Download pdf - Reference frames - GeoWebsimon/gtgk/Bristol17/pdf/14-Ref_frames.pdf · –Consistent with GPS orbits and EOP (NNR) • not an issue if network small or if orbits and EOP estimated

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).

2017/05/02 Referenceframes 4

ITRF2014


ITRF2014

Whataresomegeneralfeaturesofplatemotionthatyoucansee?• NorthAmericarotatesaroundapointinthePacificoffSouthAmerica

• EurasiaandAfricaappeartohaveverysimilarmotions

• Antarcticaismovingverylittle


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.


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


Referenceframeimplementation

• Anyvectormaybemappedfromoneco-ordinatesystemtoanotherbytheapplicationof– Translation(affectspositionofco-ordinateorigin)– Rotation(affectsorientationofco-ordinateaxes)– Scale(affectslengthofco-ordinateaxes)


1:Translation


2:Rotation• Rotationvector,ω,isdefinedasinthedirectionoftherotationaxiswith

lengthequaltothemagnitudeofangularrotation• Displacement(orvelocity)vectorthenmakesaright-handedtripletwith

therotationvector,ω,andradialvector,p.


3:Scale


Helmert transformation• Position

• Velocity

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


Examples• Expressingvelocitiesin

ITRFisnotverymeaningfulorusefulwhenwewanttolookatthedeformationataplateboundary,e.g.theSanAndreasFaultsystem

• Bettertolookatvelocitieswithoneside“fixed”sowecanseewhattheothersideisdoingrelativetoit

PANA

PANA


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


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


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


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


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.


StabilizationusingRegionalorLocalSites

• IfyourareaofstudyhasarobustcGPS network(10ormorewell-distributedsites)withaccurateapriorivelocities,thenglorg stablization isrobustandlittlethoughtisinvolved(glorg willautomaticallydiscardtheoneortwositeswhichmaybeweakorinconsistent)

• IfyourregionisshortoncGPS stationswithwell-knowncoordinates,youwillneedtothinkcarefullyaboutthechoiceofsitestoincludeinyoursolutionandusetheinitialstabilization.Astabilizationsiteshouldhave– highqualitydataoverthefullspanofyourstudy– coordinateswell-knowninITRF2008– Providesymmetriccoveragearoundyourstudyarea(exceptthatiftheregion

issmallenough,atranslation-onlystabilizationmaybepossibleanddistributionislessimportant)


IGS(IGb08)referenceframecorenetwork

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


IGS(IGb08)referenceframenetwork

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


FramerealizationsitesforPBO• PBOusedanhierarchicallistbasedon500kmsitespacing

(sh_gen_stat stabrad option).(Bluedots)


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.


PBOnetworkscaleestimates


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


VelocitiesandTimeSeries

• Thecriteriaforstabilizationaredifferentforvelocitysolutionsandtimeseries• Velocitysolutions:

– Physicalreferenceisimportant– Notsosensitivetostationdropout(solutionholdstheframetogether)

• Timeseries:– Physicalreferenceisnotimportant– Sensitivetostationdropout– Bestrepresentationofthestatisticsofthevelocitysolutionisstabilization

usingALLthewell-determinedsitesfromthevelocitysolution,nowinacommonframe


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)


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


VelocitiesofAnatoliaandtheAegeanina

Eurasianframe

• Realizedbyminimizingthevelocitiesof12sitesoverthewholeofEurasia

McClusky etal. [2000]


VelocitiesinanAnatolianframe

• BettervisualizationofAnatolianandAegeandeformation

• HerestationsinWestern/Centralareusedtoalignthereferenceframe(apriorivelocitysettozero).

• McClusky etal. [2000]


StabilizationChallengesforTimeSeries

Networktoowidetoestimatetranslation-only(butreferencesitestoofeworpoorlydistributedtoestimaterotationrobustly)


***

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

Day176 ALGOPIE1DRAOWILLALBHNANOrms 1.5mm

Day177 ALGONLIBCHURPIE1YELLDRAOWILLALBHNANO

rms 2.3mm

^^

^^

**

****

****

*

*

StabilizationChallengesforTimeSeriesStablereferenceframe


**

*

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

Day176 BRMUPIE1WILLrms 0.4mm

Day177 BRMUALGONLIBPIE1YELLWILLrms 2.0mm

^^

^^

**

**

*

*

^^

^^

StabilizationChallengesforTimeSeriesUnstablecase


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).
