JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. B5, PAGES 9961-9981, MAY 10, 1997

Global plate velocities from the Global Positioning System

Kristine M. Larson Department of AerospaceEngineering Sciences, University of Colorado, Boulder

Jeffrey T. Freymueller GeophysicalInstitute, University of Alaska, Fairbanks

Steven Philipsen Department of AerospaceEngineering Sciences, University of Colorado, Boulder

Abstract. We haveanalyzed 204 daysof GlobalPositioning System (GPS) data fromthe global GPS network spanningJanuary 1991 through March 1996. On the basisof these GPS coordinate solutions,we have estimated velocities for 38 sites, mostly located on the interiors of the Africa, Antarctica, Australia, Eurasia, Nazca, North America, Pacific, and plates. The uncertaintiesof the horizontal velocity componentsrange from 1.2 to 5.0 mm/yr. With the exceptionof siteson the Pacific and Nazca plates, the GPS velocitiesagree with absolute plate model predictions within 95% confidence.For most of the sites in North America, Antarctica, and Eurasia,the agreementis better than 2 mm/yr. We find no persuasiveevidence for significantvertical motions(< 3 standarddeviations), except at four sites. Three of these four were sites constrainedto geodetic referenceframe velocities. The GPS velocities were then used to estimate angular velocities for eight tectonic plates. Absolute angular velocitiesderived from the GPS data agree with the no net rotation (NNR) NUVEL-1A model within 95% confidenceexcept for the . Our pole of rotation for the Pacific plate lies 11.5ø west of the NNR NUVEL-1A pole, with an angularspeed 10% faster. Our relative angularvelocities agree with NUVEL-1A except for some involving the Pacific plate. While our Pacific-North America angular velocity differs significantlyfrom NUVEL-1A, our model and NUVEL-1A predict very small differencesin relative motion along the Pacific-North America plate boundary itself. Our Pacific-Australia and Pacific- Eurasia angular velocitiesare significantlyfaster than NUVEL-1A, predicting more rapid convergenceat thesetwo plate boundaries.Along the , our Pacific-Nazcaangular velocity agrees in both rate and azimuthwith NUVEL-1A.

Introduction 3.16m.y.). Thesemodels have been tremendously suc- cessfulin explainingthe large-scalefeatures of plate For almost 20 years, models of current plate mo- kinematics.Global plate modelshave shownplate in- tions have been determined using spreading rates at teriors to be rigid over geologictimescales. The vari- mid-ocean ridges, transform azimuths, and plate ousgeologic data all giveconsistent measures of global boundary earthquakeslip vectors [LePichon, 1968; plate motions, although earthquakeslip vectors have Chase, 1972; Minster et al., 1974; Minster and Jor- beenfound to be biasedin somecases due to the par- dan, 1978; Chase,1978; DeMets et al., 1990]. With the tition of slip at certain marginswhere subductionoc- exceptionof earthquakeslip vectors,these data repre- curs obliquely[DeMets et al., 1990; Argus and Gor- sent an averageover a substantialperiod of time (for don, 1990]. Absoluteplate motionshave been com- the NUVEL-1 model of DeMets et a/.[1990],the last puted based on the NUVEL-1 relative plate motions and the assumptionof no net rotation (no net torque on the lithosphere),resulting in the absolutemotion Copyright 1997 by the American Geophysical Union. modelno net rotation (NNR) NUVEL-1 [Argusand Paper number 97JB00514. Gordon,1991]. A recentrevision of the magnetictime 0148-0227/97/97JB-00514509.00 scaleled to the rescaledNUVEL-1 models,NUVEL-1A

9961 9962 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS and NNR NUVEL-1A (hereinafterreferred to as NNR- workof Argusand Heftin [1995]by includingmore sites, A) [DeMetset al., 1994]. more tectonic plates, and a longertime seriesand by us- Spacegeodetic data collectedover the last two decades ing only a subsetof the availableGPS data. This allows have made it possible to measure plate motions over us to analyze the entire data set using the same mod- the time scale of years rather than millions of years els and techniques.We also include selectedtemporary [e.g.,Robbins et al., 1993].The abilityto makeglobal- occupationsof sites rather than restricting ourselvesto scalegeodetic measurements was made possible through only permanent station data, improving the distribu- the developmentof highly sophisticatedspace geode- tion of sites on some of the plates. tic techniquessuch as satellitelaser ranging (SLR) and very long baselineinterferometry (VLBI). One of the Measurements primary scientificgoals when these techniques were be- ing developedwas to measureglobal plate motions. While some global GPS tracking sites have existed Both SLR and VLBI achieved sufficient accuracy that sincethe late 1980s, the operation and archiving of the they couldbe usedto measureboth globalplate motions network were not globally coordinated,and the distri- and plate boundarydeformation [Clark et al., 1987; bution of stationswas too sparseto supportglobal G PS Smith et al., 1990; Robbinset al., 1993; Ryan et al., studies. This changed in January-February 1991 with 1993],but both sufferedfrom the disadvantageof the the InternationalAssociation of Geodesy(IAG) spon- high costand nonportabilityof the systems,which lim- sored global GPS densificationexperiment, the first ited the number and distribution of sites worldwide. At Global International Rotation Service(IERS) roughlythe sametime SLR and VLBI werebeing devel- and Geodynamicscampaign (hereinafter referred to as oped and tested, the Department of Defensebegan de- GIG). Over 100 GPS receiverswere deployedin this ploymentof the GlobalPositioning System (GPS). Its campaign, although many were of insufiqcientquality primary missionwas and is to provide real-time nav- to be truly useful [Melbourneet al., 1993]. Analysis igation and positioningassistance. Scientistsquickly of a subset of the GIG data provided direct evidence realized that GPS could also be used for positioning of the potential of global GPS: I cm positioningaccu- with a precisionapproaching that of VLBI and SLR. racy [Blewitt et al., 1992] and submilliarcsecondpole GPS analysis softwareshas been developedover the positionestimates [Herring et al., 1991]. Following past decadefor this purpose[e.g. Dong and Bock,1989; the successof GIG, the IAG sponsoredthe develop- Beutler et al., 1987; Blewitt, 1989]. The GPS constel- ment of the International GPS Servicefor Geodynam- lation has now been completed and a global tracking ics (IGS), whichprovides timely accessto high-accuracy network is operating under international cooperation. GPS ephemeridesbased on data from a globalnetwork The focus of this paper will be to use GPS and the of permanent GPS receivers. The IGS has coordinated global tracking network to study plate . developmentof the global GPS network, which is now Why is geodeticanalysis of global plate motionsim- generallyreferred to as the IGS network. portant when geologicmodels have been so successful? Data from sites participating in the IGS network are Geodetic techniques have become increasingly promi- downloadedby the agencieswhich operate them, and nent in studiesof plate boundary deformation and have transferredvia internet to the IGS global data centers. approachedthe level of precisionof globalplate models. The number of GPS receiversparticipating in the IGS Geodetic techniquesalso measure plate motion over a network continues to expand. At present, there are period of a few years rather than a few million years, more than 70 globalsites in the IGS network,excluding so it is important to find discrepanciesthat would indi- denseregional clusters in California. The most signifi- cate if there have been any very recent changesin plate cant changeover the last few yearshas beenthe increase motions. Today, regional tectonic studiesin California in the number of IGS sites in the southernhemisphere, and elsewhereare attempting to characterizefault slip from four in 1992 to more than 5 times that number rates in plate boundary zones so completely that the today. Receiver,antenna, and softwaredescriptions for entire slip budget comparesto a global plate model to the IGS network are documented at the IGS Central within a few millimeters per year or better. Such stud- Bureau(http://igscb.jpl.nasa.gov). ies are only feasible if the rates of plate motions are For this paper, we have analyzed data for the period known to the same level of precisionand if the rates of between January 1991 and March 1996. The sites we motion over the last few years (or few hundredyears) have chosenfor this study are listed in Table I and are describedadequately by a plate motion model aver- shownin Figure 1. Of these 38 sites, 16 were first ob- agedover the last few millionyears. Early spacegeode- servedduring the 3 week GIG campaign. There is then tic studies have shown a high correlation between ob- a 1 year gap in our time series,until enoughpermanent servedrelative site velocitiesand the predictionsof the stations had been deployedfor the IGS network. Be- NUVEL-1 model[Smith et al., 1990].In this studywe ginningin March 1992, we have analyzeddata from the will compareangular velocities for eight plates and var- IGS network on a weekly basis. An analysisof IGS data ious plate pairs derived from our GPS data with the from January 1991 through November 1993 was previ- NUVEL-1A model. This study differs from the similar ouslypresented by Larsonand Freymueller[1995]. In LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9963

Table 1. Station Description Site Namea IGS Plate Lonl•itude, Latitude, First Last Total aeg deg Epoch Epoch Epochs

