667:
65:
427:
633:
earthquake. Also, previously Utsu-Omori law was obtained from a nucleation process. 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, a double power law model shows the number density decay in several possible ways, among which is a particular case the Utsu-Omori Law.
434:
655:
853:
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
440:
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
620:
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
632:
The Utsu-Omori law has also been obtained theoretically, as the solution of a differential equation describing the evolution of the aftershock activity, 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
858:, 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.
641:
The other main law describing aftershocks is known as Båth's Law 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
1431:
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
865:
which averages up to 37 mm (1.5 in) a year across
California. 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
900:
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
629:, 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.
924:
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
684:
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.
1038:
406:
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
608:
621:
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
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730:
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946:
839:
819:
797:
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756:
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is equal to 1). These patterns describe only the statistical behavior of aftershocks; the actual times, numbers and locations of the aftershocks are
271:
1524:
1329:
McGuire JJ, Boettcher MS, Jordan TH (2005). "Foreshock sequences and short-term earthquake predictability on East
Pacific Rise transform faults".
472:
The frequency of aftershocks decreases roughly with the reciprocal of time after the main shock. This empirical relation was first described by
1486:
1504:
1308:
1271:
1122:
1165:
Sánchez, Ewin; Vega, Pedro (2018). "Modelling temporal decay of aftershocks by a solution of the fractional reactive equation".
1301:"Earthquakes Actually Aftershocks Of 19th Century Quakes; Repercussions Of 1811 And 1812 New Madrid Quakes Continue To Be Felt"
540:
are constants, which vary between earthquake sequences. A modified version of Omori's law, now commonly used, was proposed by
373:
861:
Land movement around the New Madrid is reported to be no more than 0.2 mm (0.0079 in) a year, in contrast to the
671:
410:. In some earthquakes the main rupture happens in two or more steps, resulting in multiple main shocks. These are known as
456:(where the rupture initiated) lay to one end of the final area of slip, implying strongly asymmetric rupture propagation.
1387:(October 2003). "Predictability in the Epidemic-Type Aftershock Sequence model of interacting triggered seismicity".
1039:"New Science update on 2011 Christchurch Earthquake for press and public: Seismic fearmongering or time to jump ship"
961:
916:
use tools such as the
Epidemic-Type Aftershock Sequence model (ETAS) to study cascading aftershocks and foreshocks.
550:
414:, and in general can be distinguished from aftershocks in having similar magnitudes and nearly identical seismic
121:
302:
1545:
482:
445:
444:
The pattern of aftershocks helps confirm the size of area that slipped during the main shock. In both the
169:
38:
17:
867:
691:
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366:
347:
307:
889:
250:
245:
1300:
855:
449:
96:
643:
312:
279:
1279:
885:
335:
263:
136:
116:
111:
106:
666:
617:
is a third constant which modifies the decay rate and typically falls in the range 0.7–1.5.
1406:
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359:
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131:
48:
31:
8:
1540:
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1447:"Testing of the foreshock hypothesis within an epidemic like description of seismicity"
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1103:
1077:
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101:
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1426:
1186:
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1414:
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1230:
1174:
1145:
1095:
1017:
146:
1384:
926:
897:
473:
464:
Aftershocks rates and magnitudes follow several well-established empirical laws.
403:
164:
126:
674:(red dot) and aftershocks (which continued to occur after the period shown here)
64:
1178:
1099:
1534:
1472:
1304:
1123:"Generalized Omori law for aftershocks and foreshocks from a simple dynamics"
1249:
37:
This article is about the geological event. For other uses of the term, see
1360:
1006:"The centenary of the Omori formula for a decay law of aftershock activity"
913:
426:
212:
1487:"Japanese researchers diagnose hundreds of cases of 'earthquake sickness'"
1463:
1446:
845:
In summary, there are more small aftershocks and fewer large aftershocks.
1418:
1401:
1203:(San Francisco, California, USA: W. H. Freeman & Co., 1958), page 69.
1022:
1005:
985:
Utsu, T. (1961). "A statistical study of the occurrence of aftershocks".
541:
240:
207:
1352:
1272:"Present-Day Crustal Movements and the Mechanics of Cyclic Deformation"
626:
395:
387:
322:
202:
56:
1150:
879:
453:
399:
192:
86:
81:
1213:
BĂĄth, Markus (1965). "Lateral inhomogeneities in the upper mantle".
