Discrimination between induced, triggered, and natural earthquakes close to hydrocarbon reservoirs

20 Pages·2015·1.85 MB·English

by  Torsten Dahm

Originally published as:

Dahm, T., Cesca, S., Hainzl, S., Braun, T., Krüger, F. (2015): Discrimination between induced, triggered, and natural
earthquakes close to hydrocarbon reservoirs: A probabilistic approach based on the modeling of depletion-induced
stress changes and seismological source parameters. - Journal of Geophysical Research, 120, p. 2491-2509.

DOI: http://doi.org/10.1002/2014JB011778
JournalofGeophysicalResearch:SolidEarth
RESEARCHARTICLE Discrimination between induced, triggered, and natural
10.1002/2014JB011778 earthquakes close to hydrocarbon reservoirs:
A probabilistic approach based on the
KeyPoints:
•Novelprobabilisticdiscriminationfor modeling of depletion-induced stress
induced,triggered,andnaturalEQ
•Demonstratemethodwiththree changes and seismological
applications
•Studyisofrelevancetoacademia, source parameters
industry,andpublic
TorstenDahm1,2,SimoneCesca1,2,SebastianHainzl1,ThomasBraun3,andFrankKrüger2
Correspondenceto:
T.Dahm, 1GFZGermanResearchCentreforGeosciences,Potsdam,Germany,2InstitutfürErd-undUmweltwissenschaften,
[email protected] UniversitätPotsdam,Germany,3IstitutoNazionalediGeofisicaeVulcanologia,Seismology&Tectonophysics,Arezzo,Italy
Citation: AbstractEarthquakesoccurringclosetohydrocarbonfieldsunderproductionareoftenundercritical
Dahm,T.,S.Cesca,S.Hainzl,T.Braun,
andF.Krüger(2015),Discrimination viewofbeinginducedortriggered.However,clearandtestablerulestodiscriminatethedifferentevents
betweeninduced,triggered,and haverarelybeendevelopedandtested.Theunresolvedscientificproblemmayleadtolengthypublic
naturalearthquakesclosetohydro-
disputeswithunpredictableimpactonthelocalacceptanceoftheexploitationandfieldoperations.We
carbonreservoirs:Aprobabilistic
approachbasedonthemodelingof proposeaquantitativeapproachtodiscriminateinduced,triggered,andnaturalearthquakes,whichis
depletion-inducedstresschanges basedontestableinputparameters.Maximaofoccurrenceprobabilitiesarecomparedforthecasesunder
andseismologicalsourceparameters,
question,andasingleprobabilityofbeingtriggeredorinducedisreported.Theuncertaintiesofearthquake
J.Geophys.Res.SolidEarth,120,
2491–2509,doi:10.1002/2014JB011778. locationandotherinputparametersareconsideredintermsoftheintegrationoverprobabilitydensity
functions.Theprobabilitythateventshavebeenhumantriggered/inducedisderivedfromthemodeling
ofCoulombstresschangesandarateandstate-dependentseismicitymodel.Inourcasea3-Dboundary
Received17NOV2014
Accepted5MAR2015 elementmethodhasbeenadaptedforthenucleiofstrainapproachtoestimatethestresschangesoutside
Acceptedarticleonline10MAR2015 thereservoir,whicharerelatedtoporepressurechangesinthefieldformation.Thepredictedrateof
Publishedonline13APR2015 naturalearthquakesiseitherderivedfromthebackgroundseismicityor,incaseofrareevents,froman
estimateofthetectonicstressrate.Instrumentallyderivedseismologicalinformationontheeventlocation,
sourcemechanism,andthesizeoftheruptureplaneisofadvantageforthemethod.Iftheruptureplane
hasbeenestimated,thediscriminationbetweeninducedoronlytriggeredeventsistheoreticallypossibleif
probabilityfunctionsareconvolvedwitharupturefaultfilter.Weapplytheapproachtothreerecentmain
shockevents:(1)theM 4.3Ekofisk2001,NorthSea,earthquakeclosetotheEkofiskoilfield;(2)theM 4.4
w w
Rotenburg2004,NorthernGermany,earthquakeinthevicinityoftheSöhlingengasfield;and(3)theM 6.1
w
Emilia2012,NorthernItaly,earthquakeinthevicinityofahydrocarbonreservoir.Thethreetestcasescover
thecompleterangeofpossiblecauses:clearly“humaninduced,”“notevenhumantriggered,”andathird
caseinbetweenbothextremes.