I Albert Head ALBH NOAM 236.513 48.201 1992.37 1996.25 161 2 Algonquin ALGO NOAM 281.929 45.765 1991.06 1996.25 200 3 Baltra Islandb BALT NAZC 269.741 -0.461 1991.08 1996.25 9 4 Bermuda BRMU NOAM 295.304 32.198 1993.26 1996.25 125 5 Canberra CANB AUST 148.980 -35.220 1991.06 1996.25 181 6 Chatham Island CHAT PCFC 183.434 -43.766 1992.91 1996.25 16 7 EISL NAZC 250.617 -26.994 1994.07 1996.25 48 8 Fairbanks FAIR NOAM 212.501 64.832 1991.06 1996.25 199 9 Fortaleza FORT SOAM 321.574 -3.852 1993.46 1996.25 123 10 Hartebeestoek HART AFRC 27.708 -25.738 1991.06 1995.99 188 11 Hobart c HOBA AUST 147.440 -42.614 1993.20 1995.96 92 12 Hercmonceaux HERS EURA 0.336 50.681 1992.17 1996.25 143 13 Kourou KOUR SOAM 307.194 5.218 1992.88 1996.25 130 14 Kootwijk KOSG EURA 5.810 51.994 1991.06 1996.25 192 15 Kokee Park KOKB PCFC 200.335 21.994 1991.06 1996.25 173 16 Mas Palomas MASP AFRC 344.367 27.607 1992.51 1995.99 157 17 Matera, Italy MATE EURA 16.704 40.461 1992.27 1995.99 131 18 Madrid, Spain MADR EURA 355.750 40.241 1991.06 1996.25 199 19 McMurdo d MCM3 ANTA 166.675 -77.770 1991.06 1996.25 164 20 North Liberty NLIB NOAM 268.425 41.582 1993.20 1996.25 94 21 Ny Alesunde NYAL EURA 11.865 78.858 1991.08 1996.25 63 22 O'HigginsJ• OHIG ANTA 302.100 -63.168 1991.06 1995.88 37 23 Onsala ONSA EURA 11.926 57.222 1992.17 1996.25 180 24 Pamatai PAMA PCFC 210.425 -17.457 1992.17 1996.24 106 25 Pie Town PIE1 NOAM 251.881 34.124 1993.00 1996.25 71 26 Penticton PENT NOAM 240.375 49.134 1992.17 1996.25 179 27 Perth PERT AUST 115.885 -31.632 1993.77 1996.25 78 28 Richmond RCM5 NOAM 279.616 25.466 1992.57 1996.25 134 29 Santiago SANT SOAM 289.331 -32.976 1991.06 1996.25 198 30 St John's STJO NOAM 307.322 47.405 1992.41 1996.25 157 31 Taiwan TAIW EURA 121.537 24.876 1992.37 1996.25 162 32 Tromso TROM EURA 18.938 69.538 1992.17 1996.25 111 33 Townsville TOWN AUST 146.814 -19.141 1991.06 1992.88 45 34 Tsukuba TSKB EURA 140.088 36.106 1993.96 1996.25 59 35 Westford WES2 NOAM 288.507 42.424 1993.21 1996.25 82 36 Wettzell WETT EURA 12.879 48.956 1991.06 1996.25 191 37 Wellington WELL AUST 174.783 -41.086 1991.06 1995.13 61 38 ¾aragadee ¾AR1 AUST 115.347 -28.885 1991.06 1996.25 204

aUnless stated otherwise, the local surveys between different monuments at the same site were taken from ITRF94 [Boucheret al., 1996]or the IGS CentralBureau (http://igscb.jpl.nasa.gov). bThe1996 observations were made at Isla SantaCruz (GALA). Tie calculatedfor This paper: GALA minusBALT -4,973.763, 404.838,-31,181.929 m. CTie calculated for this paper: HOB2 minus HOBA 112.719, 50.737, -50.183 m. •There are observationsat four McMurdomonuments, defined as follows. McMurdo GIG: MCM1; McMurdo1992-1993: MCM2; McMurdo 1994: MCM3; McMurdo 1995-1996: MCM4. Ties calculated for This paper: MCM1 minus MCM3 -234.600, 17.358, 52.521 m; MCM2 minus MCM3 -73.423, 54.691, 36.920 m; MCM4 minus MCM3 -1,081.537, 400.997, 145.126 m. eData from 1991-1992 excluded "The antenna had been hit by a stone... and was knocked over lying on its side," IGS Mail 135. No tie available between 1991-1992 location and 1993-1996 location. fTie from GIG site and permanentsite, personnalcommunication, Andreas Reinhold: OHIG-GIG (K4) minusOHIG (K5): 4.715, -0.277, 0.849 m. that paper, a global set of stations was analyzed, but as the GIG campaign. Our decisionis based on two only the velocitiesof sites on the Pacific, Australian, characteristicsof GPS data. First, it has been shown and Antarctic plates were discussedin detail. In this that GPS estimates are highly correlated over periods study, we have expandedour analysis and interpreta- of severaldays [King et al., 1995]. Thus,if solutionsare tion to include the Eurasian, North American, African, computed each day, they will not be independent. Sec- Nazca and South American plates. ond, station velocity uncertainties are more sensitiveto Even though IGS data are availableon a daily basis, the time spanned by the data set than additional data we have chosento analyze only one day of GPS data points spacedclosely together in time. In order to ana- per week, except for special periods of interest such lyze as uniform as possiblea data set and in an effort to 9964 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

180' 0' 180'

180 ø 0 ø 180 ø Figure 1. GPS stationsused in this study. The sizeof the symbolscorrespond to the lengthof the time series,from more than 5 years,between 4 and 5 years, between3 and 4 years, and less than 3 years. avoid correlatedestimates, we analyzed global tracking The pseudorangedata are acquired by correlation of a data only once per week. By restrictingourselves to a code in the data signal, called the P code. During peri- data set of manageablesize, we havemade it possibleto odswhen the Pcodeis encrypted(antispoofing, or AS), reanalyzeas muchdata as neededto ensureconsistency all modern receiverscan extract equivalentpseudorange of our solutionsover time as modeling techniqueshave data from the signalsby using signal crosscorrelationor •mproved. Although we have analyzedmore than the other methodswhich tend to result in somedegradation 38 sites in Table 1, we computedvelocities only for the in signal to noiseratio and data quality. This varies by sites for which we feel an accurate and reliable velocity receiver type and local environment and has lessened can be estimated. Therefore we excluded all sites with over time as GPS receivers have been improved. We lessthan 2 years of data. Unfortunately, this means choosestandard data weights of I cm for the carrier that we do not discuss some of the newest IGS sites phase data and, with a few exceptions, 100 cm for the in interestingtectonic areas such as central Asia. We pseudorangedata if the receiver records it. Pseudor- also excluded data from sites that have been displaced ange data from Rogue SNR-8 and Mini-Rogue SNR- by .In additionto uncertaintyassociated 800 receiversare biasedunder AS, so we excludedthese with the coseismicdeformation, these sites may also be pseudorangedata duringperiods of AS (AS hasbeen on affectedby postseismicdeformation. As a result,we do almost continuouslysince January 30, 1994). Pseudo- not discussseveral of the long-termIGS sitesin south- range data are also excludedfrom certain Turborogue ern California. SNR-8000 receiversthat showpseudorange biases under AS. Data Analysis All raw data were passedthrough an automatic edit- ing stage,during which cycle slips (discontinuities in the All data presentedin this paper were analyzedusing phasedata) werefound and correctedand outlierswere the GIPSY/OASISII software(release 3 andrelease 4) removed. For Rogueand Turboroguereceivers, the Tur- developedat the Jet PropulsionLaboratory, California boEditalgorithm [Blewitt, 1990] was used. For all other Institute of Technology.The currentversion of the soft- receivers,the PhasEdit algorithm (J. Freymueller,un- ware is an evolution of the softwaredescribed by Lichten publishedalgorithm, 1996) was used. Both algorithms and Border[1987]. searchfor discontinuitiesin undifferencedgeometry-free GIPSY uses undifferenced carrier phase and pseu- (and clock-free)linear combinationsof the observables. dorangeobservables. For a generaldescription of the After data editing, the data from both GPS frequencies GPS observablesand data analysis, see, for example, are combined to form the ionosphere-freelinear combi- Holmann-Wellenhofet al. [1993]and Leick[1995]. The nation [see,e.g., Leick, 1995]and are decimatedto a carrier phaseis more precisethan the pseudorangebut standard 6 min interval. Additional editing of the data is ambiguousby an integernumber of wavelengthsso a is done manually based on inspection of postfit data carrierphase ambiguity must be estimatedfor eachcon- residuals, and data can be deleted or new phase ambi- tinuousphase-connected arc of GPS carrier phasedata. guity parameters inserted when outliers or cycle slips The pseudorangeis unambiguousbut has a noiselevel are found to have passedundetected through the auto- approximately100 times higherthan the carrier phase. mated editing. The number of suchediting changesre- LARSON ET AL.' GPS GLOBAL PLATE MOTIONS 9965 quired has varied somewhatwith time. In general, prior Each station position estimate is based on 24 hours of to the introduction of AS almost all data problemswere GPS data. We followeda strategysimilar to that de- detected and correctedby the automatic algorithms. scribedby Heftin et al. [1992]. The coordinatesof six Data quality worsenedconsiderably after the introduc- globallydistributed siteswere constrainedto agreewith tion of AS and has been improvingsteadily sincethen VLBI/SLR coordinateswith an a priori uncertaintyof as the receiver hardware has been improved. 10 m. The remaining sites were constrainedwith an a Parameter estimationin GIPSY is carried out usinga priori uncertainty of I km. These loose constraints are SquareRoot Information Filter (SRIF) algorithm[Bier- sufficientto avoidsingularities in the GPS solutionsbut man, 1977]which allows us to estimateparameters as are not sufficientto specify the referenceframe. constants or varying in time. We estimate both sta- We have made a considerableeffort to analyze the en- tion and satellite clock errors relative to a user-specified tire time seriesof data consistently. The same models referenceclock as white noiseparameters, uncorrelated and strategies are used throughout, which has meant from epochto epoch. We estimate the wet tropospheric reanalyzing the earlier data as models have improved. path delay at zenith as a time-dependent parameter Through this effort we hopeto avoid aliasingsystematic with a randomwalk noisemodel [Lichten and Border, errors into our estimated station velocities and tectonic 1987; Tralli et al., 1988]. Orbits are modeledby inte- interpretations. There is one unavoidable differencebe- grating the equationsof motion and estimating correc- tween data collected in 1991-1993 and data collected tions to the initial conditions,as describedby Lichten in 1994-1996. On January 30, 1994, antispoofingwas and Border[1987]. We estimatesolar radiation pres- implemented on the GPS constellation. As described sure coefficients for the ROCK4 or ROCK42 model as above, this reduced the quality of the carrier phase data appropriate[Fliegel et al., 1992]. We estimatea single and the amount of pseudorangedata which was avail- X-Z solarradiation pressurescale parameter, plus small able to us. However, we have not been able to identify independentX and Z corrections,and a Y-bias param- any significantchanges in velocitywhich correlatewith eter. For satellitesthat are eclipsing(passing through the introduction of AS. shadowon each revolution),we estimatetime- varying solar radiation pressureparameters. The GPS Reference Frame yaw attitude modelis describedby Bar-Sever[1996]. A summaryof the modelsused in GIPSY/OASIS and As describedabove, we estimate GPS station coordi- our parameter estimation strategy is given in Table 2. nates for each day of data in loosely constrained solu-

