JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. B10, PAGES 16,547-16,565, SEPTEMBER 10, 1991

Application of the Global Positioning System to Crustal Deformation Measurement 1. Precision and Accuracy

KRISTINB M. LARSON

Colorado Center.for Astrod.•tnamicsResearch, Universit.•t of Colorado, Boulder

DV•½•,• C. A•ew

Institute of Geoph.•tsicsand Planetat&t Ph.•tsics,Scripps Institution of Oceanograph•t,La Jolla, California

In this paper we assessthe precisionand accuracy of interstation vectors determined using the Global PositioningSystem (GPS) satellites. These vectorswere between stations in California separatedby 50-450 kin. Using data from tracking the seven block I satellites in campaignsfrom 1986 through 1989, we examine the precision of GPS measurements over time scales of a several days and a few years. We characterize GPS precision by constant and length dependent terms. The north-south component of the interstation vectors has a short-term precision of 1.9 mm + 0.6 partsin 10s;the east-westcomponent shows a similarprecision at the shortestdistances, 2.1 ram, with a largerlength dependence, 1.3 parts in 10s. The verticalprecision has a mean valueof 17 ram, with no clear length dependence. For long-term precision, we examine interstation vectors measured over a period of 2.2 to 2.7 years. When we include the recent results of Davis et al. (1989) for distancesless than 50 kin, we can describelong-term GPS precisionfor baselinesless than 450 kmin lengthas 3.4 mm+ 1.2 partsin 10s, 5.2 mm + 2.8 partsin 10s , 11.7mm + 13 parts in 10s in the north- south, east-west,and verticalcomponents. Accuracy has been determined by comparing GPS baseline estimates with those derived from very long baseline interferometry (VLBI). A comparisonof eight interstation vectorsshows differences ranging from 5 to 30 nun between the mean GPS and mean VLBI estimates in the horizontal components and less than 80 mm in the vertical. A large portion of the horizontal differencescan be explained by local survey errors at two sites in California. A comparison which suffers less from such errors is between the rates of change of the baselines. The horizontal rates estimated from over 4 years of VLBI data agree with those determined with 1-2 years of GPS data to within one standard deviation. In the vertical, both GPS and VLBI find insignificant vertical motion.