1.Introduction
Theproblemofinducedandtriggeredearthquakesandthediscriminationbetweennaturaland
human-relatedearthquakesisold.Alreadyin1908thefirstlocalseismicnetworkwasestablishedinBochum
intheRuhrarea,Germany,tomonitorpossibleinducedearthquakesrelatedtocoalmining[see,e.g.,
McGarretal.,2002].Sincethen,strongereventsinducedortriggeredbycoalmininginGermanyreached
magnitudesofM 4.2[e.g.,Cescaetal.,2013a;Dahmetal.,2010,andreferencestherein].Themostsevere
L
inducedearthquakesinGermany,however,wererelatedtopotashmining(M 5Heringen/Widdernhausen
L
1953,M 5.2Sünna/Werra1975,M 5.5Völkershausen1989,andM 4.9Teutschenthal/Halle1996)[see
L L L
GrünthalandMinkley,2005,andreferencestherein]andtoconventionalgasproduction(e.g.,M 4.4
W
Rotenburg2004[seeDahmetal.,2007]).Worldwide,evenlargerhuman-triggeredearthquakeshavebeen
discussed,amongwhichseveralM > 6earthquakesincludeeventsinvicinitytohydrocarbonreservoirs
(see,e.g.,McGarretal.[2002]forahistoricalreview)andartificialwaterreservoirs(e.g.,1967M6.3Koyna
earthquake,India[Gupta,2002]).Thepossiblehumaninfluenceforsuchdamagingearthquakescloseto
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geotechnicaloperationsoftenleadstolongdisputesbetweenseismologists,thepublic,andstakeholders
fromindustry,especiallysincecommonlyacceptedrulesforthediscriminationbetweenhuman-induced
andnaturalearthquakesdonotactuallyexist.
Inordertotacklethediscriminationproblem,usually,thetemporalandspatialcorrelationofearthquakesto
regionsundergeotechnicalactivitiesisinvestigated.Iftheeventis”closeenough”and”occurredwithinthe
periodofhumanactivity,”itisassumedtoberelatedtotheactivity.However,acleardefinitionof”closeness”
or”period”isnotestablished.Suchadefinitionshouldconsider,atleast,thetypeandthesizeoftheregion
affectedbythegeotechnicaloperationaswellasthesizeoftheruptureplane.
AnotherqualitativediscriminationapproachhasbeensuggestedbyDavisandFrohlich[1993]forfluid
injectionandbyDavisetal.[1995]forfluidwithdrawal,whereeithersevenornineYES-NOcriteriaare
assessed.Thequestionsinvestigatethebackgroundseismicity,theuniquenessoftheoccurrenceatthe
givenposition,theclosenesstothefieldactivityandactivityperiod,thecorrelationbetweenseismicityand
withdrawal,andthepossiblephysicalmechanism.IfmorethanhalfofthequestionsareansweredbyYES,
theeventisconsideredtobelikelyinduced.Althoughsuchadiscriminationapproachisstillqualitative,
italreadyinvolvesakindofBayesianapproachtocombineexpertopinionsanddifferentaspectsofthe
complexproblem.
However,suchweakdefinitionsandweakregulationsmaybehandableifenoughhuman-relatedseismicity
occurredinotherwisenontectonicregionswithnearlynoseismicity,as,e.g.,NorthGermany,sothatclear
statisticalcorrelationscanbeassessed.Moredifficultdiscriminationproblemsmayariseifthegeotechnical
operationsaresituatedintectonicallyactiveregions.There,earthquakesoftectonicoriginmayhavesimilar
epicentersthanthosecausedbyhumaninfluence,andtheYES-NOquestionsmaynotbesufficientto
adequatelyhandletheproblem.ThePoPlainandtheAdriaticsedimentarybasininNorthernItalymaybe
anexample,amongothers,whereoilandgasfieldshavebeenexploitedinaregionwherenaturaltectonic
earthquakeshavefrequentlyoccurred.
Thediscriminationproblemisevenmoredifficultifhuman-triggeredandhuman-inducedearthquakesare
distinguished(fordefinitions,seeMcGarr[1991],Bossu[1996],McGarrandSimpson[1997],Gupta[2002],
Dahmetal.[2013],Cescaetal.[2013b,2014],andShapiroetal.[2013]).Weuseadefinitionfortriggered
andinducedeventssimilartoMcGarrandSimpson[1997]andShapiroetal.[2013]butfurtherspecifiedin
termsofgeometricalconsiderations[seealsoDahmetal.,2013].AccordingtoMcGarrandSimpson[1997],
inducedearthquakesarecommonlyunderstoodaseventswheremostofthestresschangereleasedduring
rupturewasproducedbythehumanaction,whiletriggeredeventsreleaseasubstantialamountoftectonic
stress.McGarrandSimpson[1997]alsopointoutthegeneralmotivationforsuchadistinction:triggered
eventsoftenhaveadifferentfrequencymagnitudedistributionandadifferenthazardincomparisonto
inducedones.Onlyforsomefewtypesofhumanactions,as,e.g.,pureinjection,thedistinctionispossibly
notneededsincealleventsarealwaystriggeredandnotinduced[Gupta,2002;Ellsworth,2013].
Recently,probabilisticdiscriminationcriteriahavebeensuggestedinordertodevelopclear,quantitative,
andtestablediscriminationrules[e.g.,Cescaetal.,2013a;Dahmetal.,2013;Passarellietal.,2013].Our
contributionreferstothislineofresearchanddevelopsaprobabilisticdiscriminationschemeforthe
problemofconventionalproductionofoilandgasfieldsanddepletion-inducedanddepletion-triggered
earthquakes.Themethodisbasedonphysical-statisticalseismicitymodels.Itconsiderstheuncertaintyin
earthquakelocationandotherinputparametersanddistinguishesbetweennatural,human-triggered,and
human-inducedearthquakes.Themethodisdemonstratedandtestedforthreeexamples:(1)the2001M
W
4.3Ekofisk,NorthSea,oilfield-inducedearthquake;(2)the2004M 4.4Rotenburg,NorthernGermany;and
W
(3)the2012M 6.1Emilia,NorthernItaly,gasfield-relatedearthquakes(Figure1).
