8. Plate kinematics, rigid plate motions, plate-fixed reference frames

Lecture8:PlateKinema1cs

GEOS655TectonicGeodesy

TectonicAc1vity

BasicsofPlateTectonics

•  ReviewofPrinciples–  Rigidplates,deformingonlyatboundaries(approx)–  Typesofplateboundaries

•  Descrip1onofmo1ons–  Rigidbodymo1ononasphereisrota%onaboutageocentricaxis

–  Angularvelocity,poleofrota1on•  Quan1fica1onwithGeodesy

–  Es1matesiteveloci1esfromangularvelocity–  Es1mateangularvelocityfromsiteveloci1es

DrivenByHeat

Lisa WaldUSGS Pasadena

U.S. Department of the Interior U.S. Geological Survey

USGS Earthquake Hazards Program

PlateTectonics

PlateBoundaries•  Platesarerigid,sorela1vemo1onsbetweenplatesoccurontheirboundaries

•  Inreality,plateboundariesalwayshavesomefinitewidth–plateboundaryzones– Some1mesnarrow,<10km– Some1mesverywide,500-1000km

•  Rela1vemo1onoccursonfaults,orbreaksintheEarth’slithosphere.

RidgesandTransforms

PlateBoundaries

Faults

•  Faultsaresurfaces,usually~planar,wherethetwosidesmoverela1vetoeachother.– Direc1onofmo1on==slipdirec1on

•  Howslipoccursdependsondepth– Shallow:sidesaremostlystucktogetherbyfric1on,butslipssuddenlyinearthquakes

– Deeper:sidesmostlyslidepasteachotheratasteadyrate

•  Platetectonicsdrivesthemo1on

ThreeTypesofFaults

Strike-Slip Thrust

Normal

PlateMo1onMovies

WatchMo1ononTransformFaults

Rota1ononaSphere•  Anyrigidmo1ononthe

surfaceofasphereisarota1onaboutageocentricaxis.–  Alltectonicmo1onscanbe

describedintermsofrota1ons

•  Two(equivalent)waystodescriberota1on–  Poleofrota1onandangular

speed–  Angularvelocityvector

•  Canusethisforanysizeplateorpieceofcrust

PoleofRota1on

GeologicPlateMo1onModels

•  Rela1veplatemo1onmodelsbasedonsomecombina1onof–  Spreadingratesatmid-oceanridges

•  Frommodelingofmarinemagne1canomalies

–  Transformfaultazimuths–  Earthquakeslipvectors

•  Theseareproblema1c

•  Someplateshaveli_leornodata,forexampletheCaribbeanandPhilippineSeaPlates

•  Commonlyused:NUVEL-1,revisedtoNUVEL-1A•  Newermodel:MORVEL(DeMetsetal.,2010)

Absolutevs.Rela1veMo1ons

•  Mostevidenceforplatemo1onsaremeasuresofrela1veplatemo1on–mo1onofBrela1vetoA–  Rela1vemo1onfromgeodesy–  Plateboundarydeforma1on

•  Absoluteplatemo1onsdependonsomeexternallydefinedreferenceframe–  Hotspotreferenceframe

•  Exceptthehotspotsmoverela1vetoeachother

–  “Nonetrota1on”==Nonettorque•  Platemo1onsdefinedinageode1creferenceframe

Oblique Mercator Projection About Pole

Es1ma1ngSiteVeloci1es

•  Itiseasiesttocomputethesiteveloci1esifyouhavetheplate’sangularvelocityvector,becausethesitevelocityisjustthecrossproductofthesiteloca1onvectorwiththeplateangularvelocity:

•  Youcancomputeitfromthepoleloca1onaswell,butthatrequiressphericaltrigonometry.

€

v =ω × r

Es1ma1ngPlateAngularVelocity•  Togettheangularvelocityfromsiteveloci1es,weneedto

inverttheequa1on

•  Expandthecrossproductandrewriteitasamatrixequa1on

€

v =ω × r

€

v = zω3 − yω2( ) ˆ x + xω3 − zω1( ) ˆ y + yω1 − xω2( ) ˆ z

v1 = zω3 − yω2

v2 = −zω1 + xω3

v3 = yω1 − xω2

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

v1

v2

v3

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

=

0 z −y−z 0 xy −x 0

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

⋅

ω1

ω2

ω3

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

HowManySitesDoYouNeed?•  Thereare3parametersintheplateangularvelocityvector

•  Thereare3dataineachsitevelocity– Buttheplatemodelpredictsnover1cal,soonlythehorizontalvelocitycomponentscount

•  Youneedatleast2sitestoconstraintheplateangularvelocityvector

•  Themoresites,andthefartheraparttheyare,thebe_ertheangularvelocityisdetermined.