Table 2. Data Analysis Summary

Models Value

Data interval 6 min Elevation angle cut-off 15 ø Geopotential JGM3 degreeand order 12 Precession IAU 1976 precessiontheory Nutation IAU 1980 nutation theory Earth Orientation IERS bulletin B Difference phase center correction Schuplerand Clark [1991] Yaw attitude Bar-Sever[1996] Reference clock Algonquin Pseudorangeweight 100 mm Carrier phase weight 10 mm

Parameter Estimation Standard Deviation

Satellite position force model I km Satellite velocity force model 0.00001km/s Satellite clock white noise ls Solar pressureYbias constant 10-19' km s-•s -• Solar pressureX/Z constant 1% of Ybias Eclipsing satellites stochastic 1 hour updates Station position, reference constant 0.01 km Station position, nonreference constant I km Station clock white noise ls Phaseambiguity (real-valued) constant 0.1 km Zenith tropospheredelay random walk 10 mm/sqrt(hour) 9966 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS tions. That means that we tightly constrainedneither We can transform our solutions into ITRF94 in dif- the coordinatesof the tracking sites nor the orbits of ferentways. Larsonand Freymueller [1995] estimated a the GPS satellites(see Table 2 for a descriptionof our seven parameter transformation for each GPS solution analysisstrategy and constraintdefinitions). In our so- and then simultaneouslyestimated linear fits to all sites lutions, the orbits of the GPS satellites are not in a using the entire time series. Unfortunately, this tech- well-determined reference frame. The entire GPS con- nique is sensitiveto data outagesat the referencesites. stellation can be rotated in longitude without degrad- Owing to unavoidablerandom or systematicerrors in ing the fit of the data to our models. Equivalently,the the referencesite coordinatesand velocities,a different longitudesof our estimatedstation coordinatescan be set of referencesites will produce a different realization rotated without degradingthe data fit, although this is of the referenceframe. In this study we have applied not true for either height or latitude. However, while the referenceframe constraintsdifferently. We first es- the entire GPS network and GPS constellation can be timate the velocity and epochposition of each site from transformedas a rigid unit, our looselyconstrained solu- the unconstrainedsolutions, using the full covariance tions still determine relative frame-invariant quantities information from our GPS solutions. This velocity so- very precisely. Station geocentricheights and baseline lution is, like the individual GPS solutions,loosely con- lengthsare determinedvery preciselyin the looselycon- strained. We then apply reference frame constraints strained solutions,subject to someuncertainty in scale. by using the published ITRF94 positions and veloci- In order to use the coordinates derived from these ties for selectedreference sites as pseudo-observations, solutions, we need to transform all of the loosely con- weighted by the ITRF94 covariancematrix. strained solutions into a consistent reference frame so The reference sites we have chosen are listed in Table that we can derive•ates of site motion (and plate mo- 3, and their locations are plotted in Figure 2. These tion) from the time seriesof coordinates.The reference werechosen for their (1) high accuracy,(2) geographic frame definesthe scale, origin, and orientation of our distribution,and (3) inclusionin the time seriesfrom geodeticcoordinates. The referenceframe is specified 1991 through 1996. For geometric reasons, we would by meansof a prioriinformation about the coordinateslike to add a site in east Asia, but there were no sites and/or velocitiesof sites, or other similar quantities. that met our criteria for the period 1991-1996. There Since all plates on the Earth are moving, we must use are many other sitesin Europe and North America that a kinematic referenceframe, that is, one which includes could have been chosen, but these sites are close to- the time evolution of the reference frame parameters. gether and provide no additional geometric strength. A referenceframe is realized through the coordinates We do not want to constrainthe velocitiesof too many and covariancesof individual stations. A sevenparame- sites, becauseour objective is to study the tectonic im- ter transformation can be estimated to transform an un- plications of the GPS velocities. constrainedGPS solutioninto a specificreference frame. The quality of the transformationwill dependon the ac- Site Velocities curacyof the coordinatesand velocitiesof the reference stations which are used to derive the transformation Using the techniques described above, we estimated and on the geographicdistribution of thosestations. In velocitiesfor 38 GPS sites. Velocity estimates, trans- addition to random errors in coordinates and velocities, formed into horizontal and vertical components, are the accuracyof the referencestation coordinatescan be listed in Table 4 along with the NNR-A velocity pre- compromisedby errors in local survey ties. diction and ITRF94 velocity,if available. This velocity For this study we have adoptedthe ITRF94 reference solution is based on our entire time series of data. frame (InternationalTerrestrial Reference Frame 1994 It is instructive to compare the velocity estimates [Boucheret al., 1996]).This is the bestfit modelof po- based on all of the data with an individual time se- sitionsfor 240 geodeticsites using the VLBI, SLR, GPS, ries of coordinatesderived from the same solutionsby and DORIS techniques.Velocities for someof the sites transforming each individual solution into the ITRF94 are alsoincorporated into ITRF94 if there are sufficient data to determine an accurate velocity estimate. In practice, ITRF94 velocitiesare availablefor sites with Table 3. Reference Stations longhistories of VLBI and SLR measurements.ITRF94 closelyfollows the developmentof previousframes, in Site Name Location particular,ITRF92 [Boucheret al., 1993]and ITRF93 I Yaragadee Australia [Boucheret al., 1994],with improvementsboth in data 2 Santiago South America-Nazca quality and estimationstrategy. ITRF94 is designedto 3 Hartebeestoek Africa agreeon averagewith the NNR-A absoluteplate mo- 4 Madrid Europe tion model, so ITRF94 velocitiesof sites on plate inte- 5 Kokee Park Pacific 6 Algonquin North America riors should be directly comparableto the predictions 7 Fairbanks North America of NNR-A if the plates are rigid. LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9967

180 ø 0 ø 180 ø

.30 ø 0 ø

.60 ø _60 ø

-90 -90 ø 180 ø 0 ø 180 ø Figure 2. Stationsused to definethe referenceframe (seeTable 1 for station identifications).

Table 4. Station Velocities and Standard Deviations

GPS NNR-A ITRF94

Station North East Up North East North East Up

ALGO 2.6+1.2 -16.1+1.2 4.5+1.2 3.2 -17.0 1.0+1.4 -16.5+1.4 4.6+1.4 ALBH -7.1+1.5 -6.0+1.6 -0.9+2.0 -14.0 -14.2 BALT 9.2+1.9 41.7+5.0 -21.2+8.6 9.6 61.7 BRMU 8.04-2.0 -13.44-2.2 -1.3+2.9 8.3 -12.3 CANB 55.6+1.3 17.3+1.5 8.4+1.8 53.7 17.7 53.6 + 2.2 21.4 + 2.2 -1.6 + 2.2 CHAT 38.4+2.0 -48.3+2.5 1.54.4.4 31.4 -40.5 EISL -4.9+2.9 77.4+4.2 -4.7+6.6 -8.9 79.4 -12.0 + 2.2 75.1+2.3 -1.0 + 2.2 FAIR -21.6+1.2 -9.8+1.2 -1.6+1.2 -20.2 -10.3 -22.9 + 1.5 -8.2 + 1.6 -2.5 4. 1.5 FORT 10.14.2.1 -9.04.2.5 5.04.3.6 11.7 -5.5 HART 16.9:t:1.3 16.64.1.3 -0.24.1.3 20.1 20.7 15.2 4. 2.1 16.2 4. 2.3 -1.6 4. 2.4 HERS 15.14.1.5 16.34.1.6 -1.64.2.2 15.2 17.6 15.9 :t: 1.3 18.0 4. 1.5 1.9 4. 1.3 HOBA 55.44.2.2 16.24.2.5 5.44.3.5 54.4 12.8 KOKB 33.44.1.2 -61.44.1.2 -0.34.1.2 32.3 -58.3 33.4 4. 1.7 -60.0 4. 1.6 -1.0 4- 1.5 KOSG 15.74.1.2 19.74.1.3 -4.94.1.7 14.5 18.5 15.3 4. 1.5 18.6 4. 1.9 - 1.1 4. 1.5 KOUR 11.84.1.8 -4.44.2.1 0.14.3.1 11.1 -5.9 MADR 15.74.1.2 20.24.1.2 2.94.1.2 15.7 18.6 16.14.1.4 18.74.1.5 1.94.1.4 MASP 17.74.1.7 16.64.1.9 1.34.2.5 17.5 17.1 MATE 18.94.1.6 23.94.1.8 -4.84.2.3 12.8 22.0 18.0 4. 1.7 23.44.1.5 -2.44.1.6 MCM3 -10.54-1.4 8.74.1.5 -1.94.2.3 -11.7 7.5 NLiB -2.54.1.9 -16.24.2.1 0.04.2.7 -2.2 -15.9 -2.5 4. 2.7 -14.6 4. 1.8 -13.5 4. 2.8 NYAL 14.0:t:2.1 15.0•:2.2 9.94.4.6 13.6 12.9 OHIG 11.84.1.7 15.34.1.9 -7.44.3.1 10.2 16.3 ONSA 14.44.1.5 18.04.1.6 0.74.2.0 13.6 18.6 13.04.1.5 17.94.1.6 -1.1 4. 1.5 PAMA 32.84.1.6 -74.8 :t: 2.6 -1.54.3.5 31.5 -62.9 PENT -10.54.1.5 -14.64.1.6 -2.44.1.9 12.7 -15.1 PERT 55.54.2.4 41.34.2.7 7.64.3.9 59.2 38.0 PIE1 -8.24.1.8 -14.64.2.1 6.64.3.0 -8.7 -12.8 RCM5 2.04.1.6 -12.74.1.8 -0.54.2.4 2.2 -10.7 3.3 4. 1.4 -8.94.1.4 1.74.1.2 SANT 17.54.1.3 17.24.1.3 5.44.1.3 9.5 -0.9 20.24.2.8 18.44.3.2 3.0 + 2.8 STJO 14.64.1.6 -!6.2:t:1.7 -2.44.2.0 12.6 -14.8 TAIW -12.84.1.6 27.14.2.1 -6.24.2.6 -13.3 22.3 TOWN 56.54.3.3 23.34.4.2 19.34.7.2 54.7 30.0 TROM 16.04.1.3 16.44.1.4 1.54.2.1 12.4 17.2 15.64.1.8 16.44-1.9 -0.3+2.0 TSKB -16.64.2.6 -10.84.3.2 -1.94.4.2 15.7 -19.2 WELL 34.44.1.7 -19.44.2.2 8.34.3.2 37.1 -0.6 WES2 3.14.1.9 -15.64.2.1 -0.44.2.7 5.7 -15.7 WETT 14.84.1.2 22.14.1.3 -2.04.1.8 13.5 20.3 14.2 4. 1.2 19.7 4. 1.4 -3.3 4. 1.3 YAR1 56.5 :t: 1.2 38.44.1.2 6.24.1.2 59.1 39.0 58.44.1.4 38.54.1.4 4.24-1.3

