reference framesgeoweb.mit.edu/gg/courses/201706_unavco/pdf/21-ref_frames.pdf · reference systems...

ReferenceframesT.A.HerringM.A.Floyd R. W.KingMassachusettsInstituteofTechnology,Cambridge,MA,USA

UNAVCOHeadquarters,Boulder,Colorado,USA19–23June2017

http://web.mit.edu/mfloyd/www/courses/gg/201706_UNAVCO/MaterialfromR.W.King,T.A.Herring,M.A.Floyd(MIT)andS.C.McClusky (nowatANU)

Referencesystems

• Mathematicidealizationofgeometry• Oftenwhatonereferstoasa“datum”,e.g.forthewholeEarth,WGS84• Ellipsoidwith

• Semi-majoraxis=6,378,137.0m

• Semi-minoraxis=6,356,752.314245m

• Inverseflattening=298.257223563

2017/06/20 Referenceframes 1

Referenceframes

• Physicalrealizationofreferencesystem• Requiresfixedmeasurementsiteswhicharedefinedbypositionandvelocityinthereferenceframeandthusconstituterealizingthesystem• VLBI• SLR• GPS


Ultimately,everythingisrelative

• Even“absolutepositioning”isrelativetosomecoordinateorigin,orientationandscale• Sowhatis“globalpositioning”?• ThecenterandrotationpoleofEarthdefineourcoordinateaxes• ButhowtoweknowwherethecenteroftheEarthis?• Dowereallycare?

• Itdependsonyourgoals

• No-net-rotationcriterion(surfaceintegralofangularvelocityiszero)isusuallyusedastheconstraintondefiningaterrestrialreferenceframeinthepresenceofsurfacemotions(platetectonics)


ITRF2014


ITRF2014

Whataresomegeneralfeaturesofplatemotionthatyoucansee?• NorthAmericarotatesaroundapointinthePacificoffSouthAmerica• EurasiaandAfricaappeartohaveverysimilarmotions• Antarcticaismovingverylittle


Choicesofreferenceframe

• Chooseyourreferenceframebasedonyourgeophysicalobjectives• VelocitiesinITRFaredifficulttointerpretvisuallyfromageophysicalperspective

• Localsurroundingsofavolcano• Onesideofafault• Upperplateofasubductionzone

• Majorplatereferenceframe• Majorplatesareoftenchosentoconformwithconventionalperspectivesofvelocitysolutions

• RelativetoEurasia,Nubia,NorthAmerica,SouthAmerica,etc.• Butdon’tfeelrestrictedbythis.Sometimesyourgeophysicaldiscussionisbestvisualizedrelativetoanystableboundaryofadeformingregion

• Regionalreferenceframe• CentralValleyofCalifornia,non-deformingpartofAnatolia,smallercoherentregions,etc.

• Localreferenceframe• Sitesnearbutoutsidetheinfluenceofavolcano,geothermalfield,etc.


Examples

• ExpressingvelocitiesinITRFisnotverymeaningfulorusefulwhenwewanttolookatthedeformationataplateboundary,e.g.theSanAndreasFaultsystem• Bettertolookatvelocitieswithoneside“fixed”sowecanseewhattheothersideisdoingrelativetoit


PANA

PANA

Basicissuesinreferenceframerealization

• Conceptistoaligntheestimatedsitepositionsandpossiblyvelocitytoasetofwelldefinedlocationsthathavephysicalsignificancefortheanalysisbeingperformed(e.g.,PBOalignstoarealizationoftheNorthAmericaplatebasedonITRF2008)• glorg isthemodulewhichdoesthisandcomputesthecovariancematrixofthealignedsolutioninthereferenceframechosen.• TransformationisoftencalledanN-parameterHelmert transformation

• N=3:translationonly(couldalsobejustrotation)• N=6:translationandrotation• N=7:translation,rotationandscale

• InGLOBKanalyses,youneedtodecide• Howmanyparameters(3/6/7)• Sitestousetodeterminetheparameters(sh_gen_stats)• Valuesofthepositions/velocitiesofthereferenceframesites• Weighttobegiventoheightsincomputingthetransformationparameters(“cnd_hgtv”command;firsttwoargumentsforpositionandvelocity)


