656:
54:
416:
622:
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.
423:
644:
842:
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
429:
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
609:
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
621:
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
847:, 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.
630:
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
1420:
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
854:
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
889:
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
618:, 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.
913:
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
673:
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.
1027:
395:
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
597:
610:
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
516:
719:
1035:
935:
828:
808:
786:
765:
745:
614:
is equal to 1). These patterns describe only the statistical behavior of aftershocks; the actual times, numbers and locations of the aftershocks are
260:
1513:
1318:
McGuire JJ, Boettcher MS, Jordan TH (2005). "Foreshock sequences and short-term earthquake predictability on East
Pacific Rise transform faults".
461:
The frequency of aftershocks decreases roughly with the reciprocal of time after the main shock. This empirical relation was first described by
1475:
1493:
1297:
1260:
1111:
1154:
Sánchez, Ewin; Vega, Pedro (2018). "Modelling temporal decay of aftershocks by a solution of the fractional reactive equation".
1290:"Earthquakes Actually Aftershocks Of 19th Century Quakes; Repercussions Of 1811 And 1812 New Madrid Quakes Continue To Be Felt"
529:
are constants, which vary between earthquake sequences. A modified version of Omori's law, now commonly used, was proposed by
362:
850:
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
660:
399:. In some earthquakes the main rupture happens in two or more steps, resulting in multiple main shocks. These are known as
445:(where the rupture initiated) lay to one end of the final area of slip, implying strongly asymmetric rupture propagation.
1376:(October 2003). "Predictability in the Epidemic-Type Aftershock Sequence model of interacting triggered seismicity".
1028:"New Science update on 2011 Christchurch Earthquake for press and public: Seismic fearmongering or time to jump ship"
950:
905:
use tools such as the
Epidemic-Type Aftershock Sequence model (ETAS) to study cascading aftershocks and foreshocks.
539:
403:, and in general can be distinguished from aftershocks in having similar magnitudes and nearly identical seismic
110:
291:
1534:
471:
434:
433:
The pattern of aftershocks helps confirm the size of area that slipped during the main shock. In both the
158:
27:
856:
680:
668:
355:
336:
296:
878:
239:
234:
1289:
844:
438:
85:
632:
301:
268:
1268:
874:
324:
252:
125:
105:
100:
95:
655:
606:
is a third constant which modifies the decay rate and typically falls in the range 0.7–1.5.
1395:
1329:
1211:
1126:
1076:
348:
331:
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120:
37:
20:
8:
1529:
186:
63:
1399:
1333:
1215:
1130:
1080:
1436:"Testing of the foreshock hypothesis within an epidemic like description of seismicity"
1411:
1385:
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1171:
1092:
1066:
813:
793:
771:
750:
730:
400:
163:
130:
90:
1457:
1345:
1223:
1096:
891:
882:
851:
1415:
1175:
1447:
1403:
1357:
1337:
1320:
1219:
1163:
1134:
1084:
1006:
135:
1373:
915:
886:
462:
453:
Aftershocks rates and magnitudes follow several well-established empirical laws.
392:
153:
115:
663:(red dot) and aftershocks (which continued to occur after the period shown here)
53:
1167:
1088:
1523:
1461:
1293:
1112:"Generalized Omori law for aftershocks and foreshocks from a simple dynamics"
1238:
26:
This article is about the geological event. For other uses of the term, see
1349:
995:"The centenary of the Omori formula for a decay law of aftershock activity"
902:
415:
201:
1476:"Japanese researchers diagnose hundreds of cases of 'earthquake sickness'"
1452:
1435:
834:
In summary, there are more small aftershocks and fewer large aftershocks.
1407:
1390:
1192:(San Francisco, California, USA: W. H. Freeman & Co., 1958), page 69.
1011:
994:
974:
Utsu, T. (1961). "A statistical study of the occurrence of aftershocks".
530:
229:
196:
1341:
1261:"Present-Day Crustal Movements and the Mechanics of Cyclic Deformation"
615:
384:
376:
311:
191:
45:
1139:
868:
442:
388:
181:
75:
70:
1202:
BĂĄth, Markus (1965). "Lateral inhomogeneities in the upper mantle".
1071:
404:
306:
422:
19:"Aftershocks" redirects here. For the memoir by Nadia Owusu, see
943:
Journal of the
College of Science, Imperial University of Tokyo
643:
211:
206:
16:
Smaller earthquake which follows a larger one in the same area
396:
1057:
Guglielmi, A.V. (2016). "Interpretation of the Omori law".
441:, the aftershock distribution in each case showed that the
1494:"After the earthquake: why the brain gives phantom quakes"
448:
465:
in 1894 and is known as Omori's law. It is expressed as
1434:
Petrillo, Giuseppe; Lippiello, Eugenio (December 2020).
