reference frames - geowebsimon/gtgk/bristol17/pdf/14-ref_frames.pdf · –consistent with gps...
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Referenceframes
M.A.FloydMassachusettsInstituteofTechnology,Cambridge,MA,USA
SchoolofEarthSciences,UniversityofBristolUnitedKingdom2–5May2017
MaterialfromT.A.Herring,R.W.King,M.A.Floyd(MIT)andS.C.McClusky (nowANU)
http://web.mit.edu/mfloyd/www/courses/gg/201705_Bristol/
Referencesystems
• Mathematicidealizationofgeometry:• Oftenwhatonereferstoasa“datum”,e.g.forthewholeEarth,WGS84– Ellipsoidwith• Semi-majoraxis
=6,378,137.0m• Semi-minoraxis
=6,356,752.314245m• Inverseflattening
=298.257223563
Referenceframes
• Physicalrealizationofreferencesystem• Requiresfixedmeasurementsiteswhicharedefinedbypositionandvelocityinthereferenceframeandthusconstituterealizingthesystem– VLBI– SLR– GPS
Ultimately,everythingisrelative
• Even“absolutepositioning”isrelativetosomecoordinateorigin,orientationandscale
• Sowhatis“globalpositioning”?• ThecenterandrotationpoleofEarthisourreference– ButhowtoweknowwherethecenteroftheEarthis?
– Dowereallycare?• Itdependsonyourgoals
Basicissuesinreferenceframerealization
• Conceptistoaligntheestimatedsitepositionsandpossiblyvelocitytoasetofwelldefinedlocationsthathavephysicalsignificancefortheanalysisbeingperformed(e.g.,PBOwealigntoarealizationoftheNorthAmericaplatebasedonITRF2008.
• GLORGisthemodulewhichdoesthisandcomputesthecovariancematrixofthealignedsolutioninthereferenceframechosen.
• TransformationisoftencalledanN-parameterHelmert transformation:– N=3translationonly(couldalsobejustrotation)– N=6translationandrotation– N=7translation,rotationandscale
• InGLOBKanalyses,youneedtodecide– Howmanyparameters(3/6/7)– Sitestousetodeterminetheparameters(sh_gen_stats)– Valuesofthepositions/velocitiesofthereferenceframesites– Weighttobegiventoheightsincomputingthetransformationparameters
(CND_HGTVcommand;firsttwoargumentsforpositionandvelocity).
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ITRF2014
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ITRF2014
Whataresomegeneralfeaturesofplatemotionthatyoucansee?• NorthAmericarotatesaroundapointinthePacificoffSouthAmerica
• EurasiaandAfricaappeartohaveverysimilarmotions
• Antarcticaismovingverylittle
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Choicesofreferenceframe• Chooseyourreferenceframebasedonyourgeophysicalobjectives
– VelocitiesinITRFaredifficulttointerpretvisuallyfromageophysicalperspective• Localsurroundingsofavolcano• Onesideofafault• Upperplateofasubduction zone
• Majorplatereferenceframe– Majorplatesareoftenchosentoconformwithconventionalperspectivesof
velocitysolutions– RelativetoEurasia,Nubia,NorthAmerica,SouthAmerica,etc.– Butdon’tfeelrestrictedbythis.Sometimesyourgeophysicaldiscussionisbest
visualizedrelativetoanystableboundaryofadeformingregion• Regionalreferenceframe
– CentralValleyofCalifornia,non-deformingpartofAnatolia,smallercoherentregions,etc
• Localreferenceframe– Sitesnearbutoutsidetheinfluenceofavolcano,geothermalfield,etc.
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Waystodefineareferenceframe
• Createanapr-fileforusebyglorg1. Applyknownrotationratetoapr-file(e.g.
itrf08_comb.apr→itrf08_comb_eura.apr)2. Zerovelocityapr-filerecords(anditerateusing
sh_exglk tocreateupdatedapr-file)• Definesetofsites(mustbeincludedinGAMITprocessingorotherH-fileinputtoGLOBK)whichdefinestableregion3. plate inglobk commandfile
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Referenceframeimplementation
• Anyvectormaybemappedfromoneco-ordinatesystemtoanotherbytheapplicationof– Translation(affectspositionofco-ordinateorigin)– Rotation(affectsorientationofco-ordinateaxes)– Scale(affectslengthofco-ordinateaxes)
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1:Translation
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2:Rotation• Rotationvector,ω,isdefinedasinthedirectionoftherotationaxiswith
lengthequaltothemagnitudeofangularrotation• Displacement(orvelocity)vectorthenmakesaright-handedtripletwith
therotationvector,ω,andradialvector,p.