INTRODUCTION (GPS) satellites.The basicprinciples of this techniqueare similar to VLBI, with some important differences. Thc Many geodetictechniques have been usedto measurecrus- dio signals originate at satellites, rather than quasars, and tal deformation acrossthe North American/Pacific plate GPS receivers make an instantaneous determination of the boundary in California. The oldestdata comefrom triangu- distance between the receiver and satellite, rather than re- lationmeasurements [e.g., Hayford and Baldwin,1908]; more quiring cross correlation of noise signals to determine the recently,precise electronic distance measurement (EDM) length between two sites. From enough measurementsof has provided many details about strain acrossfaults of the signals arriving from different directions the complete vec- plate boundary[e.g., Savage,1983]. Both of these proce- tor baseline between two sites can be computed. Because duresmeasure through the atmosphereand require the mea- the signal strength at the Earth is so much higher than for surement points to be intervisible; they are thus limited to the quasar sourcesused in VLBI and becausethe signal has distancesup to a few tens of kilometers. Both require consid- a known and well-controlledstructure, G PS antennas(and erable skill and expensive equipment to pursue successfully. all other equipment)weigh at most a few hundredpounds In the past decade, measurementsusing extraterrestrial rather than the many tons needed for VLBI. A similar fa- objects,such as satellite lazer ranging (SLR) [Christodoulidisvorable ratio applies to the costsof the two techniques. For et al., 1990;Smith et al., 1990]and very longbaseline inter- all these reasons,GPS is poised to become the method of ferometry(VLBI) [Herring et al., 1986; Clark et al., 1987], choice for crustal deformation geodesyand in many areas have made possible measurements between points hundreds has indeed already become so. to thousands of kilometers apart. This has enabled a di- But since this is such a new technique, it is vital to estab- rect determination of the total contemporary plate motion lish just what its errors are. Judging from past experience acrossthe broad boundary in California. These observations with VLBI and SLR, constructinga formal error budget, are, however, even more expensiveto make than the older, while useful, is likely to give an incomplete picture because purely terrestrial, techniques. of the wide variety of semisystematic errors that are little The most recent advance in precise geodetic measure- understood(not to mentionthose that are overlooked).We ments has been the use of the Global Positioning System feel that what is neededis an empirical investigation of the precisionand accuracy of GPS measurements,judged from actual results: the precision being a measure of how exact Copyright 1991 by the American Geophysical Union. the estimate is, and the accuracy a measure of how closethe Paper number 91JB01275. estimateis to the truth [Berington,1969]. Our measureof 0148-0227/91]91-JB-01275505.00 16,547 16,548 LARSONAND AGNEW: GLOBALPOSITIONING SYSTEM PRECISION AND ACCURACY precisionis thus (as for others)the scatterof resultsabout a ography, California Insitute of Technology,University of Cal- mean value; our measure of accuracy is the agreement with ifornia, Los Angeles, and MassachusettesInstitute of Tech- someother technique(VLBI). nology,with substantial help from the U.S. GeologicalSur- This paper is the first of three that describeresults from vey(USGS) and the NationalGeodetic Survey (NGS). When nearly three years of measurementsin central and southern possible, we also included data from the North American California. This paper describes the precision and accu- network of fixed GPS trackers that are part of the Cooper- racy over baselinesfrom 50-450 km. Though some earlier ativeInternational GPS NETwork(CIGNET) [Chin,1988]. work [e.g., Dong and Bock, 1989] has demonstratedsub- Table 1 lists 22 of the GPS sites observed. The stations lo- centimeter precision over these distances,this precisionwas cated in California are shown in Figure 1. The remaining only evaluated from data collectedover a few days. Suches- sites, all located in North America, were used for preciseor- timates are likely to underestimate the long-term precision bit determination, and are discussedin paper 2. While more because a number of error sourcesprobably do not change sites than these were observedduring the 11 experiments, much over this span of time. The only paper that has looked only these 22 were measured at more than one epoch and at long-term precision and accuracy is that of Davis et al. thus can provide a useful estimate of long-term precisionand [1989],but most of the data shownthere werefor baselines accuracy. As noted above, the network formed by those of of 200 m to 50 km, not the longer regional scaleswe discuss the stations in California yields baselinelengths from 50 to here. This suite of measurements also aJlows us to discuss 450 km. the role of orbit determination(fiducial) networks in estab- In each experiment the GPS satellites were tracked at lishinga consistentreference frame [Larsonet al., this issue] eachstation using a TI-4100 dual-frequencyreceiver [lien- (hereafterreferred to as paper 2), and the effectof different son et al., 1985], recordingboth carrier phaseand pseudo- modelingprocedures for the atmosphericdelay (K.M. Lar- range data at 30-s intervals. (Carrier phaseis precisebut son and J.L. Davis, manuscript in preparation; hereinafter ambiguousby an integer number of cycles; pseudorangeis referredto as paper 3). In the next sectionof this paper,we unambiguousbut 2 ordersof magnitudeless precise.) The describe how the GPS data were collected and the analysis intention was to track for the 7-8 hours that several satel- techniques we used to determine the coordinates.of the dif- lites werevisible; for mostof the experiments(all but those ferent stations. The following sectionsdiscuss precision and donein May, June, and September)this meant trackingal- accuracy. most entirely at night. For most experiments the plan was to record data for 4 or 5 consecutivedays, a goal not always EXPERIMENTAL PROCEDURE AND DATA ANALYSIS achieved in practice. Table 2 summarizes the data available from all the sites we have considered. The receiver antenna The data we use were collected during 11 "experiments" was centered over the geodetic monument at each site us- conducted between June 1986 and March 1989. The mea- ing an optical plummet, with a nominal accuracy of about surements in southern and central California were made by 1 mm; the vertical offset between the antenna and the top a four-university consortium, Scripps Institution of Ocean- of the monument was measured by a tape, with perhaps 2-