NOAMPoles•  Withpaststudies,itis

commonthatNOAMpolesdonotliewithin95%confidenceellipsesofotherstudies–  Systema1cerrorsor

missinguncertainty

•  DifferencebetweenSNARFandSellaisarota1onaboutapoleintheSEUnitedStates.

WhatPartofAngularVelocityisConstrainedbyasinglesite’sdata?

•  Theleastcertaincomponentoftheplate’sangularvelocityvectorisarota1onaboutanaxisthroughthecentroidofthenetwork.

•  Considertheangularvelocityvectoroftheplateexpressedinthelocaleast-north-upcoordinatesatapar1cularsite:

€

ω =ωx ˆ x +ωy ˆ y +ωz ˆ z ω =ωe ˆ e +ωn ˆ n +ωr ˆ r

Thesite’svelocityis

•  Twocomponentsoftheplateangularvelocityaredirectlydeterminedbythesite’svelocity,whilethethird(localver1calcomponent)iscompletelyundetermined.€

v = ve ˆ e + vn ˆ n =ω × rve ˆ e + vn ˆ n = (ωe ˆ e × Rˆ r ) + (ωn ˆ n × Rˆ r ) + (ωr ˆ r × Rˆ r )ve ˆ e + vn ˆ n = Rωn ˆ e − Rωe ˆ n + 0ˆ r

€

ωe = −vn /Rωn = +ve /Rωr = ?

•  When sites span a small area, their local vertical directions will be similar, and this component of the angular velocity will be the least well determined.

0

MoreAboutAngularVelocity

•  Wecouldresolvetheundeterminedcomponentbytakingaminimumnormsolu1on:

•  In this case the pole is located 90° away from the site. •  The pole could also be located anywhere on the great circle that

lies between this minimum-norm solution and the site itself. •  The component of the angular velocity in the average radial

direction will naturally be the least constrained. €

ωr = 0 ; ∴ω ⋅ r = 0

Example1:TheREVEL-2000Model

Sella et al. (2002, JGR, doi:10.1029/2000JB000033)

Details

•  Globalplatemo1onmodelbaseden1relyonGPSdata

•  Dataspanfromearly1990supthrough2000.•  Combinedmanycon1nuoussitesandalsorepeatedcampaignsurveydata

•  Firstmodeltohaveessen1allycompleteglobalcoverage.

DataUsedinModel

•  Long1meseriesofdatainITRF97frame,basedonprecisepointposi1oning(PPP)solu1ons

•  Fitlineartrendsplusoffsets,combinedco-locatedsites

•  Outlierrejec1onandqualitycontrol

Australia–Antarc1ca

Arabia–Eurasia

Nazca–Antarc1ca

Nazca–Pacific

NazcaPlateMo1onOverTime

Pacific–NorthAmerica

Example2:GEODVEL(Argusetal.,2010)

GEODVELDetails

•  Basedonacombinedsolu1onofGPS,VLBI,SLR,DORIS,inITRF2005.

•  Includesanes1mateofgeocentererrorinITRF2005(es1matederrorisabout1.2mm/yrinZdirec1on).

•  Rela1veplateangularveloci1esarees1mated.ArgushasalsoprovidedabsoluteplatepolessuitableforcomparisonwithITRFveloci1es.

ComparisonofPolesandRates

GEODVELResiduals

GEODVELResiduals

GEODVELResiduals

•  FormerAfricanplatesplitintotwoplatesatEastAfricanRin–  Nubia–  Somalia

•  dd

GEODVELPoleLoca1ons

Plate-FixedReferenceFrame

•  Plate-fixedreferenceframesareveryconvenientforvisualizingandmodelingtectonicdeforma1on.

•  Touseaplate-fixedframe,weneedtohaveanes1mateoftheplatemo1oninthesamegeode1cframeofourdata.

•  Thetransforma1onissimple.Justsubtractthepredictedmo1onbasedontheplateangularvelocityfromeachsite’sobservedvelocity.

