Reference framesgeoweb.mit.edu/gg/courses/201706_UNAVCO/pdf/21-ref_frames.pdf · Reference systems...
Transcript of 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
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Referenceframes
• Physicalrealizationofreferencesystem• Requiresfixedmeasurementsiteswhicharedefinedbypositionandvelocityinthereferenceframeandthusconstituterealizingthesystem• VLBI• SLR• GPS
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Ultimately,everythingisrelative
• Even“absolutepositioning”isrelativetosomecoordinateorigin,orientationandscale• Sowhatis“globalpositioning”?• ThecenterandrotationpoleofEarthdefineourcoordinateaxes• ButhowtoweknowwherethecenteroftheEarthis?• Dowereallycare?
• Itdependsonyourgoals
• No-net-rotationcriterion(surfaceintegralofangularvelocityiszero)isusuallyusedastheconstraintondefiningaterrestrialreferenceframeinthepresenceofsurfacemotions(platetectonics)
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ITRF2014
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ITRF2014
Whataresomegeneralfeaturesofplatemotionthatyoucansee?• NorthAmericarotatesaroundapointinthePacificoffSouthAmerica• EurasiaandAfricaappeartohaveverysimilarmotions• Antarcticaismovingverylittle
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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.
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Examples
• ExpressingvelocitiesinITRFisnotverymeaningfulorusefulwhenwewanttolookatthedeformationataplateboundary,e.g.theSanAndreasFaultsystem• Bettertolookatvelocitieswithoneside“fixed”sowecanseewhattheothersideisdoingrelativetoit
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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)
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Referenceframeimplementation
• Anyvectormaybemappedfromonecoordinatesystemtoanotherbytheapplicationof• Translation(affectspositionofco-ordinateorigin)• Rotation(affectsorientationofco-ordinateaxes)• Scale(affectslengthofco-ordinateaxesandmapsintoheightsinthenetwork)
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1:Translation
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2:Rotation
• Rotationvector,ω,isdefinedasinthedirectionoftherotationaxiswithlengthequaltothemagnitudeofangularrotation• Displacement(orvelocity)vectorthenmakesaright-handedtripletwiththerotationvector,ω,andradialvector,p.
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3:Scale
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Scaleestimationhasadirecteffectontheaverageheightadjustmentsinthenetworksobecautiousifyourinterestedinheightchangesovertheregionofyourreferenceframedefinition.
Helmert transformation
• Position
• Velocity
• Usually,thetermsRv andsv areverysmallandcanbeneglected(<10-6 rad× <0.1m/yr and<0.1ppb× <0.1m/yr,respectively)
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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
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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
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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
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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)
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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
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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.
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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
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Stabilizationusingregionalorlocalsites
• IfyourareaofstudyhasarobustcGPS network(10ormorewell-distributedsites)withaccurateapriorivelocities,thenglorgstabilizationisrobustandlittlethoughtisinvolved(glorg willautomaticallydiscardtheoneortwositeswhichmaybeweakorinconsistent)• IfyourregionisshortoncGPS stationswithwell-knowncoordinates,youwillneedtothinkcarefullyaboutthechoiceofsitestoincludeinyoursolutionandusetheinitialstabilization.Astabilizationsiteshouldhave• Highqualitydataoverthefullspanofyourstudy• Coordinateswell-knowninITRF• Providesymmetriccoveragearoundyourstudyarea(exceptthatiftheregionissmallenough,atranslation-onlystabilizationmaybepossibleanddistributionislessimportant)
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IGS(IGb08)referenceframecorenetwork
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http://igscb.jpl.nasa.gov/network/refframe_core.html
CHURDRAOGOLDGUATKOKBMDO1MKEANLIBPETPSCH2SCUBSTJOUSNOWHIT
IGS(IGb08)referenceframenetwork
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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
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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)!
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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
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FramerealizationsitesforPBO
• PBOusesahierarchicallistbasedon500kmsitespacing(sh_gen_stat “stabrad”option)(bluedots)
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160˚
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70˚ 280˚
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568 Ref, 1248 Non−Ref sites com18493.b.org
Issueswithestimatingscale
• ManyGPSanalyses,automaticallyincludescalewhenaligningreferenceframes• SincetheEarthisalmostspherical,scalechangesaredirectlyproportionaltotheaverageheightdifferencebetweenthereferencesitecoordinatesandtheirapriorivalues
• Whencomparingandanalyzingheightchanges,howscaleistreateddirectlyeffectstheresults• AspectsofthisissuearediscussedinawhitepaperthatisavailablefromtheGAGEanalysisdocumentationatUNAVCOandinHerringetal.(2016)
• Scaleestimatesarerelatedthemeanheightdifferencesoverthereferencesites• Shouldthisberemovedornotisanopenquestion
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PBOnetworkscaleestimates
PBOnetworkestimatescomparedtoglobalestimatesconvertedtoaverageheightdifferences(6317kmEarth).SpikesinwinterareoftenduetoAlaskansites.
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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
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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)
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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
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VelocitiesofAnatoliaandtheAegeaninaEurasiareferenceframe
• Realizedbyminimizingthevelocitiesof12sitesoverthewholeofEurasia
McClusky etal. (2000)
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VelocitiesinanAnatolianreferenceframe
• BettervisualizationofAnatolianandAegeandeformation• HerestationsinWestern/Centralareusedtoalignthereferenceframe(apriorivelocitysettozero)
• McClusky etal.(2000)
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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
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