TABLE 1. GPS Stations

Station Location Longitude, Latitude, Height, Stamping deg deg m

1, Algonquin Ontario, Canada -78.071 45.958 209 TELESCOPE REF A 2, Blancas Monterey -121.284 35.666 50 none 3, Blackhill Morro Bay -120.831 35.360 201 BLACKHILL 1881 4, Brush Catalina Isl. -118.404 33.409 451 BRUSH 1976 5, Buttonwillow Bakersfield -119.394 35.405 64 A364 1953 6, Center Santa Cruz Island -119.753 33.996 394 CENTER 1934 7, Churchill Manitoba, Canada -94.088 58.758 31 GEOS3 8, Clembluf San Clemente Island -118.518 32.928 297 BLUFF 1933 9, Fort Ord Monterey -121.773 36.671 39 FORT ORD NCMN 1981 10, Lacumbre Santa Barbara County -119.713 34.496 1171 none 11, Lospe Vandenberg AFB -120.605 34.896 505 none 12, Madre Miranda Pine Mountain -120.067 35.077 914 MADRE ECC 1980 13, Mojave Goldstone -116.888 35.333 904 CIGNET 14, Niguel Laguna Niguel -117.730 33.516 238 NIGUEL A 1884 1981 15, Nicholas San Nicolas Island -119.479 33.233 201 TWIN 1964 16, OVRO Owens Valley -118.293 37.234 1195 MOBLAS 7114 1979 17, Palos Verdes Los Angeles -118.403 33.745 73 PALOS VERDES ARIES 1976 1980 18, Platteville Colorado -104.726 40.184 1530 PLATTEVILLE NCMN 1981 19, Richmond Florida -80.384 25.615 23 CIGNET 20, Soledad La Jolla -117.252 32.841 216 none 21, Vandenberg Vandenberg AFB -120.616 34.558 24 VLBI STA 7223 RM1 22, Westford Haystack Ohs., Mass. -71.493 42.615 125 CIGNET

Geodetic coordinates of crustal deformation sites, referenced to NAD 83. The stamping is imprinted on the geodetic marker. CIGNET refers to the antenna phasecenter of the continuouslymonitoring GPS network [Chin, 1988]. Unlessotherwise noted, all sites are in California. ]•R$ONAND AONEW: GLOBAL POSlTIONINO SYSTEIVl PI•ISlON ANDACCUI•AC-'•r 16,549

44" ' ' ' ' I ' ' ' ! I ' ' tions, satelliteinitial positionsand velocities,tropospheric , zenith delays,phase ambiguities, and satelliteand receiver clocks. The constraints we used for our standard estimation pro- cedure are summarized in Table 3. We used the broadcast ephemeristo determinenominal values for initial position and velocityof eachspacecraft. For eachsatelhte, we esti- matedan initial position,initial ;velocity,and the behavior 40" of the satellite clock. We fixed the positionsof three "fidu- cial sites",whose coordinates were derived from VLBI mea- surements. If properly chosen,these fiducial sites, whose positionsare knownto betterthan 2 cm, providesufficient strengthto determinethe satelliteorbit to better than 2 m (seepaper 2 for furtherdetail on boththe derivationof Fort Ord fiducial coordinates and their impact on orbit determina- ß oVRO tion). If morethan three "VLBI sites"were included in a GPS experiment,the nonfiducialVLBI siteswere treated as 36ø BlancasButtonwillow ß "mobile sites" and estimated with a standard deviation of 2 Blackhill ß Lospc ß Madre kin. In general,our starting(nominal) solution was within Lacumbm 1 m of the estimatedposition of all mobile stations. Vanden•rg We modeledthe clock bias at eachmeasurement point as 34ø '•, q•' Palos Verdes Ocntcr whitenoise; in otherwords, each estimate was independent Nicholasß Brushe• Niguel and uncorrelated with the clock bias at previous measure-

