aershocks, foreshocks, and mulplets : the science and ... · “there was a great shaking of the...
TRANSCRIPT
A"ershocks,foreshocks,andmul3plets:Thescienceandhistory
ofearthquakeclusteringKarenFelzer
USGS
“Therewasagreatshakingoftheearththismorning.Tablesandchairsturnedoverandknockedaround‐allofusknockedoutofbed.TheroarIthughtwouldleaveusdeafifwelived.Itwasnotastorm.whenyoucouldhear,allyoucoldhearwasscreamsfrompeopleandanimals.ItwastheworstthingthatIhaveeverwiInesed.Itwass3lldarkandyoucouldnotseenothng.Ithoughttheshakingandtheloudroaringsoundwouldneverstop.Youcouldnotholdontonothingneithermanorwomanwasstrongenough‐theshakingwouldknockyouloselikeknockinghicrornutsoutofatree.Idon'tknowhowwelivedthroughit..”–GeorgeHeinrichCrist,16December1811,Kentucky
WoodcutoftheNewMadrid
earthquake
"Whatarewegonnado?Youcannotfightitcauseyoudonotknowhow.Itisnotsomethingthatyoucansee.Inastormyoucanseetheskyanditshowsdarkcloudsandyouknowthatyoumightgetstrongwindsbutthisyoucannotseeanythingbutahousethatjustlaysinapileontheground‐notscaIeredaroundandtreesthatjustfallsoverwiththerootss3llonit.Theearthquakeorwhateveritiscomeagaintoday.ItwasasbadorworsethantheoneinDecember[….]Somethinksthatthisisthebeginningoftheworldcomingtoaend.”GeorgeHeinrichCrist,23January1812,Kentucky
TheMississippirivera7ertheNewMadridearthquakes
“Ifwedonotgetawayfromherethegroundisgoingtoeatusalive.Wehadanotheroneofthemearthquakesyesterdyandtodaythegrounds3llshakesat3mes.Weareallabouttogocrazy‐frompainandfright.Wecannotdoanythingun3lwecanfindouranimalsorgetsomemore.Wehavenotfoundenoughtopullhewagons.””–GeorgeHeinrichCrist,8February1812,Kentucky
TreesthrownoverbytheNedMadridearthquakes
NewMadridEarthquakeCluster
December16,1811,2:15 M6.7—6.9
December16,1811,7:15 M6.5—6.7
January23,1812,9:15 M6.5—7.0
February7,1812,3:45 M7.1—7.3
MagnitudesfromHoughandPage(2011)
Loca3onoftheNewMadridEarthquakes
MapfromhIp://hsv.com/genlintr/newmadrid
Closertohome:theLandersearthquakecluster
FigurebyAndrewFreed,takenfromOceanus
Morerecently:TheNewZealandCanterbury/Christchurchsequence
FigurebyRobLangridgeandWilliamRies,GNSScience
Closerin3me:theTohoku‐OkiJapan2011sequence
FigurebyC.J.Ammon,PennState
Tohoku‐Okia"ershocksequence
moviebyMorganPage
Earthquakeclustersarecommon
• ~10%ofallearthquakesoccurclosein3meandspacetoanotherearthquakeofsimilarmagnitude(withinonemagnitudeunit)
• >60%ofallearthquakesoccurasa"ershocks,foreshocks,ormul3plets
• Earthquakesclusterbecausetheoccurrenceofoneearthquaketriggersothers.
• Earthquakeclusteringcreatessignificantissuesforeffortstoforecastearthquakes.