1082:
415:
317:
433:
30:"Aftershocks" redirects here. For the memoir by Nadia Owusu, see
954:
Journal of the
College of Science, Imperial University of Tokyo
654:
222:
217:
27:
Smaller earthquake which follows a larger one in the same area
407:
1068:
Guglielmi, A.V. (2016). "Interpretation of the Omori law".
452:, the aftershock distribution in each case showed that the
1505:"After the earthquake: why the brain gives phantom quakes"
459:
476:
in 1894 and is known as Omori's law. It is expressed as
1445:
Petrillo, Giuseppe; Lippiello, Eugenio (December 2020).
929:, and usually goes away as seismic activity tails off.
1328:
1003:
884:
Some scientists have tried to use foreshocks to help
827:
807:
785:
764:
744:
694:
553:
485:
1247:
1382:
854:in a seismically quiet area; see, for example, the
833:
813:
791:
770:
750:
724:
602:
521:
1444:
695:
1532:
1250:"New Madrid fault system may be shutting down"
421:
1004:Utsu, T.; Ogata, Y.; Matsu'ura, R.S. (1995).
888:, having one of their few successes with the
367:
1389:Journal of Geophysical Research: Solid Earth
758:is the number of events greater or equal to
1525:Earthquake Aftershocks Not What They Seemed
1164:
603:{\displaystyle n(t)={\frac {k}{(c+t)^{p}}}}
402:of the main shock, caused as the displaced
374:
360:
1462:
1400:
1149:
1081:
1067:
1021:
696:
1276:The San Andreas Fault System, California
848:
665:
653:
649:
432:
425:
672:Central Italy earthquake of August 2016
460:Aftershock size and frequency with time
14:
1533:
1030:
1070:Izvestiya, Physics of the Solid Earth
944:
522:{\displaystyle n(t)={\frac {k}{c+t}}}
398:that follows a larger earthquake, in
1311:from the original on 8 November 2009
1212:
1120:
984:
1269:
1248:Elizabeth K. Gardner (2009-03-13).
1167:Applied Mathematics and Computation
1036:
947:"On the aftershocks of earthquakes"
24:
25:
1557:
1518:
1451:Geophysical Journal International
63:
1497:
1479:
1437:
1375:
1322:
1293:
1263:
1241:
1043:Christchurch Earthquake Journal
1010:Journal of Physics of the Earth
725:{\displaystyle \!\,N=10^{a-bM}}
1206:
1193:
1158:
1114:
1061:
997:
978:
938:
588:
575:
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467:
13:
1:
932:
919:
873:
636:
1235:10.1016/0040-1951(65)90003-X
1130:Geophysical Research Letters
886:predict upcoming earthquakes
446:2004 Indian Ocean earthquake
7:
908:
422:Distribution of aftershocks
39:Aftershock (disambiguation)
10:
1562:
877:
868:1812 New Madrid earthquake
677:
658:Gutenberg–Richter law for
272:Coordinating Committee for
36:
29:
1179:10.1016/j.amc.2018.08.022
1100:10.1134/S1069351316050165
960:: 111–200. Archived from
303:Adams–Williamson equation
890:1975 Haicheng earthquake
251:Seismic intensity scales
246:Seismic magnitude scales
856:New Madrid Seismic Zone
450:2008 Sichuan earthquake
835:
815:
793:
772:
752:
726:
675:
663:
644:Moment magnitude scale
604:
523:
437:
430:
313:Earthquake engineering
1201:Elementary seismology
1199:Richter, Charles F.,
849:Effect of aftershocks
836:
816:
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773:
753:
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680:Gutenberg–Richter law
669:
657:
650:Gutenberg–Richter law
605:
524:
436:
429:
336:Earth Sciences Portal
308:Flinn–Engdahl regions
274:Earthquake Prediction
1419:10.1029/2003JB002485
1383:Helmstetter, Agnès;
1121:Shaw, Bruce (1993).
1023:10.4294/jpe1952.43.1
987:Geophysical Magazine
825:
805:
783:
762:
742:
692:
551:
483:
408:a consistent pattern
298:Shear wave splitting
32:Aftershocks (memoir)
1546:Types of earthquake
1491:The Daily Telegraph
1464:10.1093/gji/ggaa611
1411:2003JGRB..108.2482H
1353:10.1038/nature03377
1345:2005Natur.434..457M
1270:Wallace, Robert E.
1227:1965Tectp...2..483B
1142:1993GeoRL..20..907S
1092:2016IzPSE..52..785G
412:doublet earthquakes
198:Epicentral distance
1511:. 6 November 2016.
1049:on 29 January 2012
945:Omori, F. (1894).