918:, and usually goes away as seismic activity tails off.
1317:
992:
873:
Some scientists have tried to use foreshocks to help
816:
796:
774:
753:
733:
683:
542:
474:
1236:
1371:
843:in a seismically quiet area; see, for example, the
822:
802:
780:
759:
739:
713:
591:
510:
1433:
684:
1521:
1239:"New Madrid fault system may be shutting down"
410:
993:Utsu, T.; Ogata, Y.; Matsu'ura, R.S. (1995).
877:, having one of their few successes with the
356:
1378:Journal of Geophysical Research: Solid Earth
747:is the number of events greater or equal to
1514:Earthquake Aftershocks Not What They Seemed
1153:
592:{\displaystyle n(t)={\frac {k}{(c+t)^{p}}}}
391:of the main shock, caused as the displaced
363:
349:
1451:
1389:
1138:
1070:
1056:
1010:
685:
1265:The San Andreas Fault System, California
837:
654:
642:
638:
421:
414:
661:Central Italy earthquake of August 2016
449:Aftershock size and frequency with time
1522:
1019:
1059:Izvestiya, Physics of the Solid Earth
933:
511:{\displaystyle n(t)={\frac {k}{c+t}}}
387:that follows a larger earthquake, in
1300:from the original on 8 November 2009
1201:
1109:
973:
1258:
1237:Elizabeth K. Gardner (2009-03-13).
1156:Applied Mathematics and Computation
1025:
936:"On the aftershocks of earthquakes"
13:
14:
1546:
1507:
1440:Geophysical Journal International
52:
1486:
1468:
1426:
1364:
1311:
1282:
1252:
1230:
1032:Christchurch Earthquake Journal
999:Journal of Physics of the Earth
714:{\displaystyle \!\,N=10^{a-bM}}
1195:
1182:
1147:
1103:
1050:
986:
967:
927:
577:
564:
552:
546:
484:
478:
456:
1:
921:
908:
862:
625:
1224:10.1016/0040-1951(65)90003-X
1119:Geophysical Research Letters
875:predict upcoming earthquakes
435:2004 Indian Ocean earthquake
7:
897:
411:Distribution of aftershocks
28:Aftershock (disambiguation)
10:
1551:
866:
857:1812 New Madrid earthquake
666:
647:Gutenberg–Richter law for
261:Coordinating Committee for
25:
18:
1168:10.1016/j.amc.2018.08.022
1089:10.1134/S1069351316050165
949:: 111–200. Archived from
292:Adams–Williamson equation
879:1975 Haicheng earthquake
240:Seismic intensity scales
235:Seismic magnitude scales
845:New Madrid Seismic Zone
439:2008 Sichuan earthquake
824:
804:
782:
761:
741:
715:
664:
652:
633:Moment magnitude scale
593:
512:
426:
419:
302:Earthquake engineering
1190:Elementary seismology
1188:Richter, Charles F.,
838:Effect of aftershocks
825:
805:
783:
762:
742:
716:
669:Gutenberg–Richter law
658:
646:
639:Gutenberg–Richter law
594:
513:
425:
418:
325:Earth Sciences Portal
297:Flinn–Engdahl regions
263:Earthquake Prediction
1408:10.1029/2003JB002485
1372:Helmstetter, Agnès;
1110:Shaw, Bruce (1993).
1012:10.4294/jpe1952.43.1
976:Geophysical Magazine
814:
794:
772:
751:
731:
681:
540:
472:
397:a consistent pattern
287:Shear wave splitting
21:Aftershocks (memoir)
1535:Types of earthquake
1480:The Daily Telegraph
1453:10.1093/gji/ggaa611
1400:2003JGRB..108.2482H
1342:10.1038/nature03377
1334:2005Natur.434..457M
1259:Wallace, Robert E.
1216:1965Tectp...2..483B
1131:1993GeoRL..20..907S
1081:2016IzPSE..52..785G
401:doublet earthquakes
187:Epicentral distance
1500:. 6 November 2016.
1038:on 29 January 2012
934:Omori, F. (1894).
892:strike-slip faults
820:
800:
778:
757:
737:
711:
665:
653:
589:
508:
427:
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164:Induced seismicity
111:Remotely triggered
1140:10.1029/93GL01058
883:East Pacific Rise
881:in China. On the
852:San Andreas Fault
823:{\displaystyle b}
803:{\displaystyle a}
781:{\displaystyle M}
760:{\displaystyle M}
740:{\displaystyle N}
659:Magnitude of the
587:
506:
373:
372:
1542:
1502:
1501:
1490:
1484:
1483:
1472:
1466:
1465:
1455:
1446:(2): 1236–1257.
