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 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.

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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 the case of the 2004 Indian Ocean earthquake and the 2008 Sichuan earthquake the aftershock distribution shows in both cases that the epicenter (where the rupture initiated) lies 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, 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 are 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. [14]

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. [15] [16]

Related Research Articles

Earthquake Shaking of the surface of the earth caused by a sudden release of energy in the crust

An earthquake is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to propel objects and people into the air, and wreak destruction across entire cities. The seismicity, or seismic activity, of an area is the frequency, type, and size of earthquakes experienced over a period of time. The word tremor is also used for non-earthquake seismic rumbling.

New Madrid Seismic Zone Major seismic zone in the southern and midwestern United States

The New Madrid Seismic Zone, sometimes called the New Madrid Fault Line, is a major seismic zone and a prolific source of intraplate earthquakes in the Southern and Midwestern United States, stretching to the southwest from New Madrid, Missouri.

Earthquake swarm Series of localized seismic events within a short time period

In seismology, an earthquake swarm is a sequence of seismic events occurring in a local area within a relatively short period of time. The length of time used to define the swarm itself varies, but may be of the order of days, months, or even years. Such an energy release is different from what happens commonly when a major earthquake (mainshock) is followed by a series of aftershocks: in earthquake swarms, no single earthquake in the sequence is obviously the mainshock. In particular, a cluster of aftershocks occurring after a mainshock is not a swarm.

A foreshock is an earthquake that occurs before a larger seismic event 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.

1857 Fort Tejon earthquake 1857 earthquake in California, United States

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.

1891 Mino–Owari earthquake

The 1891 Mino–Owari earthquake struck the former Japanese provinces of Mino and Owari in the Nōbi Plain in the early morning of October 28 with a surface wave magnitude of 8.0. The event, also referred to as the Nōbi earthquake, the Great Gifu earthquake, or the Great Nōbi earthquake, is the largest known inland earthquake to have occurred in the Japanese archipelago.

1968 Dasht-e Bayaz and Ferdows earthquakes

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.

San Jacinto 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.

2008 Chino Hills earthquake

The 2008 Chino Hills earthquake occurred at 11:42:15 am PDT on July 29 in Southern California. The epicenter of the magnitude 5.4 earthquake was in Chino Hills, c. 28 miles (45 km) east-southeast of downtown Los Angeles. Though no lives were lost, eight people were injured, and it caused considerable damage in numerous structures throughout the area and caused some amusement park facilities to shut down their rides. The earthquake led to increased discussion regarding the possibility of a stronger earthquake in the future.

Didier Sornette

Didier Sornette has been Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich since March 2006. He is also a professor of the Swiss Finance Institute, and a professor associated with both the department of Physics and the department of Earth Sciences at ETH Zurich. He was previously jointly a Professor of Geophysics at UCLA, Los Angeles California (1996–2006) and a Research Professor at the French National Centre for Scientific Research (1981–2006), working on the theory and prediction of complex systems. Pioneer in econophysics, in 1994, he co-founded with Jean-Philippe Bouchaud the company Science et Finance, which later merged with Capital Fund Management (CFM) in 2000. He left however Science et Finance in 1997 to focus on his shared position as Research Professor at the CNRS in France (1990-2006) and Professor at UCLA (1996-2006).

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 single earthquakes having two main shocks of similar magnitude, sometimes occurring within tens of seconds, but sometimes separated by years. The similarity of magnitude – often within four-tenths of a unit of 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.

1986 Chalfant Valley earthquake

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.

Brawley Seismic Zone

The Brawley Seismic Zone (BSZ), also known as the Brawley fault zone, is a predominantly extensional tectonic zone that connects the southern terminus of the San Andreas Fault with the Imperial Fault in Southern California. The BSZ is named for the nearby town of Brawley in Imperial County, California, and the seismicity there is characterized by earthquake swarms.

1978 Miyagi earthquake

The 1978 Miyagi earthquake occurred at 17:14 local time on 12 June. 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.

Sagaing Fault

The Sagaing Fault is a major fault in Burma, 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 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.