In millimeters per year. 9968 LARSON ET AL.' GPS GLOBAL PLATE MOTIONS

0.4

0.2 (o)

(b)

-0.2

04

1990 1992 1994 1996

years Figure 3. Individual epochsolutions in latitude, longitude,and height for Yaragadee,Australia. At each epoch, a seven-parametertransformation has been estimated between the unconstrained solutionsand InternationalTerrestrial Reference Frame 1994 [Boucher et al., 1996].Formal errors are one standarddeviation. The linesshown are the fits to the global GPS solutions,as described in the text.

reference frame independently. The most frequently the northernhemisphere, Kootwijk (KOSG), locatedin observedsite in this study is Yaragadee(YAR1), lo- the Netherlands. For Kootwijk, the weightedRMS de- cated in western Australia. The latitude, longitude, viation about the best fit line is 3.7, 4.9, and 9.4 mm and height estimatesof this site as a function of time for latitude, longitude, and height, respectively. The are shown in Figure 3 along with the linear fit of the improvement in position standard deviation for both global solution to the individual epoch solutions. The Kootwijk and Yaragadeefrom 1991 to the present is weightedRMS deviation about the best fit line is 4.5, due to the increase in the number of satellites in the 7.6, and 12.2 mm for latitude, longitude, and height, GPS constellation, from 15 satellites in 1991 to 24 to- respectively. In Figure 4, we show a typical site from day. The contrast in precisionbetween Yaragadee and

0.4

0.2 _(o)

0.0 _(b)

-0.2

-0.4

1990 1992 1994 1996

years

Figure 4. Individual epoch solutionsin latitude, longitude, and height for Kootwijk, Nether- lands. At each epoch, a seven-parameter transformation has been estimated between the un- constrainedsolutions and InternationalTerrestrial Reference Frame 1994 [Boucheret al., 1996]. Formal errorsare one standarddeviation. The linesshown are the fits to the global GPS solutions, as describedin the text. Note that the Kootwijk coordinatesare more precisewhen comparedto Yaragadeein Figure 3. This is due to the strength of the IGS network in the northern hemisphere relative to the southern hemisphere. LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9969

Kootwijk reflectsthe greater number of tracking sites whereO'fram e = 0.5 mm/yr, At is in years,and C = 5.5 (and better realizationof the ITRF) in the northern ram, correspondingto the upper bound additive error hemisphererelative to the southernhemisphere. suggestedfor VLBI data by Argusand Gordon[1996]. It is crucial that we properly estimate the uncertain- The afo,,m,,t2 is theGIPSY variance multiplied by 9, as ties in our velocity estimates. It has long been known discussedearlier. We considerthis to be a safe, conser- that the formal errors derivedby GIPSY usingthe anal- vative estimate of the uncertainties. In effect, for sites ysisstrategy described in Table 2 underpredictthe true present throughout the entire time series, the two ad- scatter, or repeatability, of individual estimates. We ditiveerrors add 1.44mm •'/yr •' to the varianceof each have therefore scaledthe position variancesso that the velocity component, so none of our velocities will have reduced chi squared statistic of the velocity solution is an uncertaintylower than about 1.2 mm/yr. Note that approximately1; this resultsin a variancescaling fac- for sites present throughout the entire time series, the tor of 9. This scale does not compensatefor systematic additive factors are larger than the scaleduncertainties referenceframe biases,possible non-Gaussian errors, or based on random errors. We assume that the additive possiblecorrelations between solutions. The assump- errors are uncorrelated from site to site. tion of uncorrelateddata may be optimistic, sincethere The velocity estimates and their adjusted covariance is growingevidence for temporal correlationsin GPS are then used to estimate angular velocities for eight solutions.King et al. [1995]determined autocorrela- tectonic plates: Africa, Antarctica, Australia, Eura- tions for a 10 km GPS baseline using a 384 day time sia, Nazca, North America, Pacific, and South America. series of data and found nonzero correlations for time The three-dimensionalvelocity v of a geodetic site on lagsup to 20 days,although the autocorrelationsfor all any plate can be written as componentswere 0.1 or lessfor a time lag greater than 10 days. Long-term geodeticmonument instability is v=xr (2) anotherpotential sourceof correlationsbetween our so- lutions. Langbeinand Johnson[1997] have analyzed a where • is the angular velocity of the plate and r is the long time seriesof data from two-colorlaser line length positionof the site (all Cartesianvectors). In the plate measurements in California and found clear evidence tectonic model, all station velocitiesare explicitly hori- for long-term correlationsin line length measurements zontal. The vertical componentof the site velocity thus that can be describedby a random walk process.Based contributesnothing to the estimation of the angular ve- on a similar length time seriesfor a regionalnetwork in locity, so there are in reality only two data per station. southernCalifornia, Bock [1995] suggests that a reason- With three parameters per angular velocity, velocities ablerandom walk variance would be of orderi mm2/yr, from two sites are required to determine all components althoughthere can be considerablevariation from site of the angular velocity of a plate. A priori information to site dependingon the local conditionsand the way can be applied to estimate an under-determinedangu- the GPS antenna is attached to the ground. However, lar velocity,but in this paper we only estimated angular Herring[1996] has suggested that theseGPS time series velocitiesfor plates with at least two sites on them. The are too short to determine whether a random walk er- relative angular velocity for a plate pair is simply the ror model is required. The significanceof these results differenceof the absolute angular velocitiesfor the two for the interpretation of geodetictime serieshas not yet independentplates. Angular velocitiesare frequently been answered and is still an area of active debate. expressedin terms of their pole of rotation and angular Choosinga conservativeapproach, we increasedour speed,and we follow that conventionin this paper. scaled uncertainties by additive factors to compensate for the possibleeffects of referenceframe biases and correlations in the data. Our reference frame realization Geodetic Results is not unique, and the geometryof the chosenreference stations is dictated by availability rather than optimal In this section we discuss the velocities of individ- geographicdistribution. If we vary the set of reference ual sites, and the discrepancieswith respectto NNR-A sites, we can produce small changesin our estimated (Table 4). Differencesbetween our estimatedveloci- velocities. We estimate that an additional site velocity ties for most sites in the plate interiors and the NNR-A uncertaintyof 0.5 mm/yr is sufficientto characterizethe predictions are quite small worldwide, indicating that possiblesystematic biases caused by a particular choice our referenceframe is aligned with NNR-A. Differences of referencesites. To addresslong-term correlationsin at individual sites could be due to real differences in the data, we follow the approachof Argus and Gordon plate motions, local tectonic motions or site instability. [1996]and add a time-dependentvelocity error, which In this study we have ignored effectsdue to postglacial decreasesas the length of the time seriesincreases. We rebound, although there have been observationsof post- modify the velocity varianceas follows: glacial rebound from a longer time seriesof VLBI data [Argus,1996] The effectdue to postglacialrebound is 2 2 C •. 2 primarily in the vertical component and we model the t7new-- t7formal -]-•-• -]-t7 fram e (1) horizontal velocities exclusively. 9970 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

Table 5. Plate Angular Velocities

Angular Velocity Pole Error Ellipse

Latitude, Longitude, a•, O'max, O'min, •, Source deg, deg, deg/m.y. deg deg deg deg/m.y. Africa (Hartebeestoek,Maspalomas) This paper 50.0 -86.8 0.26 5.3 2.8 90 OOl NNR-A 50.8 -74.0 0.29 Antarctica(McMurdo and O'Higgins) This paper 60.5 -125.7 0.24 6.6 3.6 1 0 03 NNR-A 63.1 -115.9 0.24 Australia(Perth, Yaragadee,Canberra, Hobart, Townsville) This paper 31.4 40.7 0.61 3.1 1.0 -61 OOl NNR-A 34.0 33.2 0.65 Europe(Hersmonceaux, Onsala, Tromso, Ny Alesund,Madrid, Kootwijk, Wetzell) This paper 56.3 - 102.8 0.26 5.7 1.7 43 02 NNR-A 50.8 -112.4 0.23 Nazca (Baltra Island and Easter Island) This paper 40.6 -100.7 0.70 7.6 1.7 -5 05 NNR-A 48.0 -100.2 0.74 North America(Bermuda, North Liberty, Westford,Richmond, Algonquin, Fairbanks, St John's) This paper -0.4 -84.5 0.22 4.3 2.0 0 Ol NNR-A -2.5 -86.0 0.21 Pacific (Pamatai, KokeePark, Chatham) This paper -63.1 95.9 0.70 2.3 0.9 -82 0.01 NNR-A -63.2 107.4 0.64 SouthAmerica (Kourouand Fortaleza) This paper -21.0 -183.5 0.16 29.6 7.4 -71 0.06 NNR-A -25.6 -124.0 0.12

One sigmaerror ellipsesare specifiedby the angularlengths of the principalaxes and by the azimuths(•b, givenin degreesclockwise from north) of the major axis. The rotation rate uncertaintyis determinedfrom a one-dimensional marginaldistribution [DeMets et al., 1990, Table 2a].

