Modelingthepost‐riftingdeformationontheKraflavolcanic

system

ChristopherDiCaprio,MarkSimonsCaltech

Outline•  GeophysicalGoals

–  Modelingthepost‐riftingdeformationontheKraflafissuresystem•  PreviousWork

–  ViscoelasticmodelsandGPSdata–  ElasticmodelsandInSARdata

•  InSARConstraints•  ModelingWorkflow

–  Whattoolsweuseandhowtheyareapplied•  IntuitionBuildingviaFEMModeling•  ChallengesandNextSteps

–  Whattechnicalissuesneedtobeaddressed

Today’sGoals:- DemonstrateuseofPyLithandmodelingworkflow- Describemodelingchallengesandneededtools

GeophysicalGoals

•  Whatarewetryingtodo?– ConstrainrheologyofnorthernIcelandiclithospherebyobservingresponsetoariftingevent

•  Howareweapproachingtheproblem?– AnalysisofthelargeInSARdataset– Structuralmodelsusinggeophysicalandgeologicalconstraints

– TwoandthreedimensionalFEMmodelsofviscoelasticdeformationusingPyLith

NVZ

EVZ

WVZ

Krafla

SeeSigmundsson,IcelandGeodynamics

NorthernVolcanicZone

Theistareykir

Krafla

Fremri‐Namur

Askja

Kverkfjoll

volcanicsystems

• 100‐150yearriftingepisodeinterval• Eachevent50‐100kmextent

1618A.D.

1724,1975A.D.

1874A.D.

historicrifting

Tryggvason,1984,B.Vol.

KraflaFires1975‐1984

Ndistancealongrift(km)

amou

ntofo

pening(m

)

S

Seriesofindividualriftingepisodeslasthourstodays

GPSRecordofPost‐RiftingDeformation

PreviousVisco(elastic)Modeling

Foulgeretal1992

HoftonandFoulger,1996 PollitzandSacks,1996

viscous

elastic

Maxwellviscoelastic

standardlinearsolid

€

1.1×1018 Pa s

€

0.3− 2 ×1019 Pa s

€

3×1018 Pa s

€

3×1019 Pa s

Hekietal1993

€

0.3− 2.2 ×1018 Pa s

Foulgeretal.1992

€

0.3− 2 ×1019 Pa s

• Materialvariesonlywithdepth(Elasticlayeroverviscouschannel)

• Onlyconsideredriftnormaldisplacementdatafrom1987and1990GPScampaign

 Solveforamountofopeninganddiffusivity(Elsassermodel)

2metersofopening

Hekietal.1993

€

0.3− 2.2 ×1018 Pa s

• Materialvariesonlywithdepth(elasticlayeroverviscouschannel)

• Modelhorizontaldisplacementdatafrom1987and1990GPScampaign

• Elasticlayeroverviscouschannel Findthreediffusioncoefficients

HoftonandFoulger1996

€

1.1×1018 Pa s

• Materialvariesonlywithdepth

• ElasticlayeroverMaxwellviscoelastic½space

• Modelthreedimensionaldisplacementdatafrom1987and1992GPScampaign

 Findviscosityof½space Refineestimatesofdikeheight,dip,andelasticlayerthickness

HoftonandFoulger1996

Horizontaldisplacementsfitfor1987‐1992

Verticalsaremoredifficulttofitbutalsomuchnoisier

PollitzandSacks1996• Materialvariesonlywithdepth

• ElasticoverSLSoverMaxwellviscoelastic

• Modelthreedimensionaldisplacementdatafrom1987,1990,1992GPScampaign

 Invertforamountofopening

 FindviscosityofVElayers

€

3×1018 Pa s

€

3×1019 Pa s

PollitzandSacks1996

Horizontaldisplacementsfitnearrift1987‐1990and1990‐1992

Krafla

ascendingdescending

InSARCoverage

Lineofsightvectors

InterferometricPairs

95/06/19‐92/09/18

deflatingKraflamagmachamber

contraction,cooling?

