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GeodeticSurveying w¡th Quosar Radio Inlerferometry

A. STOLZ et al

Abstract Front 20 April to 3 May, l,982,five Austalian radio-telescopeswere linked for the first tirne and operated in synchro_nismto fomt a single radiotelescope.The li¡tk-up was the culminatiott of two years of iniensive effort and co-operationto co-ordinatetelàscope modi!ìcøtions and overcomethe logistic problents of urulertakittgsuch an experilnent. The five telescopesare sited at the NASA Deep Space tracking føcility at Tidbinbilla near cønberra, the cslRo Radio Astronomy observatory at parkes,the |lniversitlt of rasmania's Rødio observatory near Hobart, the university of sydney's F-lannobservatory near Sydney, ønd the LANDSAT tracking statìon at Alice Springs. The stutultaneousbut independent operation of two or more widely separatedtelescopes is called Long-Baseline Interferometry. This experiment was set up to provide high-resolutionradio møps of distant Southem Hemisphere quasarsønd galaxies.However, the experiment ß of greit interest to surveyors,since it alsoprovides a meansof møking accurøteposition difference and distance meøsurements.It is expected, for instønce,thøt the distancebetween the telescopesat Parkesand Tidbinbilla will be measur.edto an accurøcyof l0cmwhile the dßtances from the Tidbinbilla telescope to those at Hobart and Alice Springs wilt be determined to an accuracy of I to 2 metres. The experiment is describedin this paper. The basicprinciples of the VLBI techníqueare ølsoreviewed in generalterms. lntroduction Astronomershave developedradio-interferometers with whichthe baselines between antennascan be measuredwith high precisionover both short and very long distances (Barc et al., 1967; Broten et al., i9í:I;Gubbay t: s!., !974). Thesetechniques, calÌeci very-Iong-Baseline Interfe¡ometry (vLBÐ have significant applicationsto geodesy (Gold, 1967; shapiro and Knight, 1970). In a generalway, the radio signalsfrom a common sourceare receivedat two or more antennasat the end of a more or lesslong basetne.The signalsare brought together,and correlatedto determinethe differencein phaseor the differencein time in which a particularburst of energyis received,at the two antennas.This quantity relatesto the length and the direction ofthe baselinerelative to the source.In conventionalinterferometry the two signalsare brought togetherthrough cablesbut in VLBI the signalsare recordedindependently at each site, againsthighÌy precise time and frequency standardsand later brought togetherin a computer. Thi

ìr A. STOLZ, B.Sürü¿,Ph.D.(N.S.IV.), School of Surveying,University of New So,rrt ililJ- B. HARVEY, Schôol of Su¡veying,University of New South Wales. D. L. JAUNCEY,Rrdiophysics Division, CSIRO. A. NEILL, D. MORABITO,R. PRESTON,Jet PropulsionLaboratory. B. GREENE, Division of National Mapping. K. LAMBECK' Researchschool of Earth sciences,Aust¡alian National university. A. TZIOUMIS, School of Physics,Sydney University. A. WATKINSON, Departmentof Eþctrical Engineering SydneyUniversity. G. W. R, ROYLE, Depattment of Physics,University of Tasmania. D. JOHNSON,School of Earth Sciences,Macquàrie University. The AustralìanSurreyo¡, March, 1983, Vol. 31, No. 5 305

