types of earthquake.

<span class="mw-page-title-main">1170 Syria earthquake</span> Extreme level earthquake in Syria

The 1170 Syria earthquake was one of the largest earthquakes to hit Syria. It occurred early in the morning of 29 June 1170. It formed part of a sequence of large earthquakes that propagated southwards along the Dead Sea Transform, starting with the 1138 Aleppo earthquake, continuing with the 1157 Hama, 1170 and 1202 Syria events. The estimated magnitude is 7.7 on the moment magnitude scale, with the maximum intensity of X (Extreme) on the Mercalli intensity scale.

In seismology, the mainshock is the largest earthquake in a sequence, sometimes preceded by one or more foreshocks, and almost always followed by many aftershocks.

The northern part of the Ottoman Empire was struck by a major earthquake on 13 August 1822. It had an estimated magnitude of 7.0 Ms and a maximum felt intensity of IX (Destructive) on the European macroseismic scale (EMS). It may have triggered a tsunami, affecting nearby coasts. Damaging aftershocks continued for more than two years, with the most destructive being on 5 September 1822. The earthquake was felt over a large area including Rhodes, Cyprus and Gaza. The total death toll reported for this whole earthquake sequence ranges between 30,000 and 60,000, although 20,000 is regarded as a more likely number.

The second shock in the 1962 Irpinia earthquake sequence was the largest and most destructive in a series of earthquakes in the southern Apennines. It occurred on 21 August at 18:19 CET, measuring Mw 6.15 and assigned a maximum intensity of IX (Violent). It was preceded by an Mw  5.68 foreshock, and followed by a 5.34 aftershock. The earthquakes resulted in nearly 20 fatalities and significant property losses.

The 1895 Charleston earthquake, also known as the Halloween earthquake, occurred on October 31, at 05:07 CST near Charleston, Missouri. It had an estimated moment magnitude of 5.8–6.6 and evaluated Modified Mercalli intensity of VIII (Severe). The earthquake caused substantial property damage in the states of Missouri, Illinois, Ohio, Alabama, Iowa, Kentucky, Indiana, and Tennessee. Shaking was widespread, being felt across 23 states and even in Canada. At least two people died and seven were injured.

The 1992 Joshua Tree earthquake occurred at 9:50:25 p.m. PDT on April 22 in Southern California. The magnitude 6.2 earthquake struck under the Little San Bernardino Mountains, near the town of Joshua Tree, California. Though no deaths were reported, the earthquake caused 32 injuries. A maximum Mercalli intensity of VII was observed in Joshua Tree and caused light to moderate damage. The event preceded the Landers and Big Bear earthquakes by two months but is now recognized as the beginning of a series of major earthquakes that culminated in two events on June 28, 1992.

References

  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". Journal of Physics of the Earth. 43: 1–33. doi: 10.4294/jpe1952.43.1 .
  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". Izvestiya, Physics of the Solid Earth. 52 (5): 785–786. arXiv: 1604.07017 . Bibcode:2016IzPSE..52..785G. doi:10.1134/S1069351316050165. S2CID   119256791.
  6. ↑ Shaw, Bruce (1993). "Generalized Omori law for aftershocks and foreshocks from a simple dynamics" (PDF). Geophysical Research Letters. 20 (10): 907–910. Bibcode:1993GeoRL..20..907S. 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. S2CID   52813333.
  8. ↑ Richter, Charles F., Elementary seismology (San Francisco, California, USA: W. H. Freeman & Co., 1958), page 69.
  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.
  10. ↑ Elizabeth K. Gardner (2009-03-13). "New Madrid fault system may be shutting down". physorg.com. Retrieved 2011-03-25.
  11. ↑ Wallace, Robert E. "Present-Day Crustal Movements and the Mechanics of Cyclic Deformation". The San Andreas Fault System, California. Archived from the original on 2006-12-16. Retrieved 2007-10-26.
  12. ↑ "Earthquakes Actually Aftershocks Of 19th Century Quakes; Repercussions Of 1811 And 1812 New Madrid Quakes Continue To Be Felt". Science Daily. Archived from the original on 8 November 2009. Retrieved 2009-11-04.
  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. S2CID   4337369.
  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. S2CID   14327777. 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. ↑ For example: Petrillo, Giuseppe; Lippiello, Eugenio (December 2020). "Testing of the foreshock hypothesis within an epidemic like description of seismicity". Geophysical Journal International. 225 (2): 1236–1257. doi: 10.1093/gji/ggaa611 . ISSN   0956-540X.
  16. ↑ "Japanese researchers diagnose hundreds of cases of 'earthquake sickness'". The Daily Telegraph. 20 June 2016.
  17. ↑ "After the earthquake: why the brain gives phantom quakes". The Guardian. 6 November 2016.
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