Broadpost‐riftingsignal(viscoelasticrelaxation)

ascendingorbit‐T1

95/06/19‐92/09/18 99/10/11‐96/10/21

Rateofdeformationslowingdown

groundtoradar

96/06/04‐93/07/31 06/06/027‐03/09/16

descendingorbit‐T9 Smallsignal20yearsafterrifting

Sigmundssonetal.1997

• ModellocaldeformationnearKraflavolcanousing3interferogramsfromtrack9

• Mogisource–drainingorcoolingofshallowmagmachamber

• Linesource–coolingorpost‐riftingductileflow

Henriotetal.2001

• ModellocaldeformationnearKraflavolcanousing14interferograms

• 3shallowelasticsourcesofdeformation

• 2sills• 1magmachamber

deZeeuw‐vanDalfsenetal.2004

• Modelwiderregionofdeformationusing4interferogramsfromtrack9

• DeepinflatingMogisource(21km)invokedtoexplainbroaddeformation

•  BigPicture:–  Threedimensionalrheologicstructure–  Theworkflowallowsustobuildcomplexmodelsthatusegeologicand

geophysicaldatasets–  Biggercomputersandparallelprocessingallowustotestmoreand

biggermodels•  Whatgroupsofrheologicalstructuresagreewiththedata?

•  ThisTalk–intuitionbuilding:–  Howdovariousrheologicalstructuresaffectthesurfacedeformation?–  Two‐dimensional–  LinearMaxwellviscoelasticity–  Nogravity–  Allriftingoccursinsingleevent

FEMModelingwithPyLith

Workflow

VTKPythonMatplotlib

ASCIIfiles

images

GMTgrids

ToolswrittenbyEricHetland

WorkflowDiagramfromBradAagaardgeodynamics.org

GOCAD

•  Faroe‐IcelandRidgeExperiment[Staplesetal1997]

•  ICECRTb[Allenetal2002]

Cubit

•  Gocadsurfacesareusedtowebcutvolumetoestablishfaultandmaterialboundaries–  TSurfsfromGocadaremeshedandanewsurfaceintheACISgeometryengineiscreatedfromthemesh

• Elasticuppercrust–5kmthick• Maxwellviscoelasticlowercrust• Maxwellviscoelasticmantle• MohofromtheFaroe‐IcelandRidgeExperiment(Staples1997)

Constructmaterialboundariesusinggeophysicaldata

VariableTimeStepping•  Simplesolution:specifyalltimestepsizes–  Notadaptive

•  PyLith:timesteppinghandledatPythonlevel•  CreatednewcomponentImplicitManualdt – ModificationofImplicitcomponent–  Readsfromfiletogettimesteppinginformation– MethodstableTimeStep()returnsnewtimestepsizewhencalled

[pylithapp.timedependent] formulation = pylith.problems.ImplicitManualdt

[pylithapp.timedependent.formulation] filename_dt = dt_var units_dt = 1.0*year

•  Inelasticmaterialshavememoryofpastriftingevents•  Stressesinmodelmustreachsteadystate•  Numberofeventsneededtoreachsteadystatescalesinverselywith

theSavageparameter(HetlandandHager2006)

Spin‐Up

η=1018Pas

η=1020Pas

€

τ 0 = T /2τM

RepeatedRiftingEvents

•  Cannotspecifyrepeatedsliponfaults•  LinearrheologyallowsustouseGreen’sfunctionapproach–  CalculateresponsetosingleeventusingFEM–  Sumsequencewithappropriatetimelags

•  Savescomputationtime

2DModels–IntuitionBuilding

10km

290km

1000km

MaxwellViscoelastic

ElasticRiftingSource

1Danalysis:

• Profilefromcenterofriftsegment

• Assumesymmetricdeformation

• Assumenegligiblesensitivitytoalongaxisdisplacements onlyvertical&X‐riftcomponents

Simonsetal,AGUFall2001

AbsoluteVelocities NormalizedVelocities

HomogeneousViscosityvelocitysnapshotsforeachyear:13–20yearsafterrifting

NomodelwithaHomogeneousviscositystructurecanmatchthedata(includesHoftonandFoulger1996)