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3:Scale
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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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Examples• Expressingvelocitiesin
ITRFisnotverymeaningfulorusefulwhenwewanttolookatthedeformationataplateboundary,e.g.theSanAndreasFaultsystem
• Bettertolookatvelocitieswithoneside“fixed”sowecanseewhattheothersideisdoingrelativetoit
PANA
PANA
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Whatdoes“withrespectto”mean?• HorizontalmotionsarerestrictedtothesurfaceoftheEarth,thereforethe
Helmert 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,“Absoluteposition”weaklydefined– Needaproceduretoexpressedcoordinatesinawelldefinedreference
frame• Twoaspects
– Theoretical(e.g.,rigidblock,mantle-fixed,no-net-rotationofplates)– Realizationthroughasetofcoordinatesandvelocities
• “finiteconstraints”:apriorisigmas onsitecoordinates• “generalizedconstraints”:minimizecoordinateresidualswhile
adjustingtranslation,rotation,andscaleparameters• Threeconsiderationsindataprocessingandanalysis
– ConsistentwithGPSorbitsandEOP(NNR)• notanissueifnetworksmalloriforbitsandEOPestimated
– Physicallymeaningfulframeinwhichtovisualizesitemotions– Robustrealizationforvelocitiesand/ortimeseries
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Framedefinitionwithfiniteconstraints• Appliedinglobk (glorg notcalled):Wedonotrecommendthisapproachsinceitis
sensitivetoover-constraintsthatcandistortvelocitiesandpositions• Example:
apr_file itrf08.aprapr_neu all101010111apr_neu algo .005005.010.001.001.003apr_neu pie1.002005.010.001.001.003apr_neu drao .005005.010.002.002.005…
• Mostusefulwhenonlyoneortworeferencesitesorverylocalarea.• Disadvantageforlargenetworksisthatbadaprioricoordinatesorbaddatafroma
referencesitecandistortthenetwork
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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 pie1drao …cnd_hgtv 10100.83.stab_it 40.52.5 j’
ij
k
k’θ
αδ
i
o
o’
j
k
• Allreferencecoordinatesfreetoadjust(anomaliesmoreapparent);outliersareiterativelyremovedbyglorg• Networkcantranslateandrotatebutnotdistort•Worksbestwithstrongredundancy(numberand[ifrotation]geometryofcoordinatesexceedsnumberofparametersiloading effects
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StabilizationusingaGlobalSetofSites
• Use40ormoresiteswithgoodvelocitiesdeterminedintheITRF2008frame• Theitrf08_comb.aprfile,whenusedtogetherwithitrf08_comb.eqtoaccount
consistentlyforinstrumentalchangesovertime,providesthewidestchoiceofsites,1992-2013.
• CombiningyoursolutionwiththeMITorSOPACglobalh-filesofferaccesstoover100siteswithouthavingtoincludetheminyourGAMITprocessing.– Youneedjust4-6commonsites,whichshouldbeofhighqualitybutneednot
bewellknowinITRF2008sincethese“tie”sitesdonotneedtobeinyourframe-realizationlist.
• ForglobalITRFstabilization,youcanusethehierarchicallistigb08_heirarchy.stab_siteingg/tables
• Althoughaglobalframemaybeaconvenientwaytodothestabilization,itisusuallynotnecessaryforregionalstudies.
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StabilizationusingRegionalorLocalSites
• IfyourareaofstudyhasarobustcGPS network(10ormorewell-distributedsites)withaccurateapriorivelocities,thenglorg stablization isrobustandlittlethoughtisinvolved(glorg willautomaticallydiscardtheoneortwositeswhichmaybeweakorinconsistent)
• IfyourregionisshortoncGPS stationswithwell-knowncoordinates,youwillneedtothinkcarefullyaboutthechoiceofsitestoincludeinyoursolutionandusetheinitialstabilization.Astabilizationsiteshouldhave– highqualitydataoverthefullspanofyourstudy– coordinateswell-knowninITRF2008– Providesymmetriccoveragearoundyourstudyarea(exceptthatiftheregion
issmallenough,atranslation-onlystabilizationmaybepossibleanddistributionislessimportant)
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IGS(IGb08)referenceframecorenetwork
http://igscb.jpl.nasa.gov/network/refframe_core.html
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IGS(IGb08)referenceframenetwork
http://igscb.jpl.nasa.gov/network/refframe.html
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FramerealizationsitesforPBO• PBOusedanhierarchicallistbasedon500kmsitespacing
(sh_gen_stat stabrad option).(Bluedots)
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160˚
170˚ 180˚
190˚ 200˚ 210˚ 220˚ 230˚ 240˚ 250˚ 260˚ 2
70˚ 280˚
290˚ 3
00˚
310˚
320˚
330˚
340˚
10˚ 20˚
30˚ 40˚
50˚ 60˚
70˚ 80˚
568 Ref, 1248 Non−Ref sites com18493.b.org
IssueswithEstimatingScale• ManyGPSanalyses,automaticallyincludescalewhenaligning
referenceframes.SincetheEarthisalmostspherical,scalechangesaredirectlyproportionaltotheaverageheightdifferencebetweenthereferencesitecoordinatesandtheirapriorivalues.