Referenceframeimplementation

• Anyvectormaybemappedfromonecoordinatesystemtoanotherbytheapplicationof• Translation(affectspositionofco-ordinateorigin)• Rotation(affectsorientationofco-ordinateaxes)• Scale(affectslengthofco-ordinateaxesandmapsintoheightsinthenetwork)


1:Translation


2:Rotation

• Rotationvector,ω,isdefinedasinthedirectionoftherotationaxiswithlengthequaltothemagnitudeofangularrotation• Displacement(orvelocity)vectorthenmakesaright-handedtripletwiththerotationvector,ω,andradialvector,p.


3:Scale


Scaleestimationhasadirecteffectontheaverageheightadjustmentsinthenetworksobecautiousifyourinterestedinheightchangesovertheregionofyourreferenceframedefinition.

Helmert transformation

• Position

• Velocity

• Usually,thetermsRv andsv areverysmallandcanbeneglected(<10-6 rad× <0.1m/yr and<0.1ppb× <0.1m/yr,respectively)


Whatdoes“withrespectto”mean?

• HorizontalmotionsarerestrictedtothesurfaceoftheEarth,thereforetheHelmert transformationmaynotcontaintranslationorscalingofpositionterms

1. Setv’ tozeroforallsitesthatyouwishtoestimateallothervelocitieswithrespectto

2. Estimatethebest-fittransformationparameters,e.g.byleastsquaresestimation,toachievethisminimizationofvelocitiesinaregion

3. Applytheestimatedtransformationtoallvelocities4. Allvelocitiesarenow“withrespectto”or“relativeto”chosensubset5. Thesubsetcouldbe,forinstance,allononetectonicplate,oranygiven

regionfromwhichyouwishtoseethedeformation


Referenceframesingeodeticanalyses

• OutputfromGAMIT• Looselyconstrainedsolutions• Relativepositionwelldetermined,“absolute”positionweaklydefined• Needaproceduretoexpressedcoordinatesinawelldefinedreferenceframe

• Twoaspects• Theoretical(e.g.rigidblock,mantle-fixed,no-net-rotationofplates)• Realizationthroughasetofcoordinatesandvelocities

• “Finiteconstraints”:apriorisigmas onsitecoordinates• “Generalizedconstraints”:minimizecoordinateresidualswhileadjustingtranslation,rotation,andscaleparameters

• Threeconsiderationsindataprocessingandanalysis• ConsistentwithGPSorbitsandEOP(NNR)

• notanissueifnetworksmalloriforbitsandEOPestimated• Physicallymeaningfulframeinwhichtovisualizesitemotions• Robustrealizationforvelocitiesand/ortimeseries


Framedefinitionwithfiniteconstraints

• Appliedinglobk (glorg notcalled)• Wedonotrecommendthisapproachsinceitissensitivetoover-constraintsthatcandistortvelocitiesandpositions• Example:

apr_file itrf08.aprapr_neu all 10 10 10 1 1 1 apr_neu algo .005 005 .010 .001 .001 .003apr_neu pie1 .002 005 .010 .001 .001 .003apr_neu drao .005 005 .010 .002 .002 .005...

• Mostusefulwhenonlyoneortworeferencesitesorverylocalarea• Disadvantageforlargenetworksisthatbadaprioricoordinatesorbaddatafromareferencesitecandistortthenetwork


Framedefinitionwithgeneralizedconstraints

• Appliedinglorg:minimizeresidualsofreferencesiteswhileestimatingtranslation,rotation,and/orscale(3–7parameters)apr_file itrf08.aprpos_org xtran ytran ztran xrot yrot zrotstab_site algo pie1 drao ...cnd_hgtv 10 10 0.8 3.stab_it 4 0.5 2.5