Clcmbluf ments. Some receivers we used were connected to hydrogen tossers;the remainderused the quartz internal clockpro- 32 • vided by the TI-4100. White noiseclock modelling is es- 120ø 116ø sentiallyidentical to the doubledifferencing used in other Fig. 1. GPS sitesin southernand centralCalifornia observed softwares[Beutler et al., 1990]. between 1986 and 1989 for crustal deformation studies. Table 1 The optimM strategyfor determiningthe atmospheric givesthe sitenames and coordinates,and Table2 givesa break- downof whichsites were observed when. All but tltree (Mojave, propagationdelay is unclearat thistime. Tralliet al. [1988] Buttonwillow,and OVRO) lie westof the SanAndreas fault. suggesttime-varying estimation techniques are preferable, whileDavis et al. [1989]achieve similar vertical component precisionsolving for a constantzenith delay parameter. Wa- mm error. While the observers at each site recorded local ter vaporradiometers (WVR) werenot in useduring 10 of pressure,temperature, and humidity,we havenot madeuse the 11 experiments,and thereforewe havechosen to ignore of thesedata (paper3 discussesthis in moredetail). what httle WVR data were available. Paper 3 will address The GPS data wereanalyzed with the GPS Inferred Po- this issue in more detail. The strategy we have used in sitioningSYstem software (GIPSY) developedat the Jet this paper was as follows: we first correctedfor the dry PropulsionLaboratory [Stephens, 19815; Lichten and Bor- tropospheredelay using a cruderelation between station el- der, 1987]. GPS carrierphase and pseudorangedata at evation,pressure, and dry zenithdelay. The pressures.for both frequencieswere reformatted from the originaldata hydrostaticzenith delay calculations were determined using tapes,and the phasedata werechecked for cycleslips. This the eHipsoidMheight of the site and an assumedsea level processwas automated by usinga computerprogram, Tur- pressureof I013.24mbar with an exponentialprofile with boedit,described by Blewitt[19_90]. In orderto reducethe scaleheight 7 kin. The temporalvariation of the wet zenith computer.storage and CPU requirements,we subtracteda path delaywas modeled as a randomwalk, with an allowed modelof satelliteand stationpositions from the observables, variation of 49 mm over 7.5 hou•rs. and a secondorder polynomialfit wasused to compressthe Finally• a station-satelliteparameter was estimatedfor 30-s data to 15-minpoints. This techniqueis valid as long eachphase ambiguity. The nominalphase ambiguity so- asthe errorsources over 15 rain (satellite and receiver clocks lution was determinedfrom the pseudorangedata. Sub- andthe ionosphere) can be modeledby a second-orderpoly- sequently,ambiguity resolution ...was attempted. We used nomial. At this point, hnear•combinationswere formed of a 99% confidencecriterion for "fixing" theseambiguities to the carrierphase and pseudorangedata, whicheliminated theirinteger values, which is describedby Blewitt[1989]. At theh!ghest-0rder effects of theionosphere. Nominal satel- this point, postfitresiduals were visually inspected, primar- lite trajectorieswere determinedby a modulewhich inte- ily to determineif cycleslips had beenincorrectly fixed. At gratesthe equationsof motionand the variationalequa- thispoint the Cartesian stat•'{on locations and their standard tions to Obtainsatellite coordinatesand partiM d•rivatives deviations •an be retained for crustal deformation studies. of thesecoordinates with respectto the satelliteinitial con- The refeience.frame we used was defined by the Goddard ditionsand force parameters. Anothe r 'module computed SpaceFlight CenterGlobal Site Velocitymodel GLB223, prefit residuMsand partial derivativesfrom nominalsta- whichis basedon over 4 yearsof VLBI data (C. Ma, per- tioncoordinates, nominal GPS orbits_, and modeis for the sonalcommunication, 1988). Furtherdiscussion of the refer- Earth'srotation, tides, and atmosphericrefraction [Sovers enceframe is left to paper 2. Earth orientationvalues were and Border,1988]. Finally,a factorizedKalman filter was takenfrom the monthly_bulletins _of the InternatipnalRadio usedto performa leastsquares adjustment of stationposi- InterferometricSurveying (IRIS) Subcommission. 16,550 LARSONAND AONEW: GLOBALl•SITIONING SYSTEMPRECISION AND ACCURACY