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antennad'ìSeparationis now limited only by the requirementthat the sourceismutually visiblefrom the two stations. The first geodetic VLBI experimentswere conducted in the United States in the early 1970's (Hintereggeret ø1., 1972; Shapiroet al., 1974} Sincethen numerous experimentshave been performedby groupsin the United States,Canada and Europe. Transcontinentalbase[nes, for example,have been measuredwith a repeatability of better than 5 cm (Shapiro,1978) and a 1.2 km baselinevector has been determined with a repeatabilityof 5 mm (Rogerset al., 1978). Two transportableantennas, 9 and 4 metres in diameter have been developedat the Jet Propulsion l:boratory (JPL) in Pasadena specifically for geodesy.Using these transportable antennas in conjunction with fixed radio-telescopesin California, triangle closuresto within 10-20 cm have been achieved over a perimeterof about 1000km (Niell et al., 1979). A number of conceptshave been proposedto use the Global PositioningSystem (GPS) sateltitesfor accuratemeasurements of distancein the range 100-1000km (Fell, t9E0). Theseinclude the interferometricmode in which the GPSsignals are used as a noise source, that is, essentiallylong baselineinterferometry techniques are used. The receiverscan be made quite small.Field deployable GPS receivers are expected to become commercially availablein 1984 (Bossler,1981). Moreover,it now appearslikely that measurementscan be made with 1 ot 2 cm açcuracyin times as short ashalf an hour or less if the system is completed as planned. The VLBI technique is thus of considerable interestto surveyors. Geodetic VLBI has not beenactively pursuedin Australia in the past. This changed in April, 1982 when five Australian telescopeswere linked for the fìrst time to measure the position differericesand.baselines. between them. We describethe experiment in this paper. The basic principles'of thlVLBI technique are also reviewed, in generalterms. Detailsmay be found in Counselman(1976) and Carter(1981).

GeodeticVLBI Radio-interferometryhas been reviewed byseveral authors (e.g. Counselman,19T6). Here we shall discussonly those aspectswhich pertain to geodeticmeasurements. Observables The basic principles of the VLBI techniqueare illustrated in Fig. I which showsthe geometry of a geodetic VLBI measurementconfìguration. Two widely separatedradio- telescopesobserve radiation from an extra-galacticradiosource, typically a distant quasar or radio galaxy. The Australian geodeticobservations were made at S-band(2.3 GlIz) and X-band (8.4 GHz). The sequenceof observationsconsists of about 100 separatemeasure- ments ingolving 10 to 20 different radio sourcesspread across the sþ. The signal received from eaclibource is amplifìed and mixed with a signalfrom a local oscillator. lndependent phase.stabtÇ.localoscillator signalsat each antenna are obtained from ultra-stableatomic oscillators,¡{ypically Rubidium standards or preferably Hydrogen masers. Practical stabilities of about I part in 1013over a spanof 103 secondsare achievable with Rubidium standardswhile Hydrogen masersyield about I part in 101s. The video frequency signal produced after the local oscillator is mixed with the radio frequency signal is then sampledat a fixed rate (4 MHz in our case)and recorded on a high-speedrecorder. The final result is a set oftapes, one from eachantenna, càrry- ing a sequenceof ones and zeroes,called bits, and each carrying its own time tags. The tapes carry a "noise" contributed by the different receiversat each site as well as the source information. These tapes are then transported to a special central processing 306 The Aus*alian Sunteyor,March, 1983, Vol. 31, No. 5

I I I l I

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facility (there are at presentthree such facilities in the world, two in the United States and one in Europe)where they areall replayedunder central computer control and are cross-relatedin pairs. During the cross-correlation,each tape nìust be appropriately delayed,since the signalwas receivedat the more distantantenna at a time z sec<>nds after it was receivedat the nearantenna. This delayis the basicobservable of geodetic VLBI measurements.Fig. I showsthat, as the earth rotatesthe delaywill vary as the anglebetween the sourceand the baselinevaries. This quantity,called the delayrate, is the secondobservable. TapeCorrelation In essence,the two stringsof bits a¡e multipliêdtogether, bit by bit, and the productsare summedover an appropriateinterval. The procedure is repeatedin step-wise fashion for a range of offsetsabout the predictedtime delay. This is done on a special correlator.The sum reachesa maimum at the correctdelay. In order to achievebetter precision in the delayobservable than can be obtained from observationsat a single frequency,a techniquecalled bandwidthsynthesis,is used in which the delay is obtainedas the changein interferometerphase across two or more frequenciesspanning up to severalhundred megaHertz.More than two frequenciesare desirablein o¡der to removethe integer-cyclephase ambiguities, analogous to the useof multiple modulatingfrequencies to resolveambiguíties in EDM.