• Whencomparingandanalyzingheightchanges,howscaleistreateddirectlyeffectstheresults.AspectsofthisissuearediscussedinawhitepaperthatisavailablefromtheGAGEanalysisdocumentationatUNAVCOandinHerringetal.(2016).
• Scaleestimatesarerelatedthemeanheightdifferencesoverthereferencesites.Shouldthisberemovedornotisanopenquestion.
• ScaleestimatesonnextslideshowmagnitudeofeffectforthePBOnetwork.
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PBOnetworkscaleestimates
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2010 2010.2 2010.4 2010.6 2010.8 2011 2011.2 2011.4 2011.6 2011.8 2012−15
−10
−5
0
5
10
15
Year
Scal
e dH
(mm
)
Scale PBOMean dH PBOGlobal ReproNorthern
PBOnetworkestimatescomparedtoglobalestimatesconvertedtoaverageheightdifferences(6317kmEarth).SpikesinwinterareoftenduetoAlaskansites.
UseofGlobalbinaryH-files
• Includeglobalh-files…ornot?Forpost-2000datanotneededfororbits• 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,addapr_svant allFFFtoglobk commandfiletofixthesatelliteantennaoffsets
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VelocitiesandTimeSeries
• Thecriteriaforstabilizationaredifferentforvelocitysolutionsandtimeseries• Velocitysolutions:
– Physicalreferenceisimportant– Notsosensitivetostationdropout(solutionholdstheframetogether)
• Timeseries:– Physicalreferenceisnotimportant– Sensitivetostationdropout– Bestrepresentationofthestatisticsofthevelocitysolutionisstabilization
usingALLthewell-determinedsitesfromthevelocitysolution,nowinacommonframe
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a prioricoordinatefiles• Wenowdistribute,andencourageGAMITeers touse,asetofapr-filesthatareaconcatenatedset
ofcoordinatesforallsitesthatare,insomepresentorpastversion,formallydefinedintheITRF(531sitesor891includingthoseinIGScumulativesolution)
• Foundin~/gg/tables/anduseinapr_file commandorglorg commandfile• ThesearealsorotatedtomajorplatesusingtheEulerpolesofITRF2008-PMM(Altamimi etal.,
2012)– 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’blocks
apr_file itrf08.aprpos_org xtran ytran ztran xrot yrot zrotstab_site algo pie1nlib drao goldsni1mkea chatcnd_hgtv 10100.83.platenoam algo pie1nlibplatepcfc sni1mkea chat
Afterstabilization,glorg willestimatearotationvector(‘Eulerpole’)foreachplatewithrespecttotheframeofthefullstabilizationsetandprinttherelativepolesbetweeneachsetofplates
Usesh_org2veltoextractthevelocitiesofallsiteswithrespecttoeachplate
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VelocitiesofAnatoliaandtheAegeanina
Eurasianframe
• Realizedbyminimizingthevelocitiesof12sitesoverthewholeofEurasia
McClusky etal. [2000]
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VelocitiesinanAnatolianframe
• 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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RulesforStabilizationofTimeSeries
• Small-extentnetwork:translation-onlyinglorg,mustconstrainEOPinglobk
• Large-extentnetwork:translation+rotation,mustkeepEOPlooseinglobk;
• ifscaleestimatedinglorg,itmustestimatescaleinglobk• 1stpassforediting:
– “Adequate”stab_site listofstationswithaccurateaprioricoordinatesandvelocitiesandavailablemostdays
– Keepinminddeficienciesinthelist• Finalpassforpresentation/assessment/statistics
– Robuststab_site listofall/moststationsinnetwork,withcoordinatesandvelocitiesdeterminedfromthefinalvelocitysolution
• Systemisofteniterated(velocityfieldsolution,generatetimeseries,editingandstatisticsoftimeseries;re-generatevelocityfield).
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