W
2.Method
Weassumethatanearthquakeoccurrednearanoilorgasfieldthatcontinuouslyproducedoveraperiod
ofseveralyearsandisdepleted.Thepurposeoftheschemeistoevaluate(estimate)theprobabilitythat
theearthquakehasbeenhumantriggeredorhasbeenhumaninduced.Weuseadefinitionof”triggered”
and”induced”suggestedbyDahmetal.[2010,2013]andsimilartoMcGarrandSimpson[1997]but
specifying—forreasonsgivenbelow—theportionoflargestressreleaseontheruptureplane,instead
ofusinganintegralvalueonly.SuchadefinitionissimilartotheonebyShapiroetal.[2013].Triggered
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Figure1.Overviewplot.Earthquakesunderstudyaredeclaredasredfilledcircles.Dashedpolygonsindicate
seismogeniczones[seeGrünthaletal.,2010;Bungumetal.,2000;Giardinietal.,2013].Greyfilledcircles(size
scaledbymagnitude)indicatetectonicearthquakespriortothestudiedevents(M >4.5from1000to2006,
W
European-MediterraneanEarthquakecatalogue[seeGrünthalandWahlström,2012]).(a)TheNorthSeaandNorthern
Germanyarea.Gasandoilfieldsareindicatedbycoloredfilledpolygons(grey=Carbon,red=Rotliegend,green=
Zechstein,yellow=post-Zechstein).Human-relatedearthquakes(1986–2012,M>3)closetofieldsareplottedbylight
redfilledcircles(cataloguesprovidedbyBGRHannover,Germany,andtheRoyalNetherlandsMeteorologicalInstitute,
DeBuilt,Netherlands).(b)TheNorthernItalyarea.TheCavoneoilfieldisindicatedbythecoloredpolygon.Thedashed
linedepictstheareaofthezoneITAS293.
isunderstoodinthesensethattheruptureinitiationwascausedbythedepletion-inducedstressrate
atthehypocenteroftheearthquake.Ruptureinitiationistestedbystudyingthe“humaninfluence”at
thehypocenter.Aninducedearthquakeisunderstoodinthesensethattherupturewasdrivenbythe
depletion-inducedstressoverthefullruptureplane,which,forinstance,foraM 6crustalearthquakemay
W
easilyreachadimensionofabout10km×10km[e.g.,WellsandCoppersmith,1994;Blaseretal.,2010].
Wefurtherassumethataseismologicalstudyhadbeenperformed”apriori”andthatboththehypocenter
orcentroidlocationincludingitsuncertainty(e.g.,1𝜎errorellipsoid)andthesourcemechanismofthe
earthquakeareknown.Ifpossible,alsothefaultandauxiliaryplaneanditsrespectiveuncertaintiesshould
havebeenidentifiedapriori.
Wespecificallyassumetwoperiodsofsteadystateconditionswithinarockvolumewithlineardimension
significantlylargerthantheruptureplane.Thereferenceperiodisbeforetheproductionhasstarted,where
aconstanttectonicstressrate𝜏̇T isactingonthefaultplaneofthestudiedearthquakeinrakedirection
ofthemomenttensorsolution(e.g.,definedasCoulombstressrate).Thebackgroundstressisrelatedto
aconstantrateofearthquakes(backgroundeventrate),rT,e.g.,expressedbytherateandstateseismicity
modelbyDieterich[1994].ThevaluerT isdefinedforagivenmagnitude(interval).Itcanbeestimatedfrom
thenumberof(similar)tectoniceventsperunitareaandtimeinterval.Kostrov[1974]establishedalinear
relationbetween𝜏̇T andrT byexploiting𝜏̇T ∼ ⟨M ⟩rT∕V,where⟨M ⟩isthescalarvalueofsummedseismic
0 0
momenttensorsdividedbythenumberofearthquakesandVtheseismogenicvolume[Catallietal.,2008;
Hainzletal.,2010].Assumingthatthefocalmechanismsaresimilar,⟨M ⟩canbeestimatedbyintegration
0
oftheproductofthescalarseismicmomentandtheprobabilitydensityforagivenmagnitudedistribution.
HereweassumeadoublytruncatedGutenberg-Richterdistribution.Thenhavingtheinformationofannual
earthquakerate10aofM≥0events(i.e.,theavalue),thebvalue,themaximummagnitudeM ,andthe
max
areaoftheseismogeniczoneAaswellastheseismogenicwidthD,thebackgroundshearstressrate𝜎̇T is
S
[e.g.,Hainzletal.,2010]
𝜎̇T =⟨M ⟩10a−bMmin =10a+9.1 b 10(1.5−b)Mmax −10(1.5−b)Mmin 1
S 0 AD 1.5−b 1−10−b(Mmax−Mmin) AD
lim 𝜎̇T =10a+9.1 b 10(1.5−b)Mmax (b<1.5) (1)
Mmin→−∞ S 1.5−b AD
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Table1.ParameterDefinitionsandNomenclaturea
Parameter Description
p (x)andp(𝜽) probabilitydensitydistributionoftheearthquakelocationandthe
e
modelinputparameter,respectively
r(x,𝜽),rT(x,𝜽), earthquakerate:total,tectonicbackground,anddepletioninduced,
andrD(x,𝜽) respectively
𝜏̇(x,𝜽),𝜏̇T(x,𝜽), Coulombstressratesonthefaultplaneindirectionofobservedslip:
and𝜏̇D(x,𝜽) total,tectonicbackground,andfielddepletion,respectively
pD(x,𝜽)and triggerpotentialofbeingcausedbyfielddepletionortectonic
pT(x,𝜽) stressing,respectively
P andP averageprobabilitythattheeventwasdepletiontriggeredor
trig ind
depletioninduced,respectively
aAll rate and event numbers are defined per unit volume for a given magnitude
interval,M≥M .
