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

Loading...

©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?