We also discussthe estimated angular velocity for procedure for Madrid and the estimation of the Eurasia eachplate (seeTable 5). We first discussthe platesfor angular velocity and found a 30% increasein standard which we have more than two sites with long time his- deviation when Madrid is removed. Only in the case tories, as theseare the best determined. Along with the of the Africanplate are our poleestimates strongly de- angular velocitiesand their uncertainties,Table 5 lists pendenton the assumedvelocity of a referencesite. the sites used to define each plate. In some cases,sta- tions that were used as reference sites were also used to Eurasia define the plate. It should be noted that while ITRF94 incorporatesinformation from NNR-A, ITRF94 veloci- All of our siteson the stableEurasia plate are located ties are in many casesdistinct from NNR-A predictions, in westernEurope. Thesesites all havelong time series, and one of our reference sites is not located in a stable as they were establishedas permanent sitesin 1992 and plate interior. For plates that include one of our refer- many were alsoobserved during GIG. Site velocitiesand ence sites, we carefully examine the pole fits to ensure residualswith respectto NNR-A are shownin Figure5. that our results are not biased by the inclusion of ref- All sitesin the plate interiorexcept Tromso agree with erencesites. For example,the North Americanangular NNR-A velocitieswithin 3 mm/yr and are well within velocity is basedon the velocitiesof sevensites, of which 95% confidencelimits. The discrepancyat Tromsoap- two, Algonquinand Fairbanks,are referencesites. If we pearsto be real, as our estimateagrees with an indepen- removeAlgonquin and Fairbanks,the estimatedpole of dent analysisof GPS data for that site [Boucheret al., rotation changesby 1.7ø in latitude and 0.3ø in longi- 1996]. Matera, Italy, is locatedin the plateboundary tude, and the maximum pole uncertainty increasesfrom zone between Eurasia and Africa, and thus we do not 4.3 ø to 7.9ø . The change in the estimate of the angu- expectit to agreewith NNR-A. Our velocity(18.9•-1.6 lar velocity is much smaller than the uncertainty, so we mm/yr north and 23.9•-1.8 mm/yr east) agreeswell conclude that the inclusion of the reference sites does with the SLR measurements(18.0•-1.7 mm/yr north not bias our estimate. The increase in standard error and 23.4+1.5 mm/yr east) reportedin ITRF94. is caused by the geometry of the sites, meaning that Our velocityfor Taiwan is surprisinglyclose to that Fairbanks is an important site for the estimation of the predictedfor the stable , even though North America angular velocity. We followeda similar it is locatedwithin a plate boundaryzone (Figure 6). LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9971

plate is 4.84-2.0mm/yr at N96øE, about 40% slower. The westward motion of Taiwan relative to Shanghai presumablyis due to elastic deformation causedby the collision of the with Eurasia. Our estimate of the Eurasia angular velocity agrees with NNR-A within 95% confidence, but the uncer- tainty in our estimate is large. In order to reduce the uncertainty, we need a better distribution of siteswithin TROM the plate rather than more precise velocities for sites in western Europe. For example, if each of the Euro- pean sites used for our angular velocity estimate had a ONSA standarddeviation of i mm/yr, the maximumpole po- sition uncertaintywould be 4.8ø (with the actual data it is 6.3ø). With the addition of an equallyprecise site KOSG in eastern Eurasia, the maximum pole position uncer- tainty would be reduced to 2.5ø . An accurate velocity from one of the new IGS sitesin Moscowwould provide •$ø HERS• /•toø a similar improvement. WETT North America

We have good geometriccoverage of the North Amer- ican plate, with seven sites in the plate interior rang- MADR MATE ing from Alaska to Bermuda. We have also included Albert Head (British Columbia), Penticton (British, oo 15ø Columbia), and Pie Town (New Mexico) in our anal- Figure 5. GPS station velocityestimates and NNR- ysis of North America, although we have not assumed A residualsfor the Eurasia plate. The 95% confidence they are on the stable interior of the North American regionsare shownattached to the residuals. plate. The site velocities and residual velocities rela- tive to NNR-A are shown in Figure 7. Fairbanks has Molnar and Gipson[1996] presented VLBI resultsfrom a marginally significant southward velocity relative to Shanghai,about 800 km to the north of Taiwan, which NNR-A (2.14-1.1mm/yr), consistentwith VLBI. Of the showthat south China is moving 8 + 0.5 mm/yr at three sites we removed from our angular velocity esti- N116øE+4.1 ø with respect to the Eurasia plate. Our mate, only Albert Head showssignificant motion rela- estimated velocity for Taiwan relative to the Eurasian tive to North America, 11.4+1.6 mm/yr at N56øW, in

1 O0 ø 120 ø 140 ø 160 ø 180 ø 200 ø 220 ø

40 ø 40 ø

20 ø 20 ø

0 o

_20 ø _20 ø

:: -40ø ...... •i•:•:•::'"•:•:•::•:•:•:•:•:'•":•:•:•:•i!iliiiiiiiiiiiI! -40ø 1 O0 ø 120 ø 140 ø 160 ø 180 ø 200 ø 220 ø Figure 6. GPS stationvelocity estimates and NNR-A residualsfor the Australiaand Pacific plates. The 95% confidenceregions are shownattached to the residuals. 9972 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

210 ø 225 ø 240 ø 255 ø 270 ø 285 ø 300 ø 315 ø

210 ø 225 ø 240 ø 255 ø 270 ø 285 ø 300 ø 315 ø Figure ?. GPS station velocityestimates and NNR-A residualsfor the . The 95% confidenceregions are shownattached to the residuals. For clarity, the velocity and residual for Alberthead, British Columbia, are not shown. goodagreement with the previousanalysis of Argusand Townsville, and Canberra were observed as early as Heftin [1995]. GIG. Perth and Hobart came on-line with Rogue re- Our data do not showevidence of significantinternal ceivers in 1993. The Townsville site was abandoned for plate deformation, which agreeswith an independent continuous observationsin 1992, but we include it here analysisof VLBI data by Argusand Gordon[1996]. We for completeness.The locations of these sites and their also see little evidence of vertical deformation from the velocitiesare shown in Figure 6. The size of the error GPS data. Algonquinrises 4.5+1.2 mm/yr, a conse- ellipsesreflects the time span of the observations. We quenceof the ITRF94 frame constraint. North Lib- find no discrepanciesbetween NNR-A and the geodetic erty (0.0+2.6 mm/yr), Richmond(-0.5+2.4 mm/yr), velocities at the 95% confidence limit. The baselines Westford(-0.4+2.7 mm/yr), and Bermuda(-1.3+2.9 betweenthe differentAustralian sitesalso showno sig- mm/yr) all showno vertical deformationwithin one nificant lengtheningor shortening,which is consistent standard deviation. Our vertical estimate for North with the NUVEL-1A assumption of no internal plate Liberty disagreeswith the ITRF94 predictedsubsidence deformation. of 13.5+2.8 mm/yr, which is basedon VLBI observa- The discrepancybetween the NNR-A pole and our tions. The resolution of this discrepancy will require geodeticpole is 2.6ø in latitude and 7.5ø in longitude, a careful comparisonby the VLBI and GPS analysis with a maximum uncertainty of 3.1ø. The Australia centers,although we note that our result is more plau- angular speedis smaller than predicted by NNR-A. Al- sible than the VLBI result and the difference could be though the NNR-A pole discrepancyis not significant explained by subsidenceof the VLBI antenna. at 95% confidence,we have conductedseveral tests to Giventhe goodagreement between predicted and ob- determinethe sensitivityof the Australia angularveloc- served velocities in stable North America, it is not sur- ity to our data. For example, if we removeYaragadee prisingthat the pole of rotation and angularspeed also as a referencesite and replace it by Canberra, the Aus- agreewell with NNR-A. Our pole agreeswith NNR-A tralia pole is still shifted 7ø east of the NNR-A pole. to within 2ø in pole position, well within one standard If we removethe Yaragadeeor Canberra data from the deviation. angular velocity estimation, the pole moves less than 1ø and the angularspeed changes less than 0.01ø/m.y. Australia Fortunately, the is wel] instrumented Our analysisof Australian plate motion is based on with GPS receivers and more accurate velocities should the motionsof five sites: Yaragadee,Canberra, Perth, be availablein a few years. Currently, the discrepancy Townsville, and Hobart. Yaragadee and Perth are lo- betweenour angular velocity for Australia and NNR-A cated on the western coast, and Canberra and Ho- is not significantat the 95% confidencelimit. bart are located on the eastern coast and on the is- Also shownin Figure 6 is Wellington, New Zealand, land of Tasmania, respectively. Of these, Yaragadee, located in the Pacific-Australian plate boundary zone. LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9973

A permanentGPS receiverwas operated there through- ceiver was installed in early 1995. The differencesbe- out 1991-1992 and then was abandoned. Fortunately we tween NNR-A predictions and our velocities for Mc- have been able to augment our Wellington time series Murdo (< 1 mm/yr) and O'Higgins(< 2 mm/yr) are with campaign measurementstaken in January 1994 remarkably small. The Antarctica pole agreesbetter and January 1995. Wellington's velocity is consistent with NNR-A in latitude than longitude, but the stan- with the plate boundarydisplacement field derivedfrom dard deviations are also larger in longitude than lat- terrestrialgeodetic techniques by Bibbyet al. [1986]. itude. The prospects for future Antarctica measure- Our newlyestimated velocity for Wellingtonagrees with ments are good. Three additional sites on the Antarc- that of Larsonand Freymueller[1995] to better than 1 tica plate were added during 1994: Casey and Davis mm/yr and 2ø in azimuth. on the continent and Kerguelen Island. All of these sitesare in the IGS networkbut were not installed early Pacific Plate enoughto contribute to this analysis.