c
withunits(Pa/y)ifAandDaregiveninunitsofm2andm,respectively.ThetectonicCoulombstressrate
employedisthen
( ) [ ( ) ] ( )
𝜏̇T = 𝜎̇T +𝜇 𝜎̇T −Ṗ = n̂ × T×n̂ ⋅𝚫û +𝜇 T⋅n̂ −Ṗ , (2)
S N f f
whereT = 𝜎 n̂,𝝈istheregionalstresstensorandn̂ and𝚫û arethenormalandslipunitvectorsofthe
i ij j
ruptureplane,respectively,P istheporepressureintherockand𝜇isthefrictionangleintheCoulomb
f
failurelaw.
Ifthetectonicsurfacedisplacementfieldhasbeenaccuratelymeasured,andthecouplingoftheplateis
sufficientlywellknown,𝜏̇Tmayalternativelybeestimatedfromstrainrates.
Thesecondperiodunderconsiderationisdefinedsomeyearsafterthestartofoilorgasrecoveryuntil
theoccurrenceoftheevent.Mostoften,theannualproductionratesareroughlyconstantafterthe
infrastructuresareinstalled.Weuseaconstantdepletionrateforsimplicity.If𝜏̇Disthedepletion-induced
Coulombstressrateonthefault,thetotalactingstressrateis𝜏̇ = 𝜏̇T +𝜏̇D.Accordingly,theexpectedtotal
earthquakerateinthevolumeunderconsiderationisr = rT +rD.Usually,rT isasmoothfunctionofspace,
whilerDand𝜏̇Darevariablefunctionsofspace,decayingtozeroifthefaultisfarfromtheexploitedfield.
EmployingtheDieterichseismicitymodel[e.g.,Dieterich,1994,1995]understeadystateconditions,itiseasy
toshowthat
r 𝜏̇ rD 𝜏̇D
= andaccordingly = . (3)
rT 𝜏̇T rT 𝜏̇T
Wewillusethisrelationtogetherwith(2)toderiverDandrandtodefineatriggerprobability.Forinstance,
thedepletion-inducedstressratecanbeestimatedbyelasticmodelingconsideringtheconceptofnuclei
ofstrain[e.g.,Geertsma,1973].Sincewedonotwanttoevaluatetheeffectofpossiblestressshadows,we
willconsideronlyvaluesof𝜏̇D≥0andthereforedefinethehuman-inducedstressrateby𝜏̇DH(𝜏̇D),where
HdefinestheHeavisidefunction.Inotherwords,wewilldiscardherethepossiblestabilizingeffectoffield
depletiononearthquakeoccurrence,whereP isapriorizero.
trig
Theprobabilisticdiscriminatorymethodisstraightforward.Anoverviewoftheparameterdefinitionsand
nomenclatureisprovidedinTable1.Thesetofmodelparameterstocalculate𝜏̇D∕𝜏̇T ismappedinto
vector𝜽.Wefirstdefineatriggerpotentialthatanevent,whichwaslocatedatpointx,hasbeentriggered
bydepletion
rD(x,𝜽) H(𝜏̇D)𝜏̇D(x,𝜽)
pD(x,𝜽))= = . (4)
rD(x,𝜽)+rT(x,𝜽) H(𝜏̇D)𝜏̇D(x,𝜽)+𝜏̇T(x,𝜽)
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Thisfunctiongivestheprobabilitythatthe
rupturenucleationwastriggeredbyfield
depletionassumingthatweknowexactly
thehypocenterlocationoftheearthquake
(Figure2,blacksolidline).Thetrigger
potential,assumingthattheeventwas
oftectoniccause,pT,issimilarlyequated
byreplacingrDbyrT inthedenominator
sothatpT(x,𝜽) = 1 − pD(x,𝜽).Note
thatthesameapproach(equation(4))is
usedtocalculatetheprobabilitytobean
aftershockorbackgroundevent[Zhuang
andOgata,2004].
Inpractice,spatialcoordinatesandparam-
etervaluesarediscretizedonregulargrids,
andwemaycalculatepDateachgrid
pointinavolumeunderstudy.Thetrigger
potentialhastobeconsideredatthe
Figure2.Sketchtoillustratetheapproachin1-D.(a)Geometryof
hypocenteroftheearthquake.Ifwewould
theproblem.Anearthquakeislocatedclosetoanoilfieldandin
somedistancetoanactivetectonicfault.(b)Thedepletion-induced notknowwheretheearthquakeoccurred,
(red)andtectoniceventrates(blue)areplottedalongprofilex, themaximumofpDwouldindicatethe
wheretheoilfieldissituatedbetween−10kmand10km.Below, mostlikelylocationandparametervalue
thetriggerpotentialpD(blacksolidline)isplottedtogetherwiththe
giventhattheeventwasdepletion
filteredfunctionf∗pD(dashed),wherethefilterlengthoftheboxcar
triggered,whilethemaximumofpT would
functionwas100km.Verticaldashedlinesspecifythecentroid
positionsoftwohypotheticalearthquakecentroids. indicatethemostlikelylocationgiventhat
theeventwastectonictriggered.