• Allreferencecoordinatesfreetoadjust(anomaliesmoreapparent),outliersareiterativelyremovedbyglorg• Networkcantranslateandrotatebutnotdistort• Worksbestwithstrongredundancy(numberand[ifrotation]geometryofcoordinatesexceedsnumberofparameters)


j’

ij

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k’θ

αδ

i

o

o’

j

k

Definingareferenceframewithglorg

• Createanapr-fileforusebyglorg1. Applyknownrotationratetoapr-file(e.g.itrf08_comb.apr→

itrf08_comb_eura.apr)2. Zerovelocityapr-filerecords(anditerateusingsh_exglk tocreate

updatedapr-file)

• Definesetofsites(mustbeincludedinGAMITprocessingorotherH-fileinputtoGLOBK)whichdefinestableregion

3. plate inglorg commandfile


Stabilizationusingaglobalsetofsites

• Use40ormoresiteswithgoodvelocitiesdeterminedintheITRFframe• Theitrf08_comb.aprfile,whenusedtogetherwithitrf08_comb.eqtoaccountconsistentlyforinstrumentalchangesovertime,providesthewidestchoiceofsites,1992–2013• CombiningyoursolutionwiththeMITorSOPACglobalh-filesofferaccesstoover100siteswithouthavingtoincludetheminyourGAMITprocessing.• Youneedjust4–6commonsites,whichshouldbeofhighqualitybutneednotbewellknowinITRF2008sincethese“tie”sitesdonotneedtobeinyourframe-realizationlist

• ForglobalITRFstabilization,youcanusethehierarchicallistigb08_hierarchy.stab_siteingg/tables• Althoughaglobalframemaybeaconvenientwaytodothestabilization,itisusuallynotnecessaryforregionalstudies.


Useofglobalbinaryh-files

• Includeglobalh-files…ornot?• Forpost-2000data,notneededfororbits

• Advantages• Accesstoalargenumberofsitesforframedefinition• Can(should)allowadjustmenttoorbitsandEOP• Easescomputationalburden

• Disadvantages• Mustuse(mostly)thesamemodelsastheglobalprocessing• OrbitsimpliedbytheglobaldataworsethanIGSF.Once-per-revolutionradiationmodelparameters(looseinglobalh-files)shouldbetreatedcarefully.

• Somebaddatamaybeincludedinglobalh-files(canremove)• Greaterdatastorageburden

• MIThfiles availableatftp://everest.mit.edu/pub/MIT_GLL/HYYWhenusingMITfiles,add“apr_svant allFFF”toglobk commandfiletofixthesatelliteantennaoffsets


Stabilizationusingregionalorlocalsites

• IfyourareaofstudyhasarobustcGPS network(10ormorewell-distributedsites)withaccurateapriorivelocities,thenglorgstabilizationisrobustandlittlethoughtisinvolved(glorg willautomaticallydiscardtheoneortwositeswhichmaybeweakorinconsistent)• IfyourregionisshortoncGPS stationswithwell-knowncoordinates,youwillneedtothinkcarefullyaboutthechoiceofsitestoincludeinyoursolutionandusetheinitialstabilization.Astabilizationsiteshouldhave• Highqualitydataoverthefullspanofyourstudy• Coordinateswell-knowninITRF• Providesymmetriccoveragearoundyourstudyarea(exceptthatiftheregionissmallenough,atranslation-onlystabilizationmaybepossibleanddistributionislessimportant)


IGS(IGb08)referenceframecorenetwork


http://igscb.jpl.nasa.gov/network/refframe_core.html

CHURDRAOGOLDGUATKOKBMDO1MKEANLIBPETPSCH2SCUBSTJOUSNOWHIT

IGS(IGb08)referenceframenetwork


http://igscb.jpl.nasa.gov/network/refframe.html

JPLMPIE1QUINVNDP

Translationand/orrotation?

• Intheexample,theinstructionssaidtocommentoutthelinepos_org xtran ytran ztran xrot yrot zrotanduncommentthelinepos_org xtran ytran ztran• Why?