2011 Oklahoma earthquake

The 2011 Oklahoma earthquake was a 5.7 magnitude intraplate earthquake which occurred near Prague, Oklahoma on November 5 at 10:53 p.m. CDT in the U.S. state of Oklahoma. The epicenter of the earthquake was in the vicinity of several active wastewater injection wells. According to the United States Geological Survey (USGS), it was the most powerful earthquake ever recorded in Oklahoma; this record was surpassed by the 2016 Oklahoma earthquake. The previous record was a 5.5 magnitude earthquake that struck near the town of El Reno in 1952. The quake's epicenter was approximately 44 miles (71 km) east-northeast of Oklahoma City, near the town of Sparks and was felt in the neighboring states of Texas, Arkansas, Kansas and Missouri and even as far away as Tennessee and Wisconsin. The quake followed several minor quakes earlier in the day, including a 4.7 magnitude foreshock. The quake had a maximum perceived intensity of VIII (Severe) on the Mercalli intensity scale in the area closest to the epicenter. Numerous aftershocks were detected after the main quake, with a few registering at 4.0 magnitude.

This is a list of different types of earthquake.

2019 Ridgecrest earthquakes July 4–5, 2019, earthquakes in California

The 2019 Ridgecrest earthquakes of July 4 and 5 occurred north and northeast of the town of Ridgecrest, California located in Kern County and west of Searles Valley. They included three initial main shocks of Mw magnitudes 6.4, 5.4, and 7.1, and many perceptible aftershocks, mainly within the area of the Naval Air Weapons Station China Lake. Eleven months later, a Mw  5.5 aftershock took place to the east of Ridgecrest. The first main shock occurred on Thursday, July 4 at 10:33 a.m. PDT, approximately 18 km (11.2 mi) ENE of Ridgecrest, and 13 km (8.1 mi) WSW of Trona, on a previously unnoticed NE-SW trending fault where it intersects the NW-SE trending Little Lake Fault Zone. This quake was preceded by several smaller earthquakes, and was followed by more than 1,400 detected aftershocks. The M 5.4 and M 7.1 quakes struck on Friday, July 5 at 4:08 a.m. and 8:19 p.m. PDT approximately 10 km (6 miles) to the northwest. The latter, now considered the mainshock, was the most powerful earthquake to occur in the state in 20 years. Subsequent aftershocks extended approximately 50 km (~30 miles) along the Little Lake Fault Zone.

1988 Lancang earthquake Magnitude 7.7 and 7.2 earthquake near the Myanmar−China border region

The 1988 Lancang–Gengma earthquakes, also known as the 11.6 earthquake by the Chinese media was a devastating seismic event that struck Lancang and Gengma counties, Yunnan, near the border with Shan State, Burma (Myanmar) in the Shan Plateau. The pair of earthquakes occurred thirteen minutes apart, with the first registering 7.7 on the moment magnitude scale, while the second shock measured 7.2 on the surface wave magnitude scale. The two earthquakes were assigned their maximum Mercalli intensities of X (Extreme) and IX (Violent) respectively. More than 930 people were killed, and at least 7,700 were injured in 20 counties across five prefectures in Yunnan, making it the worst in the country since 1976. Both earthquakes resulted in at least US $270 million in damage and economical loss. Moderately large aftershocks continued to rock the region, causing additional casualties and damages. Much information about the earthquake and its devastation was hidden by the Chinese government as the country was going through major political and cultural revolutions.

1833 Bihar–Nepal earthquake 1833 earthquake in Nepal and India

The 1833 Nepal–India earthquake, also known as the 1833 Bihar–Nepal earthquake occurred on August 26 at 22:58 local time (NPT). This earthquake had an estimated moment magnitude of 7.6–7.9 and struck with an epicenter somewhere in or near the Kathmandu Valley. The earthquake caused major damage and deaths in numerous towns and villages in Nepal, northern India and Tibet. The earthquake was so powerful that it was also felt in Chittagong, Bangladesh. Despite the extent of the damage, the number of fatalities resulted from the earthquake was very low, at around 500. This was because the mainshock was preceded by two smaller but intense foreshocks earlier that day, causing many residents to make refuge outside their homes.

References

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  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.
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  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.
  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. 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