We have analyzed data from two continuousGPS Africa sites on the Pacific plate: Kokee Park, Hawaii, and The is sampledat Hartebeesthoek,South Pamatai, French Polynesia(Figure 6). We have a 5 Africa, and on the Canary Islands(Mas Palomas). The year time seriesat Kokee Park and a 4 year time se- Mas Palomas velocity agreeswith NNR-A to within 1 ries at Pamatai. Kokee Park is a reference site and mm/yr. Hartebeestoekis one of our referencesites, so thus agreesbetter with ITRF94 than NNR-A. The re- its velocity has been constrainedto agreewith ITRF94, sultingvelocity for KokeePark is 3 + 1.5 mm/yr faster and its agreement with NNR-A is only within three than NNR-A. The NNR-A velocity for Pamatai is 70.3 standard deviations. Since we do not have enoughin- mm/yr, but our GPS velocityis 81.2 + 2.9 mm/yr, dependent data from the African plate to evaluate the about 15% faster. Initial SLR results for the nearby site significanceof the discrepancyat Hartebeesthoek, we at Huahine, French Polynesia, were reported as 874-3 cannot be sure that our estimate of African plate mo- mm/yr [Robbinset al., 1993]but havesince been revised tion differssignificantly from NNR-A. In any case,with downwardto 714-3mm/yr [Boucheret al., 1996]. To only the two sitesthe angular velocity is not determined expandour set of siteson the Pacificplate, we havealso precisely,with an uncertainty of 7ø in pole position lon- analyzedtemporary and permanentdata spanning3.3 gitude. Additional data from siteson the stable African yearsfrom Chatham Island. The velocityof Chatham plate are neededto improve the estimate of the angular Island is about 20% faster than predicted by NNR-A. velocity. At present, there is only one additional site Velocitiesof all three are fit well by a pole of rotation on the African continent, and it has a short time his- that lies 11ø (4a) to the westof the NNR-A pole of ro- tory. This site (Malindi, Kenya) is located east of the tation and has a angularspeed greater by about 10% East African Rift System, so it is not on the African (6a). The Pacificpole is the mostprecisely determined plate. We expect it will be several years before a better in our study becausethe GPS siteson the plate are so estimate of African plate motion can be obtained. widely spaced. No other plate in this study has an angular veloc- Nazca ity so differentfrom that predictedby NNR-A. To test Sites on the Nazca plate are necessarilylimited to our angularvelocity, we use it to predict the velocities islands. SLR measurementswere made prior to the in- of SLR and VLBI sites on the Pacific plate. Our pre- stallation of a permanent GPS site on Easter Island in dictedvelocities for Kwajalein(VLBI), andMaui (SLR) 1994. Our GPS velocity, shownin Figure 8, agreesat andHuahine (SLR) all agreewith the ITRF94 velocities the two standard deviation level with both the NNR- for those sites within the 95% confidence limits of the A and the ITRF94 value. With only one site on the data. If we combine ITRF94 velocities for Kwajalein, Nazca plate, we would be unable to estimate an an- Maul, and Huahineand our velocitiesfrom Pamatai and gular velocity, so we have also included data from two Chatham, the resultingpole is -63.3 ø latitude, 96.6ø temporary sitesin the GalpagosIslands that were occu- longitude,and the angularspeed is 0.68ø/m.y.We sug- pied as part of the Central and SouthAmerica (CASA) gestthat the motionof the Pacificplate overthe last experiment[Fre•maeller et al., 1993]. We includedata 5 yearsdoes not agreewith its motion over the last 3 from Isla Baltra from 1991 and 1994, and data from m.y. a site on Isla Santa Cruz, about 30 km to the south, Antarctica which was observed in 1994 and which became a per- manent site in early 1996. The two sites are 30 km There are two sites on the that meet apart and were assumedto have the same velocity. The our criteria of a 2 year time span: McMurdo and data are consistentwith this assumption,and the 5 year O'Higgins. Both McMurdo and O'Higgins were ob- time seriesyields a velocity that is significantly slower servedduring the GIG campaign.A permanentreceiver than NNR-A predictions. The difference between our was placedat McMurdo in February 1992 but has been velocity and the NNR-A prediction for that site is 20+5 movedtwice sincethen. The permanent O'Higgins re- mm/yr (Figure 8). Our estimatedpole of rotation for 9974 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

240 ø 260 ø 280 ø 300 ø 320 ø 340 ø The large uncertainty in the pole position is con- 20 ø 20 ø trolled by the relatively large uncertainty in the veloc- ity of Baltra. When the velocitiesof the Galapagos and Easter Island sites are determined with a precision 0 o 0 o of I mm/yr, thesetwo siteswill be su•cient to deter- mine a precisepole of rotation (maximumpole uncer- tainty 2.5ø), althoughdata from additionalsites would _20 ø _20 ø be required to determine whether the Nazca plate is deforming internally. Data from a regional campaign have been taken at a site in the Juan Fernandez islands _40 ø _40 ø in the southeast part of the Nazca plate, which may eventually help resolvethis issue.

South America _60 ø _60 ø We have analyzed data from three permanent GPS 240 ø 260 ø 280 ø 300 ø 320 ø 340 ø siteson the . Santiagois located Figure $. GPS station velocity estimatesand NNR- in the SouthAmerican/Nazca plate boundaryzone. On A residuals for the South America and Nazca plates. the stable portion of the plate, we have observations The 95% confidenceregions are shownattached to the from Fortaleza, Brazil, and Kourou, French Guyana. residuals. Their horizontalvelocities and NNR-A discrepancyvec- tors are shown in Figure 8. Their velocitiesagree to the Nazca plate differsby 8ø from the NNR-A pole, but better than 1 mm/yr with NNR-A in the north com- the uncertaintyis almostas large (7ø). A small shift in ponent and within two standard deviations in the east the pole position and angular speedcan accountfor a component. large differencein velocitybecause the pole is located The angular velocity for South America is the most fairly closeto the plate. poorly determined of the eight plates estimated in this Previouslypublished results for Baltra [Freymueller paper. This is simply becauseKourou and Fortaleza are et al., 1993]gave the motionof Baltra relativeto Jeru- lessthan 2000 km apart, yieldingpoor sensitivityto the salen in Ecuador based on data from 1988, 1990, and longitudeof the pole (maximumstandard deviation of 1991. The 1990 and 1991 results for Baltra are consis- 31ø). The addition of another site in southernSouth tent with the low rate obtained in this study, although Americawould substantially improve the geometryfor the 1988 data are not. The 1988 CASA results also determiningthe pole of rotation. The uncertaintyin the show an unexpectedeast-west movement of Baltra rel- angular speedwill be reducedby about 50% when the ative to Isla del Coco on the Cocosplate, which could be site in La Plata (near BuenosAires) has a sufficiently explainedif the coordinatesobtained for Baltra in 1988 precisevelocity. The longitude of the pole will remain were biased to the west. We conclude that the 1988 so- poorly constrained until a site in western South Amer- lutions for Baltra were probably biasedand that the re- ica, but east of the deformingAndes, is included. No maining data are consistentwith a rate of motion much permanent sites meeting that criterion have yet been established. lower than predictedby NNR-A. Resultsfrom 1991 and 1994 for Isla Malpelo, about 800 km to the northeast of Baltra and also on the Nazca plate, are also con- Relative Angular Velocity Vectors sistent with a lower velocity than would be predicted by NNR-A. The motion of the Nazca plate is well con- Relative angular velocities describethe relative mo- strained in the NUVEL-1A model since it is surrounded tions of a plate pair and can be derivedby differencing on three sidesby spreadingcenters, so we would not ex- the absoluteangular velocitiesfor the two plates. An- pect NUVEL-1A to havean incorrectestimate of its mo- gular velocitiesderived from GPS data are generally tion. Active volcanismin the GalapagosIslands occurs correlated, due to the correlations between sites in the about 75 km to the west, on Isabella and Fernandina GPS velocity field. Just as GPS relative velocities are islands[Simkin and $iebert,1994]. Westward motion of more precisethan absolute velocities,the uncertainties both GalapagosIslands GPS sites could be causedby of relative plate angular velocitiesare smallerthan those ongoingflexure of the lithospheredue to the load of the of absoluteplate motions. Relative angular velocities active volcanic islands if these islands were still subsid- are also lesssensitive than absoluteangular velocities ing today. However, we have no explanation that can to referenceframe errors in the GPS velocities,or the definitively account for the entire discrepancy. It may no-net-torque assumption used to derive the NNR-A be that the plate is deforminginternally. Data from the model from NUVEL-1A. We can compareour relative Galapagosand Malpelo will be examined more fully in angular velocities directly with the NUVEL-1A relative a future paper with the other CASA regionalcampaign plate motion model, and unlike NNR-A, standard de- data. viations are available for NUVEL-1A. This allows us to LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9975