Theworld’searthquakes
Shallowseismicity,1976‐2005,fromtheGlobalCMTproject
Mostearthquakesoccurwhereoneplatemovespastanother
Wherethetectonicplatesmeettheysome3mess3ck
StressesbuildunMlstress=strengthandthereissuddenmovementinanearthquake
Thismodelofhowearthquakesoccurisknownaselas3crebound
ThemodelwasformulatedbyHarryF.Reida"erobservingdisplacementsassociatedwiththe1906SanFrancisco
earthquake
Thetectonicplatesmoveataslow,constantrate
Soelas3creboundshouldallowustoeasilyforecastearthquake3mes
Theseismologist’s
dream
ButrepeatedaIemptstouseelas3creboundtoforecastearthquakeshave
notmetwithsuccess
TheParkfieldPredicMon:95%chanceofaM6earthquakebyJanuary1993(BakunandLindh,1985)
Reality:NoM≥6earthquakeun3l2004
Myhypothesis:Elas3creboundforecastsfailbecausetheshakingfromoneearthquakecancausecatastrophiclossinstrengthinloca3ons
onneighboringfaults
Thiscausesthestress=strengthrela3onshiptobesa3sfiedontriggeredfaultsmuchmorerapidly,andresultsinearthquakesoccurringinclustersratherthanatregularrepea3ngintervals
Housewithlossofstrengthduetoearthquake
shaking
Fault1
Howearthquaketriggeringusurpselas3creboundbasedforecas3ng
strength
strength
stress
stress
Fault2
Beforetriggering,Fault2shouldrupturefirst
Fault1
strength
strength
stress
stress
Fault2Eart
hqua
ke!!
Buta"eranearthquakeoccursnearFault1,itgoesfirst
So:Ourunderstandingofearthquakeclusteringmaybeourmostpowerful
forecas3ngtool
USGSSTEPa"ershockforecastfor4/28/2011
A"ershockforecastsaremadepossiblebythefactthata"ershocksaregoodatadheringtothesamesta3s3cal
distribu3onsin:• Time
• Magnitude
• Space
2005IncomeDistribu3on,from
VisualizingEconomics
IfIhadalonglistofrandomnames,theincomedistribu3ontellsmethat60%earn<$57,600,5%>$166,000,etc. Butthedistribu3ondoesn’ttellmewhichindividualsareinthattop5%,orwhoIshouldcallforabigdona3on!
Exampleofasta3s3caldistribu3on:IncomesintheUnitedStates
A"ershockdistribu3ons#1:Time
Thenumberofa"ershocksvariesas1/3me
Omori’slaw,Omori(1894)
Applica3onofOmori’slaw:Thefrac3onofthea"ershocksequence
thatisoveratdifferent3mes
10minutes 12%
1hour 21%
1day 49%
1week 73%
1year 95%
50years >99%
Note:Latelargea"ershocksdohappen!
TheM7.1HectorMinea"ershockoccurred7
yearsa"ertheM7.3Landersmainshock
A"ershockdistribu3ons#2:Magnitude
ChinoHill,M5.4
Japan,M9.0
Thedistribu3onofa"ershockmagnitudesisthesameasthedistribu3onofallearthquakemagnitudes,world‐wide
Theworld’searthquakes,1975‐2005 Datafrom
theGlobalCMT
catalog
TheGutenberg‐Richterdistribu3on
Foreach10earthquakesofmagnitudeM,thereis1eqofmagnitudeM+1
ChinoHill,M5.4 Christchurch,M6.3
A"ershockmagnitudedistribu3onisindependentofmainshockmagnitude
Some3mesana"ershockislargerthantheearthquakethattriggeredit,whichisthen
renameda“foreshock”
Gutenberg‐Richter
distribuMon
Largermainshocksdohavelargera"ershocksonaveragebecausethey
havemorea"ershocks
MainshockmagnitudeAveragenumberofa7ershocksM≥3.5
M6 20
M7 200
M8 2,000
M9 20,000
Havingmorea"ershocksproducesalargerprobabilityoftriggeringalargeone
Analogy:LargeearthquakesbuymoreloIery3ckets,sohavealargerchanceof“winning”
Probabilitydistribu3onforthelargesta"ershockmagnitude
Themeanmainshockmag–largesta"ershockmag=1.2(Båth’slaw,Båth,(1965)
Example:Expecta3onsforthelargesta"ershocka"eranM7earthquake
Largesta7ershock Probability
M>8 0.5%
M>7 5%
M>6.5 12%
M>6 31%
M>5.7 53%
M<5.0 2%
Asmallerearthquaketriggeringalargerone:examplefromJapan
• AM7.2foreshockoccurredonMarch9,twodaysbeforethemainshock.
