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Aftershock Language Watch Edit This article is about the geological event For other uses of the term see Aftershock disambiguation 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 Contents 1 Distribution of aftershocks 2 Aftershock size and frequency with time 2 1 Omori s law 2 2 Bath s law 2 3 Gutenberg Richter law 3 Effect of aftershocks 4 Foreshocks 5 Modeling 6 Psychology 7 References 8 External linksDistribution of aftershocks Edit 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 EditAftershocks rates and magnitudes follow several well established empirical laws Omori s law Edit 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 n t k c t displaystyle n t frac k c t 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 n t k c t p displaystyle n t frac k c t p 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 Bath s law Edit The other main law describing aftershocks is known as Bath 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 Edit 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 Main article Gutenberg Richter law 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 N 10 a b M displaystyle N 10 a bM Where N displaystyle N is the number of events greater or equal to M displaystyle M M displaystyle M is magnitude a displaystyle a and b displaystyle b are constants In summary there are more small aftershocks and fewer large aftershocks Effect of aftershocks EditAftershocks 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 EditMain article Foreshock 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 EditSeismologists use tools such as the Epidemic Type Aftershock Sequence model ETAS to study cascading aftershocks 14 Psychology EditFollowing 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 References Edit 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 Utsu T 1961 A statistical study of the occurrence of aftershocks Geophysical Magazine 30 521 605 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 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 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 Shaw Bruce 1993 Generalized Omori law for aftershocks and foreshocks from a simple dynamics Geophysical Research Letters 20 10 907 910 Bibcode 1993GeoRL 20 907S doi 10 1029 93GL01058 Sanchez 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 Richter Charles F Elementary seismology San Francisco California USA W H Freeman amp Co 1958 page 69 Bath 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 Elizabeth K Gardner 2009 03 13 New Madrid fault system may be shutting down physorg com Retrieved 2011 03 25 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 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 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 For example Helmstetter Agnes 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 Japanese researchers diagnose hundreds of cases of earthquake sickness Daily Telegraph 20 June 2016 After the earthquake why the brain gives phantom quakes The Guardian 6 November 2016External links EditEarthquake Aftershocks Not What They Seemed at Live ScienceRetrieved from https en wikipedia org w index php title Aftershock amp oldid 1023256184, wikipedia, wiki, book,

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