Thehypocenterlocationuncertaintycanbegivenintermsoftheprobabilitydensityfunction
(pdf)p (x).Forinstance,well-locatedearthquakesmayhaveaGaussianlocationlikelihoodas
e
pe(x) = [2𝜋]3∕12s s s e−12(x−s2xx̄)2 e−12(y−s2yȳ)2e−12(z−s2zz̄)2,where(x̄,ȳ,z̄)declaresthebesthypocenterlocationand
x y z
(s ,s ,s )the1𝜎standarddeviation.Iftheuncertaintyofthelocationislarge,p maybeaflatconstantlike-
x y z e
lihoodoversomedistancewithradiusr.Forinstance,rmaybedefinedfrommacroseismicdataandthen
usedtodefineavolumeVtosuggestanequaldistributionlocationlikelihoodasp =1∕V(orp =1∕Aforan
e e
areaapproach).Ifweconsiderthelocationpdfandequivalentlythepdfoftheinputparameter,p(𝜽),the
triggerprobabilitycanbeequatedby
P = pD(x,𝜽)p (x)p(𝜽)d𝜽dx. (5)
trig ∫ ∫ e
V 𝜃
Ifuncertaintiesarepresent,P istheweightedaverageofthetriggerpotentialfromthevaluessampled
trig
bythepdfsoftheinputparameterandthehypocenterlocation(Figure2).Wecalculatetheprobabilitybya
bootstrappingapproach:locationsandparametersarerandomlysampledfromtheirpdfs,andtheresulting
distributionofthetriggerpotentialisanalyzedintermsofitsaverageormediananditsspreadintermsofa
standarddeviationorpercentile.
Equation(5)isusedtoestimatethetriggerprobabilityofthehypocenteroftheevent,i.e.,thenucleation
pointofrupture.Thiscorrespondstotheprobabilitythattheearthquakewastriggeredbyfielddepletion,
independentofthequestionwhetheralargeportionoftherupturewasdrivenbytectonicstressornot
andwhetheralargeportionoftheruptureplaneliesoutsidethevolumeinfluencedbyfielddepletion.
Ifwewanttotestwhetherthecompleterupturewaslikelydrivenbydepletion-inducedstressrates,we
calculatetheaveragetriggerprobabilityofallpossiblenucleationpointsontheruptureplane,independent
ofthequestionwherethetruenucleationpointwas.Iftheearthquakeruptureisviewedasasubsequent
triggeringofmanysmallrupturesegments,eachsinglerupturesegmentwouldhavehad,onaverage,a
highlikelihoodofbeinghumantriggered.Althoughthissimplifiedmodelisonlyaroughapproximation
ofaphysicalrupture,i.e.,sincesegment-segmentinteractionisneglected,itcanbeusedasaproxyfor
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Figure3.StressandlocationmodelfortheEkofiskcase.Thegreenlineindicatestheerrorellipsederivedfromtravel-
timeinversion.TheEkofiskandWestEkofiskoilfieldsareindicatedbythickgreylines.Thebluefilledpolygonsshow
anareaoflocalizedpreseismicupliftduetounintendedwaterinjection[seeOttemölleretal.,2005].(a)Comparisonof
measured(coloredcontours)andmodeledsubsidencebowl(coloredgrid)in2001bysimulatingnucleiofstrainat3km
depthatthegivenrectangularboundaryelements.(b)SimulatedCoulombstressrate(coloredgrid)onasubhorizontal
planein2kmdepthparalleltotheassumedfaultplane.Thesourcemechanismoftheearthquakeisindicatedbylower
hemisphericalprojectionofthePwaveradiationpattern.Thethickblackarrowindicatesthecentroidlocationand
rupturedirectionasderivedfromthekinematicwaveforminversion[Cescaetal.,2011].Theblueandredarrowsshow
theGPS-observednear-fieldcoseismicgroundmotioninhorizontalandverticaldirection,respectively.Theblackcrossis
areferencepoint.
thediscriminationbetweentriggeredandinducedearthquakes.Thetestmayberealizedbydefininga
representativevolumeembeddingtheruptureplane.Thisiseitherretrievedfromaseismologicalkinematic
sourceinversionorbymeansofscalingrelations.Forinstance,thevolumemaybeformedbytherupture
planewithlengthLandwidthWasbaseandonegridsizeinperpendicularheight.Ifthelocationofthe
ruptureplaneisnotwellconstrained,theperpendicularheightmaybeincreasedoracubearoundthe
centroidmaybechoseniftheruptureplaneorientationisuncertain.Then,eachcentroidpointx inpDhas
i
tobeintegratedineachcoordinatedirectionoverthelengthintervaldefinedbythechosenvolume,e.g.,
inlengthdirectionalongstrikeintheinterval[x −L∕2,x +L∕2].Theintegrationrepresentsasmoothing
i i
operation,e.g.,aconvolutionwithafault-likeboxcarfunction(faultfilter).Forthetestofaninduced
earthquake,wethereforefirstsmooththetriggerpotentialwithafaultfilterf(x,L,W,strike,dip)andapply
i
thenequation(5)tothefilteredresultsoff ∗pD
[ ]
P = f(x,L)∗pD(x,𝜽) p (x)p(𝜽)d𝜽dx, (6)
ind ∫ ∫ e
V 𝜃
where∗declaresaconvolutionintegral.Thefaultfilterisnormalizedsothatitsintegralisequalto1.