ForeshocksMainshock
• Duringanaverageweek,thechanceofaM9somewherenearJapanis~1in50,000
• A"eranyM7.2weknowthattheprobabilityofanM9occurring(becauseitmaybetriggered)risesto1in1000(503mesmoreprobablethanusual).
Useofthisinforma3onwouldresultin999falsemassevacua3onspersuccess
Evacua3onfromHurricaneRita
Wecan’tdoanybe_erbecausewedonotknowwhichindividualearthquakeswillbelarge.Whycan’twefigurethisout??
FigurebyCharlesAmmon
Allearthquakesactuallystartor“nucleate”ata3nypointonafault,
knownasthehypocenter
Faultslipoccursatthehypocenter,whichtriggerssurroundingfaulttoslipnext.Theearthquakegrowsasthetotalareaand
amountoffaultslipgetslarger.
FigurebyKianH.Chong
Asearthquakespropagate,however,theyencountermanybarriersonthefaultthattry
tostopgrowth
Asaresultmostearthquakesonlyruptureasmallareaofthefault.Theyproducea3nyamountofshakingand
arenotfelt.
DatafromtheGlobal
CMTcatalog
TheGutenberg‐Richterdistribu3on
Mostearthquakesaresmall
Afewearthquakesmanagetoovercometheoddsandproducelargeslipoveralargearea,anddevasta3ngshaking.
1980,ElAsnam,Algeria,M7.3
ImagefromNOAAwebsite
Importantforourstory:Triggeringoccursatthehypocenter.Atthispointsmallandlarge
earthquakesarethesame
Howlargetheearthquakebecomesistheresultofcomplexdynamicinterac3onsa"er
theini3altriggering
Thetriggeringcascade
• Karen’smodel:Themainshockweakensasmallfaultarearightaroundthehypocenter.
• Dynamicwavesproducedbyruptureatthehypocenterweakenssurroundingfaultarea.
• Iftherupturespreads,addi3onalfaultisweakenedbytheaddi3onaldynamicwaves.
• Howfarthisprocesswillcon3nuebeforeitisstoppedcannotbean3cipated.
Howlargeanearthquakewillgrowisaspredictableasflippingpennies…
Youflipapenny1003mes.Oneachflipthereisanequal50%chanceof
ge�ngheads
Earthquakesize~numberofheadsinarow
Smallevents
Largeevent
Ge�ngalargeeventisunlikely‐‐butithappensunderthesamestar3ngcondi3onsassmallerevents
PutinCalPolyanima3on
A"ershockdistribu3ons#3:Distance
OldMilestone
Thedensityofa"ershocksdecaysas~1/distancefromthemainshockfaultplane
8656M1—2NorthernCalifornia
mainshocksfromtheNCSNcatalog,notprecededbylargereventfor3days/200km
Earthquakesofallmagnitudesproducea7ershocksouttodistancesof≥50‐‐100km(FelzerandBrodsky,2006)
Putonownslide
M≥7earthquakestriggerseismicityworldwide
EarthquakestriggeredinNorthAmericabytheDenali,Alaskaearthquake
(Gombergetal.,2004)
DistantearthquaketriggeringcanbedetectedfromincreasesintheamountofcataloguedseismicityatdifferentlocaMons
Distanttriggeringby
the1992M7.3Landers
earthquake,fromHilletal
(1993)
TriggeringatMt.RanierbysurfacewavesoftheDenaliearthquake,fromPrejeanetal.(2004).
Thetriggeringcanalsobeobservedbyhighfrequencyfilteringofseismogramsatdistant
loca3ons
Distanttriggeringprobablyrepresentsadifferentphysicalprocessthan
a"ershockzonetriggering• Distanttriggeringoccursataverylowrate.Stresschangeisbothverylowatdistance,andappearstobelesseffec3veattriggeringseismicitythanitisinthenearfield(VanDerElstandBrodsky,2010).