• Theexamplehadaverysmallnetworkaperture(spatialextent)overanareaofsouthernCalifornia• Withalargeraperturenetwork,thecurvatureoftheEarthissignificantandthereismoreneedtoallowthenetworktorotate• Thereforeweneedtoestimatebothtranslationandrotation


Referenceframeimplementation

• Themainpointofreferenceframedefinitionistousesiteswithwellknowncoordinatestostabilizeyourprocessednetwork• Ifyourprocessednetworkalreadycontainssiteswithknownaccuratecoordinates,e.g.in~/gg/tables/itrf08_comb.apr,thenthereisnoneedtoaddadditionalsitestoyourprocessing• Your“stab_site”listinglorg commandfileshouldbeguidedbyandcloselyassociatedwiththecontentsofanaccurateapr-file,e.g.itrf08_comb.aprbydefaultbutcouldbeanyaccurateapr-fileyouchooseincludeinglobk andglorg commandfiles• ~/gg/tables/igb08_hierarchy.stab_siterelatesto~/gg/itrf08_comb.apr

• Decideearlyinyourprocessingwhetherornotyouwillneedtoincludeadditional,e.g.IGS,sitesinyourGAMITprocessingtouseultimatelytorealizeyourpreferredreferenceframe• Thefirstdecisionyoumustmake(choosingsitestoprocess)isgreatlyinfluencedbytheultimateprocessingstep(referenceframerealization)!


Rulesforstabilizationoftimeseries

• Small-extentnetwork:translation-onlyinglorg,mustconstrainEOPinglobk• Large-extentnetwork:translationandrotation,mustkeepEOPlooseinglobk• Ifscaleestimatedinglorg,mustestimatescaleinglobk• First passforediting:

• Adequate“stab_site”listofstationswithaccurateaprioricoordinatesandvelocitiesandavailablemostdays

• Keepinminddeficienciesinthelist• Finalpassforpresentation/assessment/statistics

• Robust“stab_site”listofall/moststationsinnetwork,withcoordinatesandvelocitiesdeterminedfromthefinalvelocitysolution

• Systemisofteniterated(velocityfieldsolution,generatetimeseries,editingandstatisticsoftimeseries;re-generatevelocityfield)• Ifyouhavetimeseries,youcantestoptionsusingtscon


FramerealizationsitesforPBO

• PBOusesahierarchicallistbasedon500kmsitespacing(sh_gen_stat “stabrad”option)(bluedots)


160˚

170˚ 180˚

190˚ 200˚ 210˚ 220˚ 230˚ 240˚ 250˚ 260˚ 2

70˚ 280˚

290˚ 3

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568 Ref, 1248 Non−Ref sites com18493.b.org

Issueswithestimatingscale

• ManyGPSanalyses,automaticallyincludescalewhenaligningreferenceframes• SincetheEarthisalmostspherical,scalechangesaredirectlyproportionaltotheaverageheightdifferencebetweenthereferencesitecoordinatesandtheirapriorivalues

• Whencomparingandanalyzingheightchanges,howscaleistreateddirectlyeffectstheresults• AspectsofthisissuearediscussedinawhitepaperthatisavailablefromtheGAGEanalysisdocumentationatUNAVCOandinHerringetal.(2016)

• Scaleestimatesarerelatedthemeanheightdifferencesoverthereferencesites• Shouldthisberemovedornotisanopenquestion


PBOnetworkscaleestimates

PBOnetworkestimatescomparedtoglobalestimatesconvertedtoaverageheightdifferences(6317kmEarth).SpikesinwinterareoftenduetoAlaskansites.