Equation(5)canbeinterpretedasaspecialcaseof(6)forwhichthelengthLisreducedtothegridsizeof
thecentroidpointsundertesting.
P isusuallysmallerthanP .ThisisillustratedinFigure2.Forinstance,theearthquakeunderstudymay
ind trig
havehadamagnitudeofM7andafaultsizeof10km×100km.Thedimensionofthestressrateanomaly
oftheoilfieldispossiblyonly20kmindiameter.Iftheearthquakenucleatedinadistanceof40kmfrom
thecenteroftheoilfield,thetriggerprobabilityinourcasewouldbezero.Ifitnucleateddirectlyabovethe
field,thetriggerprobabilityinourexamplewouldbenearly80%.However,theprobabilitytobeinduced
overthefaultlengthof100kmislessthan20%evenabovethefield(Figure2,dashedcurve),soP will
ind
besmalleveniflocationuncertaintieswouldbetakenintoaccount.ThenucleationofthehypotheticM
7earthquakewouldhavebeenhumantriggered,butthe100kmlongrupturewouldbeclassifiedtobe
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nothumanrelatedandmostlydrivenbytectonicstress.Thisisinlinewithinterpretationsgivenbyothers
[e.g.,McGarrandSimpson,1997].
3.Applications
3.1.The2001M 4.3Ekofisk,NorthSea,Earthquake
W
The7May2001M 4.3EkofiskinducedearthquakewaslocatedincloseproximitytotheEkofiskoilfields
W
intheNorthSeawithawaterdepthofabout80m(Figure3aand,e.g.,Ottemölleretal.[2005]).TheEkofisk
oilfieldissituatedinabout3.1kmdepthwithinthepost-Zechsteinformationbelowanoverburdenmostly
composedofclayandshales,interbeddedbysiltystreaks[Abdulraheemetal.,1994].Theearthquake
locationuncertaintieswere4.7kminlatitudeand7.6kminlongitude[Ottemölleretal.,2005].Adetailed
waveformmodelingcombiningbroadbandregionalandteleseismicdatawithnear-fieldGlobalPositioning
System(GPS)dataretrievedabestfocalmechanismwithstrike161◦,dip77◦,rake−100◦,scalar
moment2.85⋅1015Nm,anddepthof2km.Especiallythenear-fieldGPSdatawithobservedupliftcould
demonstrate,incombinationwiththeretrievedsourcemechanism,thattheseismicsourcecentroidwas
shallowabovethefieldformationattheeasternborderofthefield[Cescaetal.,2011].Akinematicinversion
forparametersoftheextendedsourceandrupturefurtherindicatedthatthesubhorizontalplaneruptured
unilaterallyoveralengthofabout6kminazimuthaldirectionofabout133◦[Cescaetal.,2011].The
kinematicsolutionfurtherindicatedaveryslowrupturevelocityofonlyabout500ms−1(equalto0.26
timestheshearwavevelocity)andalongrisetimeofabout7s.Theunusualslowandlongruptureexplains
thatsuchamoderate-strongearthquakewasabletoradiateenergeticlow-frequencyRayleighandLove
waveswellobservedupto2000kmepicentraldistance.AssuggestedbyOttemölleretal.[2005]and
supportedbythekinematicsourceinversionofCescaetal.[2011],therupturewaslikelytobetriggeredby
anunintendedwaterinjectionduringabout2yearsof1.9⋅106m3in2kmdepthnearthenortherncentral
partofthefield[Ottemölleretal.,2005](seeFigure3aforlocation).Thetriggeringoftheearthquakerupture
mayhavebeenrealizedbytheformationandslowgrowthofalargehorizontalhydrofracturewithinthe
overburdeninabout2kmdepthwithintheshaleandmudrocks.Thecreationandsubhorizontalorientation
ofsuchahydrofracturewaslikelyduringtheperiodofthewaterleakagebecauseofthehighinjection
pressureexceedingthetensilestrengthofthesediments[seeOttemölleretal.,2005,Figure11]andbecause
oftheshapeofthedepletion-inducedstressellipsoidwasfavorableforhorizontalfracturegrowth.Theuplift
retrievedbydifferentialbathymetrybeforeandaftertheearthquakeintheregionofthewaterinjection
hole[seeOttemölleretal.,2005]supportstheideathatasubhorizontalhydrofracturedidform.
Knowingtheearthquakehypocenterandcentroidlocation,therakedirectionandthesizeanddepthofthe
faultplane,weaimtotestwhethertheearthquakewasnatural,depletiontriggered,ordepletioninduced.