• Distantlytriggeredearthquakesshowastrongpreferenceforvolcanicandgeothermalareas.
• Theoccurrenceofdistanttriggeringissta3s3callysignificantonlyforsmall(M<5)earthquakes(Michael,2010;ParsonsandVelasco,2011).
Therearesomeen3cingexamplesoflargefarapartearthquakesoccurring
closetogetherin3me
• 1901:August9,M~8earthquakesinVanuatuandtheKurilesseparatedby5hours.
• 1902:M~8earthquakesoffoftheMarianasandMexicoseparatedby1day.
• 1906:M~8earthquakesintheAleu3ansandChileseparatedby30minutes.
• 2004:M8.1northofMacQuarieIslandsandM9.0Sumatraearthquakeseparatedby3days
4/29/11 1:01 PMAleutians West, Alaska to Sumatra - Google Maps
Page 1 of 1http://maps.google.com/maps?f=d&source=s_d&saddr=Aleutians+West,…irflg=d&ll=-1.757537,-151.875&spn=135.33682,286.171875&z=2&pw=2
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©2011 Google -
We could not calculate directions between Aleutians West, Alaska and Sumatra.
Aleu3ans
Chile
Sumatra
MacQuarieIslands
Ithasseemedlikewearecurrentlyinaglobal“mega‐cluster”
Butthenumberoflargeearthquakesthathaveoccurredsofar,outsideofeachother’sa"ershockzones,arealso
consistentwithpurelyrandomoccurrence
Conclusions
• >60%ofallearthquakesoccurasa"ershocks,foreshocks,ormul3plets.Earthquakesclusterbecausetheoccurrenceofoneearthquaketriggersaddi3onalearthquakestooccur.
• Wehavegoodconstraintsonthehowmanyearthquakeswillturnouttobeforeshocks,butnowaytoknowaheadof3mewhichoneswillbeforeshocks.
• Mostearthquaketriggeringoccursoververyshortdistances,butsometriggeringoververylargedistancesalsooccurs.Whetherlargeearthquakescanbetriggeredthiswayhasyettobedetermined.
Tofindapossibleanswer,weinspectsomea"ershockandearthquake
conundrums
Conundrum#1:Thesta3cstresstransferredfromthemainshockis<<thana"ershockstressrelease
Soitseemsthatthea"ershockswereabouttogoontheirown–butthisisinconsistentwithhowmanyearthquakesarea"ershocks
Conundrum#2:Theaveragefaultshouldneed>60MPaofshearstressbeforeanearthquake
FigurebyCharlesAmmon
7kmofoverlyingrockandwater=100MPax0.6coefficientof
fric3on
buttheshearstressonmostfaultsatruptureisonly~10MPa(e.g.HardebeckandHauksson,2001)
Karen’ssoluMon:
FigurebyCharlesAmmon
Shakingfromthemainshockcan
severelyweakenMnyvolumes,allowingearthquakestostartunderlowstress
=>Thereisalongperiodof3meduringwhichafaultisfarfromthestressthatwouldallowittorupture
spontaneously,butmayruptureiftriggered
Analogy:Thisbuildingmayhavetakenalong3metofalldownwithoutanearthquake
buta"erseismicshakingas3ffbreezemightcausemoredamage
Hottopicsinearthquakeclustering:
Canwepredictwhichearthquakeswillbeforeshocks?
ExamplefromJapan• AM7.2foreshockoccurredonMarch9,twodaysbeforethemainshock.
ForeshocksMainshock
• Duringanaverageweek,thechanceofaM9somewherenearJapanis~1in50,000
• A"eranyM7.2weknowthattheprobabilityofanM9occurring(becauseitmaybetriggered)risesto1in1000(503mesmoreprobablethanusual).
• Theoccurrenceofanyearthquakewarrantsheightenedawarenessthatalargerquakemightfollow(eachearthquakehasa~5%chanceoftriggeringsomethinglargerthanitself).