1430:
1424:
1423:
1393:
1391:cond-mat/0208597
1374:Sornette, Didier
1368:
1362:
1361:
1315:
1309:
1308:
1306:
1305:
1286:
1280:
1279:
1277:
1276:
1267:. Archived from
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1250:
1249:
1247:
1246:
1234:
1228:
1227:
1199:
1193:
1186:
1180:
1179:
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1144:
1142:
1116:
1107:
1101:
1100:
1074:
1054:
1048:
1047:
1045:
1043:
1034:. Archived from
1023:
1017:
1016:
1014:
990:
984:
983:
971:
965:
964:
962:
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887:transform faults
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136:Earthquake swarm
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33:
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1541:
1540:
1539:
1520:
1519:
1516:at Live Science
1510:
1505:
1492:
1491:
1487:
1482:. 20 June 2016.
1474:
1473:
1469:
1431:
1427:
1384:(B10): 2482ff.
1369:
1365:
1328:(7032): 445–7.
1316:
1312:
1303:
1301:
1288:
1287:
1283:
1274:
1272:
1257:
1253:
1244:
1242:
1235:
1231:
1200:
1196:
1187:
1183:
1152:
1148:
1125:(10): 907–910.
1114:
1108:
1104:
1055:
1051:
1041:
1039:
1024:
1020:
991:
987:
972:
968:
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938:
932:
928:
924:
916:motion sickness
911:
900:
871:
865:
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463:Fusakichi Omori
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1508:External links
1506:
1504:
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1229:
1210:(6): 483–514.
1204:Tectonophysics
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1065:(5): 785–786.
1049:
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1294:Science Daily
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1271:on 2006-12-16
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1241:. physorg.com
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956:on 2015-07-16
952:
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903:Seismologists
895:
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858:
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848:
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830:are constants
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430:fault plane.
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389:the same area
386:
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1498:The Guardian
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1428:
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1381:
1377:
1366:
1325:
1319:
1313:
1302:. Retrieved
1284:
1273:. Retrieved
1269:the original
1264:
1254:
1243:. Retrieved
1232:
1207:
1203:
1197:
1189:
1184:
1159:
1155:
1149:
1122:
1118:
1105:
1062:
1058:
1052:
1040:. Retrieved
1036:the original
1031:
1026:Quigley, M.
1021:
1002:
998:
988:
979:
975:
969:
958:. Retrieved
951:the original
946:
942:
929:
912:
901:
872:
849:
841:
833:
788:is magnitude
723:
672:
648:
629:
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611:
608:
603:
601:
526:
522:
520:
460:
457:Omori's law
452:
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380:
374:
281:Other topics
86:Blind thrust
80:
269:Forecasting
230:Seismometer
224:Measurement
197:Shadow zone
46:Earthquakes
1530:Seismology
1524:Categories
1304:2009-11-04
1275:2007-10-26
1245:2011-03-25
1072:1604.07017
1042:25 January
982:: 521–605.
960:2015-07-15
922:References
909:Psychology
863:Foreshocks
626:BĂĄth's law
616:stochastic
385:earthquake
381:aftershock
377:seismology
312:Seismology
253:Prediction
192:Hypocenter
126:Supershear
106:Megathrust
101:Intraplate
96:Interplate
81:Aftershock
1462:0956-540X
1162:: 24–49.
1097:119256791
885:however,
869:Foreshock
701:−
533:in 1961.
443:epicenter
405:waveforms
182:Epicenter
159:Volcanism
121:Submarine
76:Foreshock
71:Mainshock
1416:14327777
1350:15791246
1298:Archived
1176:52813333
1005:: 1–33.
898:Modeling
437:and the
332:Category
307:Seismite
38:a series
36:Part of
1421:(ETAS).
1396:Bibcode
1358:4337369
1330:Bibcode
1212:Bibcode
1127:Bibcode
1077:Bibcode
724:Where:
131:Tsunami
91:Doublet
1460:
1414:
1356:
1348:
1321:Nature
1174:
1095:
602:where
521:where
212:S wave
207:P wave
148:Causes
1412:S2CID
1386:arXiv
1354:S2CID
1172:S2CID
1115:(PDF)
1093:S2CID
1067:arXiv
954:(PDF)
939:(PDF)
393:crust
379:, an
64:Types
1458:ISSN
1346:PMID
1044:2012
810:and
531:Utsu
525:and
116:Slow
1448:doi
1444:225
1404:doi
1382:108
1338:doi
1326:434
1220:doi
1164:doi
1160:340
1135:doi
1085:doi
1007:doi
375:In
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687:N
649:b
612:p
604:p
582:p
578:)
574:t
571:+
568:c
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550:t
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544:n
527:c
523:k
503:t
500:+
497:c
493:k
488:=
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482:t
479:(
476:n
364:e
357:t
350:v
30:.
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