903:strike-slip faults
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811:
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748:
722:
676:
664:
600:
519:
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175:Induced seismicity
122:Remotely triggered
1151:10.1029/93GL01058
894:East Pacific Rise
892:in China. On the
863:San Andreas Fault
834:{\displaystyle b}
814:{\displaystyle a}
792:{\displaystyle M}
771:{\displaystyle M}
751:{\displaystyle N}
670:Magnitude of the
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517:
384:
383:
16:(Redirected from
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1457:(2): 1236–1257.
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1402:cond-mat/0208597
1385:Sornette, Didier
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1373:
1372:
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1278:. Archived from
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1210:
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1045:. Archived from
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147:Earthquake swarm
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1527:at Live Science
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1493:. 20 June 2016.
1485:
1484:
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1442:
1438:
1395:(B10): 2482ff.
1380:
1376:
1339:(7032): 445–7.
1327:
1323:
1314:
1312:
1299:
1298:
1294:
1285:
1283:
1268:
1264:
1255:
1253:
1246:
1242:
1211:
1207:
1198:
1194:
1163:
1159:
1136:(10): 907–910.
1125:
1119:
1115:
1066:
1062:
1052:
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1035:
1031:
1002:
998:
983:
979:
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927:motion sickness
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911:
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823:
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1221:(6): 483–514.
1215:Tectonophysics
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914:Seismologists
906:
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441:fault plane.
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428:
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409:
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400:the same area
397:
394:is a smaller
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1509:The Guardian
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1313:. Retrieved
1295:
1284:. Retrieved
1280:the original
1275:
1265:
1254:. Retrieved
1243:
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1208:
1200:
1195:
1170:
1166:
1160:
1133:
1129:
1116:
1073:
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1051:. Retrieved
1047:the original
1042:
1037:Quigley, M.
1032:
1013:
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999:
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986:
980:
969:. Retrieved
962:the original
957:
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883:
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852:
844:
799:is magnitude
734:
683:
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631:
622:
619:
614:
612:
537:
533:
531:
471:
468:Omori's law
463:
443:
439:
391:
385:
292:Other topics
97:Blind thrust
91:
280:Forecasting
241:Seismometer
235:Measurement
208:Shadow zone
57:Earthquakes
18:Aftershocks
1541:Seismology
1535:Categories
1315:2009-11-04
1286:2007-10-26
1256:2011-03-25
1083:1604.07017
1053:25 January
993:: 521–605.
971:2015-07-15
933:References
920:Psychology
874:Foreshocks
637:BĂĄth's law
627:stochastic
396:earthquake
392:aftershock
388:seismology
323:Seismology
264:Prediction
203:Hypocenter
137:Supershear
117:Megathrust
112:Intraplate
107:Interplate
92:Aftershock
1473:0956-540X
1173:: 24–49.
1108:119256791
896:however,
880:Foreshock
712:−
544:in 1961.
454:epicenter
416:waveforms
193:Epicenter
170:Volcanism
132:Submarine
87:Foreshock
82:Mainshock
1427:14327777
1361:15791246
1309:Archived
1187:52813333
1016:: 1–33.
909:Modeling
448:and the
343:Category
318:Seismite
49:a series
47:Part of
1432:(ETAS).
1407:Bibcode
1369:4337369
1341:Bibcode
1223:Bibcode
1138:Bibcode
1088:Bibcode
735:Where:
142:Tsunami
102:Doublet
1471:
1425:
1367:
1359:
1332:Nature
1185:
1106:
613:where
532:where
223:S wave
218:P wave
159:Causes
1423:S2CID
1397:arXiv
1365:S2CID
1183:S2CID
1126:(PDF)
1104:S2CID
1078:arXiv
965:(PDF)
950:(PDF)
404:crust
390:, an
75:Types
1469:ISSN
1357:PMID
1055:2012
821:and
542:Utsu
536:and
127:Slow
1459:doi
1455:225
1415:doi
1393:108
1349:doi
1337:434
1231:doi
1175:doi
1171:340
1146:doi
1096:doi
1018:doi
386:In
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958:7
829:b
809:a
787:M
766:M
746:N
718:M
715:b
709:a
701:=
698:N
660:b
623:p
615:p
593:p
589:)
585:t
582:+
579:c
576:(
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567:=
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561:t
558:(
555:n
538:c
534:k
514:t
511:+
508:c
504:k
499:=
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493:t
490:(
487:n
375:e
368:t
361:v
41:.
34:.
20:)
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