• Buttheprobabilitythatarandomearthquakewillbeaforeshockisgenerallytoolowtojus3fymasspublicac3ons.
Conclusions
• Earthquakeclusteringiscommon.>60%ofallearthquakesoccurasa"ershocks,foreshocks,ormul3plets.Earthquakesclusterbecausetheoccurrenceofoneearthquaketriggersaddi3onalearthquakestooccur.
• Themajorityoftriggeredearthquakesoccurclosein3meandspacetotheirtrigger.
• Wehavegoodconstraintsonthehowmanylargeearthquakeswillbetriggeredovermanysequences,butnowaytosaywhichpar3cular3mes,loca3ons,orsequenceswillcontaintheseevents.
A"ershockmagnitudedistribu3onisindependentofmainshockmagnitude
Hilletal.1993
EvidenceforStaMsMc#2:A"ershockmagnitudedistribu3onsareindependentofmainshockmagnitude
A"ershockstakenfrom2days/5kmaroundeachmainshock.3,200a"ershocksineachdistribu3on
Gutenberg‐Richterdistribu3on
Foreshockratescanbeaccuratelypredictedfromtherateofa"ershocks
smallerthanthemainshock1. No.a"ershocks≥M=F(Mmain)10‐bM
2. F(Mmain)~10Mmain‐1.3inCalifornia,fora"ershockswithin1dayand1faultlengthofmainshock;b=1.
GRdistribu3on
Predictedratethatanearthquakewillproduceana"ershocklargerthanitselfwithinoneday:
=10Mmain‐1.3‐M=10Mmain‐1.3‐Mmain=0.050
Observedrate:0.047+‐0.0054
(6,086M≥3Californiaearthquakes,1984‐2004)
SouthernCaliforniaM1.8—4.0mainshocks(alldepths)produce0.254—0.259M≥1.8
a"ershocks/M=3mainshockinthefirsthour
Thecalcula3onusesatotalof17,021mainshocksfromthe1984‐2009SCSNcatalogthatarenotprecededbyalargerearthquakeover3days/100km.Thereare3199a"er‐
quakes,156—203ofwhichmaybebackgroundearthquakes.
No:A"ershocktriggeringat<150kmwheremainshock‐inducedsta3cstresschangesare3ny
suggestthatthesestressesarenotneeded
8656M1—2NorthernCalifornia
mainshocksfromtheNCSNcatalog,notprecededbylargereventfor3days/200km
Theproblemisthattheearthquakeruptureprocessisverycomplex,sowhetherornotanearthquakewillcon3nuetogrowpastanygivenpointcanonlybe
givenbyaprobability,notacertainty.
Alterna3ve:The“HaroldLloyd”ModelBinary,notpropor3onal,stressresponse
Op3on1:S3ffclockorlightHarold=>noclockadvance
Op3on2:Thehandgiveswaymaximumclockadvance
IfHaroldisheavier,aclockadvanceismorelikely
ButHarold’sweight≠clockadvancesize
TheGutenberg‐Richtermagnitudefrequencyrela3onship
1976‐2005GlobalCMTcatalog
log(N)=a‐bM
Slope=b=1.0
“Earthquakepredic3onprovidesahappyhun3nggroundforamateurs,cranks,andoutrightpublicity‐seekingfakers."
‐CharlesRichter
Landersmainshock:Groupsof200a"ershocksatdifferentdistancesshowthesamenumberofa"ershocks/day
KolmogorovSmirnoffTest:Alldistribu3onssimilarat95%confidence
4.5 5 5.5 6 6.5 7 7.50
10
20
30
40
50
60
70
mainshock ML
Num
ber
of fo
resh
ocks
2.2
ML
4.5 r = 0.0715
4.5 5 5.5 6 6.5 7 7.50
1
2
3
4
5
6
7
8
9
10
mainshock magnitude
radi
us o
f for
esho
ck c
lust
er, i
n km r = -0.06
0 2 4 6 8 100
5
10
15
foreshock zone radius
frequ
ency
of o
ccur
renc
e(A)
(B)Foreshocksareeventswithin10km,2days
1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -310-5
10-4
10-3
10-2
10-1
100
Mainshock ML - Aftershock ML (!1 " !2)
Afte
rsho
cks/
mai
nsho
ck
aftershock > mainshockaftershock <mainshock
"aftershocks" "foreshocks"
predicted relationship
Figureuses101,680M>2.2earthquakesfromCalifornia,1975‐2001
Earthquakeclusterdefini3ons
• A7ershock:Anearthquakethatfollowsalargerearthquake.