Geometryof VLBI Observables From Fig. l, the geometricaldelay is =-l's , c whereB is the baselinevector between the observingantennas, S is the unlr vecrorpolnt- ingin the direction of the sourceand c is the velocity of light. In the following discuìsion, c is setto unity for convenience. ln a referenceco-ordinate system where the sourceco-ordinates are fixed. the vector B will changein orientation but not in magnitudeas the earthrotates. For simplicity,-of assumethe co-o¡dinateaxes are arrangedso that the z-axis is in the direction the earth's instantaneousspin axis. The baselinevector É can then be split into two parts,a polar or z'componentparallel to the spinaxis and an equatorialor *y-.ornponentperpen- dicular to the spin axis.Thus - 1É,+ B*v) .(3" * 3*y) =:*n - (bzsz* Ê*v'\v)

whereb, and Sj are the magnitudeof the polar conponents. By definitlon, the polar componentcannot changewith the earth'sdiurnal rota- tion. Accorrlingly, part of the geometricdelay is constant and dependsonly on the z-componentof the baselinevector and that of the source.However, is the earth rotates, the equatorialcomponent of the baselineis carriedaround on a platform and its pro¡ec- tion onto the sourcedirection varies sinusoidallv â,= É*r, ' S*y b*y Sxy sin (cot + O) . where b*, and S*, are the componentsof Band s in the earth'sequatorial plane, respec-

The Aust¡alisn Surtcyor, March, 1983,Vol. 31, No. 5 307

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FIGURE1 THECONCEPT OF VLBI

308 The AustralianSurueyor, March, 1983, Vol. 31, No. 5

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it J.i, i. . ...''.'., GEODETIC SURVEYING WITH QUASAR RADIO INTENNEROMETRY tively, <.ris the earth's rotation rate, t is time and O is the phaseangle at a reference epoch.The total geometrÍcdelay is - (4Sr) - bry Sn, sin (<,rt+ @) The time derivativeof the geometricdelay, the delayrate, dependsonly on the equatorial componentsof the baselineand source vectors and is givenby r = - u¡ bxy S*, cos (c^rt+ O) By observinga number of sourcesrepeatedly throughout a ðay and by combiningthe resultingmeasurements in a leastsqì¡ares adjustment, tÌ¡e baseline vectors, source positions and variousother parameterscan be determined.

Comp[ications There are several physical phenomenawhich complicate the geometry of a vLBI observation.These are briefly discussedbelow: 1. The motions of the earth's axis of rotation in ínertial space(precession and nuta- tion) and of the physical earth relative to th-eaxis of rotation (polar motion) need to be accountedfor. The earth,moreover, does not rotate at a constantrate, but disphys both systematicand irregular variations in the Ìength of the siderealday; nor is the earth truly rigid" and the attractions of other bodies in ou¡ sola¡ system causesigrificant time varying distortions (earth tides). 2. The times recorded on the tapes along with the digitized signal are from indepen- dent station clocks. Due to imperfections, these will not run at preciselythe same rate; nor can they be perfectly synchronisedso that there will be a constant offset. The use of Hydrogen maserfiequency standardsresult in the diffutencë in r'ätes being quite small - of the order of a few parÉsin l0-1s. However,higher order variations can occur evenwith hydrogen masersor within the frequency distribu- tion system,and selectingthe right clock model is important. 3. The radio signalsmust pæs tfuough the earth's atmosphereen route to the obser- 'vatories which adds about I nanosec to the transit time of the signals.This is equivalent to 2.4 m in distance. For antennasseparated by only a few kilometres this presents no problem, as both are looking through similar atmospheres.\ilhen ,antennasare so far apart that atmospheric conditions are no longer correlated, variations in the atmospherewill contribute signifìcant'lyto r. The ionosphere usuatrlycauses a much smaller effect than does the tropo- sphere, $aving a worst cæe effect of 30 cm in the zenith direction for X-bind signals.;The ionosphereis a region of ionized air and free electronsaround the earth in the ealth's upper atmocphere,extending from a height of about 50 km to lO00km.¡ifhe troposphereis the atmosphere'slower layer which extendsto a height of about l0 km. The conéction for ionospheric refraction is made by using the dispersivenature of the mediurn whereby the delay of the signal at a giveñ frequency is inversely proportional to the squareof the frequency. Moteover,iince the ionospheric effect will be 13 times larger at 2.3 Gllz than at 8.4 GHz, a suitable comparison of the simultaneousobservations will allow the effect of the ionosphere to be removed. The contributions of the troposphereare non-dispersiveat micro. \ryavefrequencies, which means that indépendent measurementsare required to determine the required conection.