2010 2010.2 2010.4 2010.6 2010.8 2011 2011.2 2011.4 2011.6 2011.8 2012−15

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Scale PBOMean dH PBOGlobal ReproNorthern

Velocitiesandtimeseries

• Thecriteriaforstabilizationaredifferentforvelocitysolutionsandtimeseries• Velocitysolutions:• Physicalreferenceisimportant• Notsosensitivetostationdropout(solutionholdstheframetogether)

• Timeseries:• Physicalreferenceisnotimportant• Sensitivetostationdropout• BestrepresentationofthestatisticsofthevelocitysolutionisstabilizationusingALLthewell-determinedsitesfromthevelocitysolution,nowinacommonframe


a prioricoordinatefiles

• Wenowdistribute,andencourageGAMITeers touse,asetofapr-filesthatareaconcatenatedsetofcoordinatesforallsitesthatare,insomepresentorpastversion,formallydefinedintheITRF(531sitesor891includingthoseinIGScumulativesolution)

• Foundin~/gg/tables/andusein“apr_file”commandin glorg commandfile• ThesearealsorotatedtomajorplatesusingtheEulerpolesofITRF2008-PMM(Altamimi etal.,2012)orITRF2014-PMM• itrf08_comb_amur.apr(relativetoAmurian plate)• itrf08_comb_anta.apr(Antarctica)• itrf08_comb_arab.apr(Arabia)• itrf08_comb_aust.apr(Australia)• itrf08_comb_carb.apr(Caribbean)• itrf08_comb_eura.apr(Eurasia)• itrf08_comb_indi.apr(India)• Itrf08_comb_na12.apr(NorthAmerica,afterBlewitt etal.,2013)• itrf08_comb_nazc.apr(Nazca)• itrf08_comb_noam.apr(NorthAmerica)• itrf08_comb_nubi.apr(Nubia)• Itrf08_comb_nu13.apr(Nubia,afterSaria etal.,2013)• itrf08_comb_pcfc.apr(Pacific)• itrf08_comb_soam.apr(SouthAmerica)• itrf08_comb_soma.apr(Somalia)• itrf08_comb_sund.apr(Sunda)


Referencingtoahorizontalblock(“plate”)

• Appliedinglorg• Firststabilizeintheusualwaywithrespecttoareferencesetofcoordinatesandvelocities(e.g.ITRF-NNR),thendefineoneormore“rigid” blocksapr_file itrf08_comb.aprpos_org xtran ytran ztran xrot yrot zrotstab_site algo pie1 nlib drao gold sni1 mkea chat cnd_hgtv 10 10 0.8 3.plate noam algo pie1 nlibplate pcfc sni1 mkea chat

• Afterstabilization,glorg willestimatearotationratevector(“Eulerpole”)foreachplatewithrespecttotheframeofthefullstabilizationsetandprinttherelativepolesbetweeneachsetofplates• Usesh_org2vel toextractthevelocitiesofallsiteswithrespecttoeachplate


VelocitiesofAnatoliaandtheAegeaninaEurasiareferenceframe

• Realizedbyminimizingthevelocitiesof12sitesoverthewholeofEurasia

McClusky etal. (2000)


VelocitiesinanAnatolianreferenceframe

• BettervisualizationofAnatolianandAegeandeformation• HerestationsinWestern/Centralareusedtoalignthereferenceframe(apriorivelocitysettozero)

• McClusky etal.(2000)


StabilizationChallengesforTimeSeries

Networktoowidetoestimatetranslation-only(butreferencesitestoofeworpoorlydistributedtoestimaterotationrobustly)


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Exampleoftimeseriesforwhichtheavailablereferencesiteschangesday-to-daybutisrobust(6ormoresites,welldistributed,withtranslationandrotationestimated)

Day176 ALGOPIE1DRAOWILLALBHNANOrms 1.5mm

Day177 ALGONLIBCHURPIE1YELLDRAOWILLALBHNANO

rms 2.3mm

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StabilizationChallengesforTimeSeriesStablereferenceframe


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Exampleoftimeseriesforwhichtheavailablereferencesiteschangesday-to-dayandisnot robust(only3sitesononeday)NOTE:Distantframedefinitionsitescanhaveverysmallerrorbarswhenusedandlargeerrorbarswhennotused.

Day176 BRMUPIE1WILLrms 0.4mm

Day177 BRMUALGONLIBPIE1YELLWILLrms 2.0mm

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StabilizationChallengesforTimeSeriesUnstablecase


reference framesgeoweb.mit.edu/gg/courses/201706_unavco/pdf/21-ref_frames.pdf · reference systems...

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