Afirststepistoderiveadepletion-inducedstressratemodelforthevolumeoftheoverburdenabovethe
oil-bearinglayer.Asaconsequenceoftheporepressuredecreaseinthereservoir,thereservoirformation
compactsandtherockvolumeaboveandbelowthereservoirdeforms.Weusethemodelofnucleiofstrain
[Geertsma,1973]andsimulatethedepletioneffectconsideringtheextent,shape,anddepthoftheEkofisk
oilfield.Theoilfieldisapproximatedasathinporouslayerembeddedinanimpermeablehalf-space.We
assumeahalf-spacemodelwithashearmodulusof6GPaandaPoissonratioof0.25.Notethattheabsolute
valuesoftheelasticmodulesarenotveryimportant,sincewecalibratethestressandporepressuremodel
bythemeasuredseafloorsubsidence.Forinstance,assumingastifferoverburdenpredictslargerpore
pressurereductionstoexplainagivensubsidencerate(deformation)butleadstosimilarstressratesin
therock.
Fieldgeometryisoftenirregularandoflargeextent,and3-Dmodelingisneededtoanalyzetheproblem.
Wemodifya3-Ddisplacementdiscontinuitymethodtoconsidertheeffectofundrainedporoelasticfield
depletion.Thethickness,Biot’sconstant,andeffectiveuniaxialcompactioncoefficientofthefieldare
considered(AppendixB).
Themaximalvalueofthedepletion-inducedsubsidenceoftheseaflooroveraproductionperiodofabout
30yearsoccurredroughlyinthemiddleoftheEkofiskfieldandwasmorethan8.26m(Figure3a).The
Ekofiskfieldisneithercircularnordiskshaped,andoursimulatedsubsidencepatternisthereforenot
exactlybowlshapedaspredictedbyanalyticalsolutions[e.g.,Geertsma,1973;Chan,2004].Ourreservoir
porepressuremodelexplainswellthegeneralpatternandquantitativevaluesofthesubsidenceinterms
ofmagnitudeandshape(Figure3a).Aporepressuredecreaseofabout47MPaisneededtoexplainthe
DAHMETAL. ©2015.AmericanGeophysicalUnion.AllRightsReserved. 2497
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Table2.SeismicityParameters(TakenFromSHAREProject[Giardinietal.,2013])andtheResultingTectonicStressRate
FromEquation(1)WithItsStandardDeviation(inBrackets)a
Earthquake SourceZone A(km2) a N(M≥5/year) b M (Weight) D(km) 𝜏̇T (Pa/yr)
max
Ekofisk NLAS037 174,800 2.8 0.006 1.0 6.5(0.5),6.7(0.2),6.9(0.2),7.1(0.1) 20 1.1(0.4)
Rotenburg BAAS191 39,800 3.7 0.158 0.9 7.3(0.5),7.5(0.2),7.7(0.2),7.9(0.1) 16.0 521.7(274.5)
Emilia ITAS293 11,080 3.7 0.050 1.0 7.3(0.5),7.5(0.2),7.7(0.2),7.9(0.1) 10.0 714.7(388.0)
aDetailsofthedeterminationoftheseismicityparameterscanbefoundathttp://www.share-eu.org.Uncertainties
aretakenintoaccountby(i)probabilitiesforM asprovidedbySHARE(seetable),(ii)uniformdistributedrates
max
N(M≥5/year)within±50%,(iii)uniformdistributedbvalueswithb±0.1,and(iv)uniformdistributedDvalueswithin
D±5kmthecorrespondingdistributionofavaluesiscalculatedbya = log(N) + 5b.Thescalefactorofw = 1is
assumedin(2)sincetheearthquakeswerefavorableorientedwithrespecttotheregionalstressorientation.
subsidenceovertheperiodof30years.Ifweassumeahomogeneousproductionrate,thisresultsinapore
pressurereductionrateofabout1.6MPa/yr.Thisestimateiswellinagreementwithaninitialporepressure
intheEkofiskfieldofabout47MPa,droppedtonearlyzeroduringtheproductionperiod[Ottemölleretal.,
2005]andsupportsthechoiceofparameterinthemodelingstudy.
Fromthereservoirdepletionmodelwecalculatethestressrateforeachstresscomponentateach
half-spacegridpointwithaspacingof500m.Figure3bshowstheCoulombstressrateindirectionofthe
slipvectoroftheearthquakeonahorizontalplaneat2kmdepth.ItisnoteworthythatthehighestCoulomb
stressratesupto120kPa/yroccuralongthenorthernandeasternbordersofthefieldwheretherupture
waslocatedbyCescaetal.[2011].TheCoulombstressrateinFigure3bisassociatedwith𝜏̇D,aparameter
neededinthediscriminatoryequation(5).
Theotherquantityneededisthenaturalstressrate𝜏̇T.TheEkofiskoilfieldislocatedwithintheNorthSea
Centralgrabensystem,afailedcontinentalriftsystemthatwasformedduringtheTriassicandJurassic
periodsandisinactivetoday.Thehistoricalandinstrumentalseismicityoverthelast100yearsisminor.