The Austalian Surueyot, March, 1983, Vol. 31, No. 5 309

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iÌìii,ìiii:l! A. STOLZer al

The troposphericeffects can be dividedinto two parts,(i) a dry componenr causedby ali componentsof the troposphereexcept water vapour, and (ii) a wet componentcaused by the watervapour. The dry componentcan be estimatedto a few per cent by measuringthe atmosphericpressure at eachof the telescopes. The wet componentcan be estimatedby measuringthe temperature,pressure and dew point at each telescope,but this is not fully satisfactorysince the dew point at a telescopeis not alwaysrepresentative of the water vapour contentalong the wave path. To achievea better calibration of the wet componenteach VLBI observingsite needsto be instrumentedwith a water vapour radlometerthat will measurethe microwavê brightnessin the vicinity of the 22 GHz water vapour emissionline. Tests have shown that this brightnessis well correlatedwith total water vapour along the line of observation.Radiometers were not availablefor the Australianexperiment. +. The telescopesare subject to distortions due to temperaturevariations, wind lo¿ding and gravitationaÌloading. Thesedisto¡tions can causesignificant changes in the time required for the signalto traversethe telescopes,and can also change the location of the mechanicalcentre of the telescoperelative to the groundrefer- ence point. Models basedon independentmeasurements and structuralanalyses must be developedfor eachtelescope to deriveappropriate corrections. 5. The time delays through the receivers,amplifiers and cabiesmay also vary. The delaysassociated with the cablesconnecting the ¡eceiverslocated on the telescopes, to the timing electronicslocated in the .control centres,are of particularconcern becausethey are subject to variations resulting from temperaturechanges and flexing. 6. The radio sources,in general,are not point sources,but are extendedand usually exhibit fine angular structure, at the level of milliarcsecondsin their brightness distributions.A sourceposition uncertai.ntyof 1 milliarcsecÇonespondsto a'ba^se- line uncertaintyof about a centiitet¡e for a baselinelength of 400 km. 7. Further complicationsinclude relativisticeffects on the clocksand on the signalsas they propagatethrough the sun'sgravitational fìeld and the changein the location of the second station durine the time interval ¡ due to both franslationaland rotat[onalmotions of the eartl.

The AustralianGeodetic VLBI Experiment From 20 April to 3 May, 1982, the fìve Australian radio-telescopesshown in Fig. 2 were, for the first time, operatedin synchronismto performboth astronomicand geodetic measurements.The telescopesare sited at the NASA Deep SpaceStation at TidbinbilÈa,the CSIRO Radio Observatoryat Parkes,the Universityof TasmaniaRadio Observadofonear Hobart, the Universityof Sydney'sFleurs Observatory near Sydney, and the LAND$AT trackingstation at Alice Springs.The antennasat Fleurs,Hobart and Alice Springs,aretìhstrumentãdto receivesignais af $band only, while thoseat Tidbinbilla and Parkes can observeat both X- and S-band.The Tidbinbilla station is equipped with Hydrogenmasers and one wasinstalled at Parkesespecially for the experiment.Rubidium frequencystandards are available at the other sitesexcept Hobart where one wasobtained on loan from the Dvision of National Mapping. The goals of the geodesypart of the experimentare: I. to measurebaselines around the triangle formed by Tidbinbilla,Parkes and Fleurs, with expectedaccuracies of 15 cm for the two horizontal domponentsofposition 310 The Australian Surueyor,March, 1983, Vol. 31, No. 5