better assessthe significanceof discrepanciesbetween estimate agrees well with both NUVEL-1A and God- the plate model predictionsand our geodeticanalysis. dard but has a relatively large uncertaintyin the pole In Table 6 we compare our relative angular velocity positionestimate due to the poor geometryof the GPS estimatesto NUVEL-1A and other published geodetic siteson the Eurasian plate. The GPS-only solutionwill studies. We have listed all plate pairs which share a be improvedwhen sitesoutside of westernEurope con- boundary. For comparisonwith an independent GPS tribute. The JPL-GPS and VLBI pole positionsare lo- analysis,we list Argusand Heftin [1995]values when catedmore northerly of NUVEL-1A. Our angularspeed available(hereafter Jet PropulsionLaboratory (JPL)- agreeswith NUVEL-1A, as do all of the other geodetic GPS). Our study usesa longertime seriesthan JPL- solutionswith the exception of the VLBI solution. GPS, and includes more sites. We have also made a greater effort to augmentour velocitiesby using data Pacific-North America from temporary occupationsof sites. The JPL-GPS pa- per also showedangular velocities derived from VLBI Pacific-NorthAmerica relative plate motion has crit- data, which they have made available(D. Argus and ical implicationsfor deformationin the plate boundary R. Gordon, manuscriptin preparation, 1997) (here- zonesof Californiaand Alaska. Our estimatedangu- after VLBI). For comparisonwith a recent multiple- lar velocity (Figure 10) is significantlydifferent than techniqueanalysis, we list Smithet al. [1996](hereafter NUVEL-1A, both in pole locationand angularspeed. Goddard). This group combinedseparate analyses of Our angularvelocity disagrees with the other geode- VLBI, SLR, GPS, and DORIS data to'estimateangu- tic studiesin longitudebut agreesin latitude and rate. lar velocities for many of the plates we discuss. The All of the geodetictechniques estimate a fasterangular Goddardstudy has the advantageof havingmore data speedthan NUVEL-1A, but only our rate and the VLBI and more sites becausethey use severaltechniques, al- rate exclude the NUVEL-1A rate from the 95% confi- though inconsistenciesbetween the velocity solutions denceregion. The VLBI and Goddard angular veloci- used could potentially cause biasesin the results. For ties are basedon different sets of stations. For VLBI, severalplates, they rely only on GPS data, and we ex- the sites are in the northern hemisphere,specifically pect good agreementof resultsfor theseplates. Marcus Island, Hawaii, and Kwajalein. The GPS esti- We note two trends in Table 6. First of all, there mates are based on Hawaii and sites from the southern is good agreementbetween nearly all our GPS derived Pacific. The Goddard solutionwill averageboth north- relative angular velocitiesand NUVEL-1A, with the ex- ern and southernhemisphere as VLBI, SLR, and GPS ception of someof those involvingthe Pacific plate. In data contribute to the angular velocity estimate. We general, there is also good agreementbetween the in- are the only analysis listed in Table 6 which uses mea- dependentgeodetic analyses, This is encouraginggiven surementsfrom Chatham Island. OngoingGPS mea- that VLBI, SLR, DORIS, and GPS are quite distinct surementsfrom sites such as Kwajalein and Chatham geodetictechniques and the data were analyzedand ref- Island shouldresolve issues regarding the Pacific plate. erenceframe constraintsapplied in very different ways. Despite the significantdifference between our pole The one exception to this good agreement is for the and the NUVEL-1A pole, both predict the samerelative North America-Africa pole position. Upon closer in- motion along almost the entire Pacific-North America spection, it becomes clear that pole uncertainties are plate boundary(Table 7). For a point in southernCal- poorly definedat extremelyhigh latitudes (the pole is ifornia near VandenbergAir Force Base, we predict a locatedat a latitude of 79ø). In this case,we havealso relativeplate motionvector of 46.4+ 2.8 mm/yr toward inspected the Cartesian uncertainties, which indicate N40.3øW+1.8, 2.7ø westerly of NUVEL-1A but with agreementwith NUVEL-1A at better than two stan- the samerate to within 0.4 mm/yr. The azimuthdiffer- dard deviations. enceis not significantat the two sigmalevel. In the Gulf In Table 7 we show the predicted relative motion at of California, our model predicts relative motions 1.3 severallocations along plate boundaries. Two angular mm/yr fasterthan NUVEL-1A towarda direction5.6 ø velocitiesfor a given plate pair may be significantlydif- more westerly. The rate differenceis insignificant,but ferent and yet predict motionsalong the plate boundary the azimuth differencewith NUVEL-1A is possiblysig- that are not significantlydifferent. This is the casefor nificant. Our predicted rate and azimuth all well within our Pacific-North America angular velocity, for exam- the one sigmauncertainty range for spreadingrates and ple. Where our predicted relative motions on the plate transformfault azimuthsin the Gulf of California,how- boundary differ from those predicted by NUVEL-1A, ever[DeMets et al., 1990]. DeMets[1995] showed that we can compare our relative motions to the raw data the 3.16 m.y. averagespreading rate in the Gulf of Cali- from which NUVEL-1A is derived. forniais slowerthan both the 0.78 m.y. averagespread- ing rate and the NUVEL-1A closure-fittingrate (the Eurasia-North America Pacific-NorthAmerica relative motion predicted by the NUVEL-1A data excludingdata from that plate bound- In Figure 9, we showthe pole positionof the Eurasia- ary), probablybecause the Gulf of Californiaspreading North American angular velocity. In eachcase, we have centers did not accommodate the entire Pacific-North plotted the position and its 95% confidenceellipse. Our Americarelative motion until about 2 m.y. ago. Our 9976 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

Table 6. Relative Angular Velocitiesfor Plates Sharinga Boundary

Angular Velocity Pole Error Ellipse

Latitude, Longitude, c•, Ëmax, O'min, • Source deg deg deg/m.y. deg deg deg deg/m.y.

Europe-North America This paper 68.1 126.6 0.24 6.5 3.9 -30 0.02 NUVEL-1A 62.4 135.8 0.21 4.1 1.3 -11 0.01 VLBI 74.0 111.3 0.26 5.4 2.4 -48 0.02 Goddard 66.7 126.8 0.22 3.0 1.2 -39 0.01 JPL-GPS 78.5 122.0 0.23 8.2 4.9 -8 0.03 Pacific-North America This paper -49.6 95.7 0.83 2.0 1.0 -86 0.02 NUVEL-1A -48.7 101.8 0.75 1.3 1.2 61 0.01 VLBI -50.5 104.1 0.78 2.0 0.8 -84 0.01 Goddard -49.8 103.1 0.77 2.6 1.1 -86 0.02 JPL-GPS -49.1 107.0 0.79 4.1 2.2 -83 0.03 Africa-North America This paper 76.3 103.5 0.21 7.1 5.7 76 0.01 NUVEL-1A 78.9 38.3 0.24 3.8 1.0 77 0.01 Goddard 78.8 39.2 0.24 6.3 3.4 36 0.02 JPL-GPS 80.9 16.7 0.22 14.5 11.1 15 0.04 South America-North America This paper -11.1 126.7 0.29 6.6 3.9 27 0.08 NUVEL-1A -16.4 121.9 0.15 6.2 3.9 9 0.01 JPL-GPS -6.5 124.4 0.28 8.3 7.4 -55 0.12 Pacific-Europe This paper -61.5 90.0 0.97 2.1 0.9 -68 0.02 NUVEL-1A -61.2 94.2 0.86 1.3 1.2 -90 0.02 Goddard -61.9 98.4 0.90 2.4 0.8 -76 0.02 JPL-GPS -60.2 95.6 0.95 3.3 2.2 -88 0.05 Australia-Europe This paper 8.6 48.5 0.65 3.7 1.4 -46 0.02 NUVEL-1A 15.2 40.5 0.69 2.2 1.2 -45 0.01 Goddard 12.4 44.6 0.66 1.7 0.6 -51 0.02 JPL-GPS 9.9 47.4 0.72 4.9 4.0 -53 0.05 Africa-Europe This paper -23.5 -29.8 0.05 35.0 21.4 25 0.02 NUVEL-1A 21.2 -20.6 0.12 6.2 0.8 -4 0.02 Goddard 18.4 -24.6 0.10 13.3 10.0 -71 0.03 JPL-GPS -11.7 -27.3 0.07 41.7 36.1 36 0.03 Australia-Pacific This paper 65.7 2.9 1.04 1.7 1.5 2 0.02 NUVEL-1A 60.2 1.7 1.07 1.1 1.0 58 0.02 Goddard 60.8 3.9 1.07 1.9 1.0 29 0.02 JPL-GPS 57.2 6.5 1.13 2.6 2.4 43 0.04 Antarctica-Pacific This paper 63.6 -95.0 0.93 2.0 1.5 44 0.03 NUVEL-1A 64.5 -84.0 0.87 1.2 1.1 82 0.01 Goddard 64.8 -82.3 0.90 2.7 1.7 84 0.06 Africa-A ustralia This paper -10.6 -127.3 0.65 3.3 1.9 58 0.02 NUVEL-1A -12.5 -130.2 0.63 1.3 1.0 39 0.01 Goddard -10.1 -127.0 0.63 2.5 1.8 -62 0.03 JPL-GPS -11.2 -127.4 0.71 6.1 4.3 -22 0.04 Antarctica-Australia This paper -9.8 -136.8 0.65 4.4 2.6 20 0.01 NUVEL-1A -13.2 -141.7 0.65 1.3 1.0 63 0.01 Goddard -11.1 -138.6 0.64 5.2 2.5 30 0.03 LF -12.8 -143.1 0.65 6.7 3.5 15 0.03 South America-Africa This paper -47.4 131.4 0.35 14.0 4.6 3 0.06 NUVEL-1A -62.6 140.6 0.31 2.7 0.8 11 0.01 JPL-GPS -39.9 131.7 0.38 16.2 7.4 -7 0.01 Nazca-Pacific This paper 52.2 -94.5 1.37 4.2 1.4 2 0.04 NUVEL-1A 55.8 -90.1 1.36 1.9 0.9 -1 0.02 Goddard 67.3 -81.1 1.27 6.3 1.5 26 0.03 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9977

Table 6. (continued) Angular Velocity Pole Error Ellipse

Latitude, Longitude, •o, er,•ax, er,•i•, •p er•, Source deg deg deg/m.y. deg deg deg deg/m.y.

South America-Antarctica This paper -63.75 126.5 0.29 20.2 4.4 6 0.05 NUVEL-1A -86.44 139.3 0.26 3.1 1.2 24 0.01 Africa-Antarctica This paper -4.49 -42.5 0.11 24.2 13.8 3 0.02 NUVEL-1A 5.64 -39.2 0.13 4.6 1.4 -41 0.01 Goddard 5.6 -39.1 0.13 26.1 14.1 19 0.04 Nazca-Antarctica This paper 30.0 -94.0 0.49 10.7 2.9 2 0.06 NUVEL-1A 40.7 -95.9 0.52 4.7 2.0 -9 0.02 Goddard 73.3 -77.0 0.37 21.4 4.1 -30 0.06 South America-Nazca This paper -43.8 95.2 0.74 9.1 5.5 18 0.07 NUVEL-1A -56.1 86.0 0.72 3.7 1.5 10 0.02

NUVEL-1A from DeMets et al. [1990]and DeMets et al. [1994];VLBI from D. Argus and R. Gordon (manuscriptin preparation,1997); Goddardfrom Smith et al. [1996]; JPL-GPS from Argusand Herin [1995];LF from Larson and Freymueller[1995]. Pole error ellipse convention defined as in Table 5 predicted spreadingrate agreesalmost exactly with the tion at both the Pacific-Australia and Pacific-Eurasia NUVEL-1A closure-fittingrate, and the 0.78 m.y. av- plate boundariesthan NUVEL-1A. In thesecases, rela- eragespreading rate of DeMets [1995]lies within our tive plate motion on the boundary is significantlyfaster onesigma uncertainty. At Kodiak Island in Alaska,our in our model but with the same azimuth as NUVEL- polepredicts relative motion 1.6 mm/yr morerapid and 1A. Because both of these boundaries are oriented 3.1ø more northerly than NUVEL-1A; again, boundaries where the plate boundary data are sen- these differencesare not significant.Only in the west- sitive to the azimuth of relative plate motions, our ern Aleutians is our predicted Pacific-North America model is just as consistentwith the data from those relative motion significantlydifferent than NUVEL-1A, plate boundaries as is NUVEL-1A. No data from the and there it is different in rate rather than azimuth. Pacific-Australia plate boundary were usedin determin- Since the only plate boundary data from the western ing NUVEL-1A. On the basisof the faster convergence Aleutians come from slip vectors, which are rates predicted by our model, about 22% faster for the sensitive to the azimuth of relative plate motion, our Pacific-Australiaboundary and about 12% faster for the faster rate of subduction here remains consistent with Pacific-Eurasiaboundary, our data are consistentwith the available plate boundary data. a correspondinglyhigher rate of seismicmoment release Pacific-Australia and Pacific-Eurasia at these boundaries. Similar implicationshold for the Unlike at the Pacific-North America plate boundary, otherplate boundariesin the westernPacific, including our model predicts significantlydifferent relative mo- the Pacific-PhilippineSea plate boundary.