TheVikinggraben,whichisnorthoftheCentralgraben,appearsslightlymoreactivethantheCentral
grabensystem[e.g.,Bungumetal.,1991].ThelargestinstrumentallyrecordedearthquakeintheNorthSea
wastheM 6.11931DoggerBankearthquakeoffcoastSEEngland.However,thisisabout300kmsouth
L
ofEkofiskandnotassociatedwiththeseismiczoneofCentralgrabenatEkofisk.Theaveragerecurrence
periodforM>3.8intheseismiczoneoftheEkofiskeventisabout100years,withabvalueofabout1
[Bungumetal.,2000;Grünthaletal.,2010;Giardinietal.,2013].Theaveragetectonicstressrateisestimated
𝜏T≈(1.1±0.4)Pa/yr(5%and95%percentilesat0.5Pa/yrand2.0Pa/yr,respectively)dependingonthe
assumedseismogenicthicknessandmaximalmagnitudeM .TheestimatesinTable2areconsideredto
max
containtheminimalandmaximalboundsofthetectonicstressrate.Theestimatedupperlimitispossibly
toohigh.Forcomparison,thetectonicstressrateintheCentralAppenninesgrabensystemintheregion
ofAquila,whereseveralM < 6earthquakeswerereportedduringhistoricaltimes,isestimatedatabout
0.7kPa/yr[Catallietal.,2008].
Figure4showstheresultofthediscriminationtestsbyusinganupperboundvalueof𝜏̇T = 0.0015kPa/yr
andaporepressuredropintheoilfieldofΔP≈47MPa(5%and95%percentilesat44MPaand50MPa,
respectively).Figure4ashowsthediscriminationtriggerpotentialpDinaplaneat2kmdepth.Overthe
regionofthelocationuncertainty,pDisalmostalwayscloseto1.TheestimatedprobabilitythattheEkofisk
earthquakehasbeentriggeredbyfielddepletioniscloseto0.99.
WetestwhethertheEkofiskeventwasnotonlytriggeredatthenucleationpointbutdepletiondrivenover
thefullsizeofitsruptureplane.Figure4bshowstheprobabilitytohavebeeninducedifwefilterpDwith
faultfilterof10×10kmsothatthefaultwouldcovernearlyhalfoftheareaoftheEkofiskfield.Thetrigger
potentialfunctionisthereforespatiallysmoothed.Theprobabilitytobeinducedisestimatedstillveryhigh
atP ≈0.74±0.28.
ind
3.2.The2004M 4.4Rotenburg,NorthernGermany,Earthquake
W
The20October2004M 4.4Rotenburgearthquakeoccurredincloseproximitytothethreemost
W
productivegasfieldsinNorthGermany,theSöhlingen,theRotenburg,andtheVölkersenfields(Figure5a).
ThreeaftershockswithM between1.7and2.2couldbedetectedandlocatedduringthefirst4daysafter
L
themainshock.TheeventswereinproximitytothesouthwesternborderoftheSöhlingenfield,whichis
situatedintheRotliegendDethlingensandstonein5.8kmdepth.ThetightgasfieldiscoveredbyZechstein
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Figure4.(a)Thetriggerpotentialat2kmdepthfromdepletionoftheEkofiskoilfield(coloredgrid)isplottedtogether
withthelocationerrorellipse(greensolidline).Thetriggerpotentialwascalculatedforthesubhorizontalplane.Oil
platformsareindicated.(b)SameasinFigure4abutforthepotentialthattheM 4.3earthquakewasinducedassuming
W
afaultfilterdimensionof5×5km.Theinletfigureshowsthefrequencydistributionoftheinducedprobability.
salt,whichformedatthepositionoftheSöhlingenfieldasaltdome.ThesubsaltRotliegendlayeriscutby
severalNNW-SSEstriking,deepanglenormalfaultswithoffsetsofabout100–200m(e.g.,GeotectonicAtlas
[Baldschuhetal.,2001]andfrompublishedgeologicalcrosssectionsatdrillingsiteofZ16boreholein2006).
Adetailedseismologicalstudy[e.g.,Dahmetal.,2007]revealedanepicentrallocationat9.625◦longitude
and53.009◦latitudewithanerrorellipseof7.3kmand5.8kmhalf-lengthoftheprincipalaxis(inclinedby
azimuthof100◦).Thehypocentraldepthwasestimatedbetween5.0and6.4kmfromteleseismicdepth
phasesatseismologicalarraysinUSAandCanada[Dahmetal.,2007].Inthepresentstudyweuseadepth
at(6±5)km.TheretrievedseismicmomentwasM 4.4,theruptureduration1.32±0.6s,andtherupture
W
Figure5.Coulombstressratemodels(coloredgrid)areplottedtogetherwiththelocationofthemainshockandthree
aftershocksoftheRotenburgsequence(bluestars).(a)Thegreenlineindicatestheepicentererrorellipsederived
fromtraveltimeinversion.TheSöhlingengasfieldandotherneighboringgasfieldsareindicatedbygreypolygons.
Themomenttensorsourcemechanismisgivenbylowerhemisphericalprojection(seeDahmetal.[2007]fordetails).
Coulombstressratewascalculatedonahorizontalgridin6kmdepthinearthquakeslipdirectionforplanessubparallel
totheNEdippingfaultplane.Dashedgreylinesindicatemappedbasementfaultsinabout6kmdepthfromtheTertiary
period[Brückner-Röhlingetal.,2004].Z16showsthepositionofafrackingboreholedrilledin2006(seetextforfurther
explanation).(b)Coulombstressrateisplottedonagridalongstrikeanddowndipontheassumedfaultplane(seegrey
solidprofileinFigure5a).TheprojecteddepthoftheSöhlingenfieldisindicatedbythethickgreyline.
DAHMETAL. ©2015.AmericanGeophysicalUnion.AllRightsReserved. 2499