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and 30 cm for the verticalcomponent, 2. to measurethe Parkes-Ticlbinbillabaseline with an expectedaccuracy of 7 cm for the horizontalcomponents and t 5 cm for the verticalctmponent; and 3. to measurethe Tidbinbilla-AliceSprings and Tidbinbilla-Hobartbaselines with an expecteduncertainty of l-2 m for all threecomponents. Two passesof 24 hours' durationat both S- and X-bandwere observedon the Tidbinbilla'Parkes baseline.Fleurs, Hobart and Alice Springsjoined in at night at S-band, One additional12-hour night-timepass with all five ståtioñsparticipating ar S-bandwas also observed. The S-bandmeasurements were madeonly ai night'becaúseof the large ionospheric erro¡s which occur at this frequency with daytiire measurements.The Mark II recordingsystem (gl1rk, 1973) was usedin the experiment.In this system,a spanned bandwidthof 40 MHz is synthesisedand digitally¡ãco¡ded ,".g".ú;;;;; tapes' The practical advantageof usingvideo recordeisis the ability to", record continu- ously for up to severalhours on a singlereel of tape, experiment ^ ^ Th. which was coñceivedand årganisedby staff of the CSIRODivision oI Kâdtophysics is a bi'national and multi-institutional effort to involve Aust¡alian geodesistsamongst others,in-VLBI.The geodeticdata processing,that is, the tape co¡rela- tion and the 4djustment of the geodeticparameters must be ãone in the United States as the proper facilities arenot availablehere. The work, which is now in progress,is being done at JPL and the MassachusettsInstitute of Téchnologyby Australians.JpL provided special equipment, the parkes Hydrogen maser for the site and expert personnelto supervisethe experiment. This aspectwas partially supportedby NASA under the Crustal Project. ,Dynamics The Division of National Mapping distributed time at all fìve o¡ser- vatories by means of a travelling CaesiumcloóË irime¿iately beiore the start of the experiment, connected the antennasto the Australian primaiy geodeticnetwork, and assistedwith operations at Tidbinbilla. The school or sururyiãg, university of New South Wales assistedwith operationsat Fleursand Tidbinhilte.'Thãlt¡straljan National U-niversity(ANU), ResearchSchool of Earth Sciencesassisted with operationsat the Alice Springsstation. Ea¡th scientistsat ANU and MacquarieUniversity are interested in the techniquefor studiesof crustalmovements in Austrafia. BaselineMeasurement Errors ' Both random and systematice¡rors are presentin geodeticVLBI measurements, with the systematic errors dominating.The main sourcesof random error are the noise temperatures of the receivers,variations in the frequency standardsand distribution systems, and radio source position and structure uncertainties.These can be reduced simply by acquiringmore data' The principalsources of systematicerror areuncertainties in the earth's orientation parametersand àtmosphe¡icefiects. The systematiceffects are not so easily;Ìti¡noved. ThËestimated .tro. U,rAg.tfor the Parkes-Fleursbaseline measure- ment is shownig Table t. the mçqnitud_esof the systematicerrors are unknown, it is not possibleto assess the accuracy of the VLBI baselinemeasurements. However, by independentlysolving for each.baseline defining the Parkes-Fleu¡s-Tidbinbillatriangle, it is possibleto check the consistency and quality ofthe dataand of the reductionsb! evaluatingthe vectorclosure. As an independentcheck, we also proposeto comparethe resultsirith those obtained from classicalmeasurement techniques.