ITRFvs.Plate-fixedframe

WesternNorthAmerica

•  Deforma1onofwesternNorthAmericaresultsfromacombina1onof:–  ExtensionacrossBasinandRange

–  ShearonSanAndreasfaultsystem

–  Subduc1onstraininCascadiaandAlaska

–  Distributeddeforma1oninN.CanadaandAlaska

BacktoReferenceFrames

•  SmalldifferencesbetweendifferentversionsofITRFturnouttobebigenoughtoaffectes1matedplaterota1ons.– Orienta1ondifferences(rota1ons)betweenframesaffectabsoluteangularveloci1es,butaffectallplatesequally(rela1veplateveloci1esarenotaffected).

– Geocenterdifferences(transla1ons)affectbothabsoluteandrela1veveloci1es.

ImpactofGeocenterError•  Supposeourframehasan

errorinthegeocenter.Howaresiteveloci1esaffected?–  Suchanerrorproducesa

combina1onofver1calandhorizontalmo1on,dependingonsiteloca1on.

–  Theerroraffectseachplatedifferently

–  Impactonangularvelocitydependsonsitedistribu1on.

ITRF2000Veloci1es–Sellapole

ITRF2000Veloci1es–otherpoles

Black – Sella 2007 White – REVEL Yellow – SNARF

Note systematic residual in REVEL, 2-3 mm/yr. REVEL used ITRF97.

NOAMPoles•  Withpaststudies,itis

commonthatNOAMpolesdonotliewithin95%confidenceellipsesofotherstudies–  Systema1cerrorsor

missinguncertainty

•  DifferencebetweenSNARFandSellaisarota1onaboutapoleintheSEUnitedStates.

WhyisNOAMpolepoorlydetermined?

•  Ac1veTectonicsinwesternNorthAmerica

•  GlacialIsosta1cAdjustmentinnorthernNorthAmerica

•  OnlytheSEpartisstablebothongeologicandgeode1c1mescales.

•  Limitedareafordetermina1onofplateangularvelocity,andsuscep1bletobias.

Addi1onalUncertaintyRota1onOnly

UncertaintyinITRF

•  UncertaintyinITRFcommonlyignored.•  TheTZratedifference(1.8mm/yr)betweenITRF2005andITRF2000hasgo_enalotofa_en1on.

•  Theremayactuallybeasimilar(orlarger)differencebetweenITRF2000andITRF97

•  Ifso,uncertaintyinframe(geocenterorigin)maybemuchlargerthanprecisionofGPSbaselinerates.

Howtodefinethe14parameters?«DatumdefiniAon»

•  Origin&rate: CoM(DynamicalTechniques)•  Scale&rate: dependsonphysicalparameters•  OrientaAon: convenAonal•  Orient.Rate:convenAonal:Geophysicalmeaning

(TectonicPlateMoAon)•  ==>LackofinformaAonforsomeparameters:

–  OrientaAon&rate(alltechniques)–  Origin&rateincaseofVLBI–  ==>RankDeficiencyintermsofNormalEq.System

GeocenterMoAonTranslaAonalmoAonofthetrackingnetworkduetovariaAonoftheCoMposiAoninducedbymassredistribuAon

–  Likelyinvolvesperiodicandsecularcomponents–  SatellitetechniqueshavelimitedabiliAestoaccuratelymeasurethismoAon

–  TRForiginfromsatellitetechniquescoincideswiththeCoMaveragedovertheperiodoftheusedobservaAons

InternaAonalTerrestrialReferenceSystem(ITRS):DefiniAon

•  Origin:CenterofmassofthewholeEarth,includingoceansandatmosphere

•  Unitoflength:meterSI,consistentwithTCG(GeocentricCoordinateTime)

•  OrientaAon:consistentwithBIH(BureauInternaAonaldel’Heure)orientaAonat1984.0.

•  OrientaAonAmeevoluAon:ensuredbyusingaNo-Net-RotaAon-CondiAonw.r.t.horizontaltectonicmoAonsoverthewholeEarth

StrategyforAugmentedCovariance

•  SellaandSNARFdifferbyalmost1mm/yrinAlaska,significantrela1vetoCGPSsiteveloci1es,andwereallycan’ttellwhichis“right”

•  Wethusaugmentthecovarianceintwoways:–  AddanuncertaintycorrespondingtothedifferenceinangularvelocitybetweenSellaandSNARF

–  AddanuncertaintyinZdotof1.8mm/yrasaconserva1veuncertaintyintheITRF.

Addi1onalUncertaintyRota1on+Zdot

AugmentedCovariance

ITRF2008horizontalvelociAes

ITRF2008verAcalsitevelociAes