ComparetoaverageInSARvelocities

Dataandmodelde‐ramped

Whataretheeffectsofhorizontalgradientsin

viscosity?50km

100km

200km

AbsoluteVelocities NormalizedVelocities

Horizontaldeformation:• Modelsaredifficulttodistinguish

Verticaldeformation:• Widerviscositygradientsresultinwiderdeformationfields(notsurprising)

HorizontalViscosityGradientsvelocitysnapshotsforeachyear:13–20yearsafterrifting

StronglowercurstWeakmantle

WeaklowercrustStrongmantle

Whatistheeffectofstronglowercrustoverweakmantlevs.weaklowercrustoverstrongmantle?

100km

VerticalViscosityGradientsvelocitysnapshotsforeachyear:13–20yearsafterrifting

AbsoluteVelocities NormalizedVelocities

Horizontaldeformation:• Modelsaredifficulttodistinguish

Verticaldeformation:• Modelseasilydistinguishedbyshapeofdeformationfield

Impactofalocalizedviscosityanomalybeneatharift

d

MaxwellViscoelastic

Elastic

Abilitytodetectanomalydependsonviscositycontrastandtimeperiodofobservation

ChangingViscosityofAnomalyvelocitysnapshotsforeachyear

13–20yearsafterrifting3–10yearsafterrifting

€

ηbulk =1020 Pa s, R =10 km, d = 20 km

• Sensitivitytoanomalydepthnotmonotonic

ChangingDepthofAnomalyvelocitysnapshotsforeachyear:13–20yearsafterrifting

AbsoluteVelocities NormalizedVelocities

€

ηanomaly =1020 Pa s, ηbulk =1020 Pa s, R =10 km

• NosingletestmodelfitsInSARdata• Wewillrequirelarge,localizedcontrastsinrheology

Preliminaryconclusions•  Verticaldisplacementsareimportantfordistinguishingamongpost‐riftingmodels–  InSARhashighsensitivitytoverticals(ERSlookangleis23°fromvertical)

•  Itisnotpossibletomatchthepost‐riftingdeformationasmeasuredbyInSARusinganelasticlayeroveranviscoelastichalfspacemodel

•  Verticalgradientsinviscosityhavealargeimpactonshapeofdeformationfield.

•  Localizedanomalieswilllikelyberequired

•  Existingworkflowgreatlyfacilitatesexplorationofdifferentmodels

NextSteps

•  Continueintuitionbuildingexercise–  Localizedanomalies

•  Three‐dimensionalmodels•  Spatiallyandtemporallydiffusediking•  Maywanttoinvertfordikingparameters

–  Openingmaynotbeuniformwithdepth•  Otherrheologies

–  Non‐Maxwell–  Non‐linear

•  InSARProcessing–  Reprocesswithoutre‐estimatingbaseline

tokeeplong‐wavelengthdeformation–  Timeseriesanalysis

Challenges•  Non‐uniqueness

–  Elasticsource(s)–  Non‐Maxwellrheologies

•  Non‐linearrheologiesremovetheabilitytousetheGreen’sfunctionapproachtomultipleevents–  Morecomputationalcost–  Needmultipleearthquakesonasinglefault–  Largedeformations

•  RepeatedEQ ✓1.2•  Nonlinearrheologies 1.4•  Gravity ✓1.2•  Adaptivetimestepping 1.3•  Higherordershapefunctions 1.5

Krafla

Askja

Fremri‐Namur

Accommodationofrift‐tipstress?

• Inelasticmodelsmustbespun‐uptosteadystateoverseveralriftingcycles

• Howdoweaccommodatethestresscreatedatthecracktipduringrepeatedriftingevents?

• St.Venant'sPrinciplemayallowustouse“easiest”mechanism

 Thelocalizedeffectscausedbyanyloadactingonthebodywilldissipateorsmoothoutwithinregionsthataresufficientlyawayfromthelocationoftheload.