The Australian Surveyor,March, 1983, Vol. 31, No. 5 311

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FIGURE2 THE AUSTRALIANGEODETIC VLBI ÐGERIMENT (Courtesyof RadiophysicsDivision, CSIRO) 3tz The AustralianSun¡e'ttor, March, 1983,Vol' 31, No' 5

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.l:i:l:' ì:É : l GEODETIC SURVEYINC WITH QUASAR RADIO INTERFEROMETRY TABLE1

ERROR BUDG ET FORPARKES-FLEURSB ASELINE MEASUREMENT*

ERRORSOURCE EFFECT.cm

FrequencyStandards / Distribution 5 SourcePositions

Atmosphere/ lonosphere 6 GeophysicalEffects 6

+ Total error=.1 0 cm Conclusions

vLBI is one of the rnost promising tools now under developmentfor making transcontinentaland inte¡continenfalgeodetic measurements. The siàesof the parkesl -Tidbinbilla-Fleurs triangle avercgearound 300 km. Conventionalgeodetic measurement techniqueswould at best givean accuracyof 30 cm for thesebase.-lines. The Tidbinbilla- Hobart and ridbinbilla-Alice Springsbaselines are about 900 krn and 2000 km long, respectively.An accuracyof l-2 m should be achievablefor thesebaselines by.onueíl tional methods. For the baselinesa¡ound the Parkes-Tidbinbilla-Fleurstrian$ä, that is, the baselinesbetween the better instrumented sites, VLBI shouk yiela väues more accurate.by a factor of about three. Thesemeasurements are thus of immediatebenefit for strengthening the Australiangeoderic nerwork. The Tidbinbilla-Hobartand ridbinbilla- Alice Springs baselines will provide a valuable check on the terrestriãlly.detennined distances. For theseobservations the Mark II recordingsystem was employed. This is not the most accuratesystem available.A new, more sensitiveMark III system of broad-band receivers, tape recordersand data processorshas receñtly beendeveloped which in com- bination with other instrument improvementswill allow determinatùnsof time delay and baselinemeasurements potentially accurate to I cm with modest size antennai. keliminary discussionshave taken place to instrument the proposedAustralia Telescope for Mark III VLBI geodesy,and there are prospectsfor bringinga mobile Mark III VLBI systemto lAustralia¡in the 1985 86.time-frame.Mark III dataacquisition systems will also be usedat Parkesand Tidbinbilla for the telemetryarraying during the Uranusencounter of Voyager in 1986' Thus, theseinstruments will also bJavailablefor higher accuracy measurementsin the 1985/86time-frame. t" Acknowledgèments :{ The.activltiesreported paper ,, . in this could not havebeen accomplished without the collaboration oT.several organisations and many individuals.It is nôt possiblehere to detail the cont¡ibutions of each.lVe would like to emphasisethe criticaliole of the close co'operationand supportprovided by Dr Nck Renzettiof the Jet Propulsionlaboratory, Pasadena. we also wish to acknowledgethe contributionsmade by: Ian Harvey,Jim Roberts, Bruce slee, Alan lvright, Bob Batchelor,Graham Moorey, John Gates,-David cooke, Ray Haynes,Dick Manchester,warwick wilson and Bob Ftãtãr, csrRo; Doug 'The AustralianSurveyor, March, 1983,Vol. 31, No. 5 313

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Mudgway,Ben Joh¡son, Lyle Skjerve,Al Kirk, RolandTaylor, Marty Slade,Dave Meier, Ann Werle,Jack Fanselow,John Faulknerand Alan touie, JPL;John Luck, DaveAbreu and Grant Moule,Division of NationalMapping; Peter lvlcCulloch, Pip Hamilton,Gordon Gowlancl,Philip Button, John Greenhill,Barry Wilsonand Barry Giles,University of Tasrnania;PeterAngus-lrppan, David Close, Col Wardropand BernieHirsch, University of New South Wales;Tom Rei