• MulMplet:Anearthquakethatoccurswithotherearthquake(s)ofsimilarmagnitude.
• Foreshock:Anearthquakethatprecedesalargerearthquake.
• Swarm:Therapidoccurrenceofaseriesofearthquakesofsimilar,andgenerallysmall,magnitude(usuallygeothermal/volcanic).
outline
• Theonlyshorttermpredictabilityofearthquakesisthattheytendtooccurinclusters
• Somehowthestressreleasedbyoneearthquakeencouragesotherstooccurinasta3s3callypredictablefashion.Infact,atleast60%ofearthquakesoccurthisway–andpossiblymanymore.Itmightbeverydifficultforanearthquaketonucleatewithoutstressingfromapriorevent,becauseoftotalstressdropvs.highnormalstressatdepth.
• Butnotalllargeearthquakesarefollowedbyotherlargeearthquakes.Therulesofnumbersandchance,addingupto100%ifallearthquakeswerea"ershocks.
• WhatcanIexpectinana"ershocksequence:Thea"ershocksequence,closeandfar,powerlawdecay,magnitudeindependencewith3me,thenearnessfactor,mgasatura3on,whatcanIexpecttofeel,thedistanttriggeredevent–gobacktooriginalsequencesforthis.
• Howforeshockscomeintotheequa3on,thepostdic3onillusion,thelandersstory• Rehash–whatwecanforecast,whataretheabsolutelimita3ons,whyclusters
maIertoyou.
60MPa
60MPa
60MPa
Analogy:Abunchofturtlesareonalongrace.Theycanfinishbyploddingthewholewayortakingaridefroma
birda"erthey’vegoneatleast10"
Ifthebirdcomesbyfrequentlyenoughmostturtleswillenduptakingaride–likemostfaultswillbetriggeredwhiletheirstressiss3lllowratherthan
remainingsta3onaryun3lhighstresscanaccumulate
Cangetaride
Cangetaride
Cangetaride
Whatdoesitmeanto“knowadistribu3on”?
2005IncomeDistribu3on,from
VisualizingEconomics
IfIhadalonglistofrandomnames,theincomedistribu3ontellsmethat60%earn<$57,600,5%>$166,000,etc. Butthedistribu3ondoesn’ttellmewhichindividualsareinthattop5%,orwhoIshouldcallforabigdona3on!
A"ershocksta3s3csthatweknow
• ThedistribuMonofa"ershock3mes• ThedistribuMonofa"ershockmagnitudes
• Theprobabilitythatana"ershockwillbelargerthanit’smainshock
• ThedistribuMonofa"ershockloca3ons
ApplyingOmori’sLawExample#1:AveragenumberofM≥3.5a"ershocksa"eranM6.5mainshock
0–10minutes 8(48/hour)
10minutes–1hour 5‐6(6.8/hour)
1hour–1day 19(0.8/hour)
1day–1week 16(0.11/hour)
1week–1year 14‐15(0.002/hour)
1year–50years 3‐4(0.000008/hour)
• Karen’ssolu3onismo3vatedbythefindingofHardebeckandHauksson(2001)thattheshearstressonfaultstendstobe<<ordinaryfaultstrengthattheMmeofrupture
• Thissuggeststhatsomethingmaybecausinganunusualdecreaseinfaultstrengthrightbeforeruptureoccurs
Thesta3cstresstransferredtomosta"ershocks<<stressreleasedbythea"ershock
Whatisgoingon?