Table 7. Relative Plate Motions at Selected Locations on Plate Boundaries

This study NUVEL1-A

Location Latitude, Longitude, Rate Azimuth Rate Azimuth deg deg

, , Vandenberg 34.6 -120.6 46.44-2.8 -40.3 4- 1.8 46.8-4-1.3 -37.64-1.5 Gulf of California 23.5 -108.5 48.74-2.8 -59.8 4- 2.0 47.44-1.2 -54.24-1.5 Kodiak, Alaska 57.6 -152.2 58.34-1.7 -18.34-2.5 56.7 4- 1.4 -21.4 4- 1.2 West Aleutians 51.0 173.1 79.44-1.7 -42.84-1.9 74.34-1.4 -45.64-0.9 Alpine fault, New Zealand -43.5 170.0 45.44-1.7 -103.64-2.6 37.04-1.4 -109.14-2.1 Tokyo, Japan 36.1 140.1 103.44-2.6 -67.64-1.2 92.74-1.7 -69.04-0.9 East Pacific Rise -10.0 -110.0 136.34-3.6 100.6 4- 1.4 139.9 4- 1.6 102.04-0.8 East Pacific Rise -19.0 -113.0 145.54-3.6 101.84-1.3 147.44-1.5 103.04-0.8 East Pacific Rise -30.0 -112.0 151.34-4.0 100.84-1.2 151.14-1.6 102.24-0.7

All rates are given in millimetersper year, and azimuthsin degreesclockwise from north. Uncertaintiesare one standard deviation. 9978 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

10 mm/yr for NUVEL-1A. The increasedfault-normal contraction predicted by our model should be observ- able geodetically,and ongoingGPS observationsin this area should be capable of testing our model prediction in the future. GPS results from the southwest Pacific [Beyiset al., 1995; Taylor et al., 1995]are consistent with our proposed Pacific-Australia convergencerate but are too impreciseto test the differencebetween our model prediction and NUVEL-1A. The rate of underthrusting of the Pacific plate be- neath the Japaneseislands depends on both the Pacific- Eurasia relative plate motion and the motion of the Japaneseislands relative to Eurasia, which we will not attempt to addresshere. At a location near Tokyo at 6•0o the southern end of the main Japaneseislands bound- ary with the Pacific plate, our model predicts 103.4+2.6 mm/yr of relative motion of the Pacific and Eurasian plates,11.7 mm/yr fasterthan predictedby NUVEL-1A and oriented at the same azimuth within uncertainties.

Pacific-Nazca 110ø 120 ø 130 ø .•40o Figure 9. Eurasia-NorthAmerican pole position,with Although our velocity for Baltra Island was signifi- 95% confidenceregion for DeMets et al. [1994](trian- cantly different than that predicted by NNR-A, the an- gle), Smithet al. [1996](circle), VLBI (D. Argusand R. gular velocity for the Nazca plate agreed with NNR- Gordon,manuscript in preparation,1997) (square),Ar- A within its stated uncertainties. We have tested our gusand Heftin [1995](diamond), and this paper(star). Nazca-Pacific angular velocity by looking at predicted velocitiesat severallocations along this plate boundary. On the Alpine fault in New Zealand, our model As shown in Table 7, the agreement between NUVEL- predicts significantlyfaster relative plate motion, 8.4 1A and our model is very good. At -19.0 ø latitude, mm/yr fasterthan NUVEL-1A and directedmore obli- our model predicts145.5+3.6 mm/yr at an azimuth of quely to the trend of the Alpine fault. Projectedonto 101.8ø + 1.3ø, whereas NUVEL-1A predicts 147.4+1.5 the N55E trend of the Alpine fault, our velocity givesa mm/yr. For the samelocation, Wilson[1993] finds a fault-parallelrate of 42 mm/yr and a fault normalcon- spreadingrate of 153.7 mm/yr, slightlyfaster than our tractionrate of 16 mm/yr, comparedto 36 mm/yr and rate but within 95% confidence limits. Ant arct ica- A ust r alia

100 ø 110 ø In Figure 11 we showthe pole of rotation for Antarc- 9O' 1•0o tica-Australia. There are no VLBI or SLR angular ve- locity estimatesfor the Antarctica plate. Goddard com- bined DORIS and GPS. For completeness,we compare our estimatewith the Larsonand Freymueller [1995] es- timate for data that spanned 1991-1993. In that paper, the z componentof the angular velocity was constrained to agreewith NNR-A becausethere was only one site on the Antarctica plate. Our new estimate is basedon the velocitiesof two sites on Antarctica, so there is no need to constrain the angular velocity. Again, the pole of ro- tation latitude agreeswell between NUVEL-1A, God- dard, and our estimate. The angular speedsalso agree within two standard deviations. The pole longitudes, as with Pacific-North America, agree lesswell. ø60ø '60' 9o' øøø øø o Africa-Australia Figure 10. Pacific-NorthAmerican pole position,with 95% confidenceregion for DeMetset al. [1994](trian- The Africa Euler pole is not well determined by any gle), Smithet al. [1996](circle), VLBI (D. Argusand R. of the geodetic techniquesdiscussed in this paper, but Gordon,manuscript in preparation,1997) (square),Ar- the Africa-Australia relative angular velocity pole is rel- gusand Heftin [1995] (diamond), and this paper(star). atively well determined. The NUVEL-1A standard de- LARSON ET AL.: GPS GLOBAL PLATE MOTIONS 9979

220 ø 230 ø signals. We are thus able to compare GPS velocities •0 ø o with plate models, specificallythe NUVEL-1A absolute plate motion model NNR-A. For all but a few sites, the agreementwith NNR-A is better than 95% confidence. Specifically,sites in North America, Antarctica, South " 0" America, Eurasia, Africa, and Australia with long time seriesagree with NNR-A to better than 3 mm/yr. The discrepanciesthat do exist on the Pacific and Nazca plates are intriguing. GPS sites from the Pacific are faster than plate models would predict. In addition, sites in the south Pacific have larger discrepanciesthan sites in the north Pacific. On the Nazca plate, Baltra Island is almost 50% slowerthan NNR-A predictions. A nearby permanent GPS installation on the Galapa- gosIslands will be able to confirm this result within the eoo next few years. For the most part, significant vertical ,Z•Oø 220' 230' deformation is limited to reference sites that required it or sites where we mixed permanent installations and Figure 11. Antarctica-Australia and Africa-Australia campaigns(e.g., Wellington and Baltra). In these lat- pole positions,with 95% confidenceregion for DeMets ter cases,antenna height recording errors can produce et al. [1994] (triangle), Argusand Heftin [1995] (di- amond),Smith et al. [1996](circle), Larsonand Frey- significantvertical error. mueller[1995] (inverted triangle), and this paper(star). The data used in this analysis were available as the result of a cooperative international effort to install and operate G PS receiversthroughout the world. With just 5 years of data, we were able to estimate angular ve- viation for this plate pair is also quite small. Figure locities for eight tectonic plates. Continued expansion 11 showsthat all the geodeticestimates agree within a of the IGS network should allow for angular velocity few degrees,and all are offset from NUVEL-1A by 3ø. estimation for most of the remaining tectonic plates by The agreementbetween the different geodeticanalyses the end of the century. We currently assumethat all is likely because all three are controlled by the GPS site velocities vary linearly in time. With extension of data from Mas Palomas and Hartebeesthoek. The dis- thesetime series,we will be able to addressthe validity crepancybetween NUVEL-1A and the geodetic anal- of that assumption,as well as investigatingthe signifi- cance of vertical deformation. yses is most likely controlled by the GPS data from Hartebeesthoek, as discussedearlier.

North America-South America Finally, we show a plate pair, North America-South P90ø300 ø 310ø $20ø America (Figure 12), for which there are no conven- tional plate motion data (i.e., seafloorspreading rates, transformfault azimuths,earthquake slip vectors). The NUVEL-1A pole uncertainty for this plate pair is as large as the geodetic standard deviation, as shown in Figure 12. The differencesbetween our estimate, NU- VEL-1A, and JPL-GPS are not significantat the 95% confidence limit.

Conclusions 0 o 0 In this paper, we have summarized the results for the analysisof a 5 year time span of global G PS data. We have concentratedon sites with long time histories, and for the most part, we have avoided sites in plate P90o $•0ø boundary zones. In several cases,we have been able to 300 ø 310' supplement continuousGPS measurementswith earlier Figure 12. North America-SouthAmerica angular campaignstyle measurements,thus extending the time velocitypole position,with 95% confidenceregion for series by many years. We have also avoided sites con- DeMetset al. [1994](triangle), Argus and Heftin [1995] taminated with coseismicand postseismicdeformation (diamond),and this paper(star). 9980 LARSON ET AL.: GPS GLOBAL PLATE MOTIONS

Acknowledgments. This research was funded by Boucher, C., Z. Altamimi, and L. Duhem, ITRF 92 and its NASA NAG5-1908. We are grateful to many organizations associatedvelocity field, IERS Tech. Note 15, IERS Cent. and individuals for providing data and software support, Bur., Obs. de Paris, 1993. includingZuheir Altamimi, John Beavan, Geoff Blewitt, Boucher, C., Z. Altamimi, and L. Duhem, Results and anal- Yehuda Bock, Claude Boucher, James Campbell, Chuck ysis of the ITRF 93, IERS Tech. Note 18, IERS Cent. DeMets, Carey Noll, AndreasReinhold, Wolfgang Schlueter, Bur., Obs. de Paris, 1994. TeresaVan Hove, and JPL section335. We thank Don Ar- Boucher,C., Z. Altamimi, M. Feissel,and P. Sillard, Results gus,Richard Gordon, Michael Heftin, Jim Ray, JohnRob- and analysisof the ITRF 94 , IERS Tech. Note 20, IERS bins, and GeorgeRosborough for helpful discussionsand Cent. Bur., Obs. de Paris, 1996. providingus with their current results. Chuck DeMets Clark, T.A., D. Gordon, W.E. Himwich, C. 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