References BARE,C. C., CLARK,B. G., KELLERMAN,K. I., COHEÑ,M. H. andJAUNCEY, D. L., 196.7: InterferornetryExperiment with IndependentLocal Oscillators,Science, 157, 189-191. tsOSSLER,J. D., 198i. A note on Global PositioningSystem Activities,Am,CorryressSun'. Mapping Bull., August,198 1, 39-40. BROTEN,N. W., LEGG, T. H., LOCKE,J. L., McLEISH,C. W., RICHARDS, R. S., CHISHOLM, R. M., GUSH,H. P.,YDN, J. L. andGALT, J. A.,1967.Long Baseline Inte¡ferometry: A NewTechnique, Science,I 5 6, 1592-159 3. CARTER, W. E., 1981. An ElernentaryIntroductjon to Radio Interfe¡ometricSurveying..9arrey Review.26.17-31. CLARK, B. G., 1973..The NRAO Tape RecorderInterferometcr System, Proc. Inst. Elcc. Electron. Engineers,6 I, 1242-1248. COUNSELMAN,C. C., 1976.Radio Astrometry, /r n. Revs.Astron. Astrophys., 14, 197-214. FELL, P. J., f980. Geodetic Posirioning Using a GIobol Positioning System of Satellites, Dept. of GeodeticScience Rep. No. 299,Ohio State University, Columbus, Ohio. GOLD, T., 1967. Radio Method fo¡ the PreciseMeasurement of the Rotation Periodof the Eârth, Science,I 57, 302. GUBBAY, J. S., LEGG,A. J. and ROBERTSON,D. S., 1974:Position Solution of CompactRadio Sou¡cesUsing Coherence VLBI, in W. Glieseet al (erJsjNew Problemsin AslronÊtry,!ÀLr Sympc- siumNo. 61, D. Reidel,Do¡d¡echt. HINTEREGCER,H. F., SHAPIRO,I. I., ROBERTSON,D. A., KNIGHT,C. A., ERGAS,R. A., WHITNEY,A. R., ROGERS,A. E. E., MORAN,J. M., CLARK,T. A. and BURKE,F. G.,1972. RadioInte¡ferometry. Science, I 78, 396-398. NIELL, A, E. ONG, K. M., MACDORAN,P. F., RESCH,G. M.,MORABITO, D. D., CLAFLIN,E. S. and DRACUP, J. F., 1979. Comparisonof a Radio Inte¡fe¡ometricDifferential Baseline with ConventionalGeodesy. Tectonophysics, 52, 49-58. ROGERS,A. E. E., KNIGHT, C. A., HINTEREGGER,H. F., WHITNEY,A, R., COUNSELMAN,C. C. SHAPIRO,I. I., GOUREVITCH,S. I. andCLARK T. 4., 1978.Geodesy by RadioInte¡ferometry: Determinationof a 1.24 km BaselineVector with -5 mm Repeatability.J. Geophys.Res.,83, 32s-334. SHAPIRO,I. I., 1978.Principles of Very-Long-BaselineInte¡ferometry, in W. I. Muelle¡(ed) Applicø- tions of Geodesyto Geodynamics,Dept. Geod.Sci. Rep. 280, 29-33,The Ohio StateUniversity, ColumÈus.Ohió. SHAPIRÓ,i¡ I. and KNIGHT, C. 4., 1970.Geophysical Applicafions of Long-BaselineInterferometry, in D. E.rSmylie and A. E. Beck (eds) Earthquake DispløcementF'ields and the Rotation of the Earth, DlReidel, Dordrecht,284-301. SHAPIRO,I. I., ROBERTSON,D. S., KNIGHT,C. A., COUNSELMAN,C. C., ROGERS,A. E. E., HINTEREGGER,H. F., LIPPTNCOT-I,S., WHITNEY, A. R., CLÄ.RK,T. A'., NIELL, A. E. and SPITZMESSER.D. J., 1974.T¡anscontinental Baselines and the Rotation of the Ea¡th Measured by RadioInterferometry . Science,186, 920422.

(Received5 October I 982;accepted for publication 29 Octobcr 1982.)

3t4 Thc Australian Stçve,'or, March, 1983, Vol. 31, No. 5

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