, LARSONAND AONEW: GLOBALPOSITIONINO SYSTEM PRECISION AND ACCURACY 16,551

TABLE 3. Parameter Estimation

,

Parameter Estimation Standard Steady Stgte Time Behavior Deviation Standard Deviation

, ,

Satellit•position, km fori:e model lOO Satellite velocity, km/s force model 1 Satellite clock, s stochastic 1 I white noise

Station position(fiducial) fixed (not estimated) Station position (mobile), km constant 2 Station clock, s stochastic I ! white noise Phase ambiguity, s constant 10 Zenith troposphere delay stochastic 300mm 3 x 10-7k•/• randomwalk

Data weights, mm pseudorange 250 carrier phase 10

PRECISION In general, the RMS postfit scatter ranged from 4 to 6 mm, dep•e.ndingonthe Station, and the scaling quantity was ap- Introduction . • proximately1.5. Thisresulted in a dataweight of 6-9 min. Tocharacterize the pr6cision of thevectors estimated by {n aneffokt to beconservative, wechose 10 •nm and applied

GPS, we usethe scatterof independentlyestimated results. it unifbrmly to all stations. We , determined the pseudorange Forshort-term precision, we will useresults from 18 stati0n• data weightin the samemanner. This data weightwould observedduring a singleexperiment in March 1988..Short- ha/•eto be changed.if we substantiallyincreased the number term precisionwill be definedby the weightedRMS scatter of parameterswe estimated,0k we changedthe data rate aboutthe mean of dallyestimates, each determined •rom a (i.e., from 6 to 3 rain points). For the •xperimentslisted single-dayorbit solution. If we have N independentvalues in Table2, we had fairly commondata sets,in numbers y•, y•_,...y•vwith (formal) standarderrors •r•, •r2,...a•v,this of satellites,and we Usedconsistent estimation procedures. scatter is Smean, Thus, while our formal errorsmay be incorrect,they W•re computedin an identical •ashion for each experiment. Later in thissection we will discuss whether our weighting sche•me 2 was appropriate. ' Sineart---- i--1 ø'i Weexpect that short-ter•m precision might underestimate '•v (1) the true precision, because over this time scale some errors changeless than they would over longer times. Possibleer- rors in this class are wet and dry troposphericdelays and where isthe weighted mean ofthe y's. (This quantity set-up errors. To estimate long-term precison we use mea- h• sometimesbeen termed the repeatab•ty, a term we es- surementsspanning 1.2-2.7 yearsfor 22 stations(including chewbecause it leadsto ambiguity' a high repeatabi•ty may all thoseused for the short-termprecision estimates). We be highly repeatable(good), or a large v•ue (bad).) The coulduse equation(1) for long-termprecision, but by ne- reducedX 2 statisticis definedfor the weightedRMS about glecting actual plate motion we unnecessarilydegrade the the mean • precisionof the GPS estimate. Therefore,for long-termhor- izontalß precision, we adopt a standardtechnique [Ma et al., 1990]and calculatethe weightedRMS about the bestfitting 2 • I • (yi-2(Y) line. (For long-term vertical precision,we assumeno true XmeanN- I i=1 ai verticalmotion, and use equation•(1) 0nly.) The weighted Whereyi, ai, and(y)are defined asbefore. A reducedX2 of RMS about the best fitting line, s•i,½, is defined 1 indicates that the formal errors, •ri, agree with the actual , scatter in the measurements. Sinceour measureof precisionis weighted..lJy our expectrid error,we needto describehaw these formal errors Were cal- culated. The measurementstandard deviation is calculated (3) by propagating standard deviations of the carrier phase and pseudorangedata through the variance-covariancematrix. i---1 Our formal errors then are dependenton the data weights where a and b are the intercept and slope of the best fitting we assumed•for the carrier phase and pseudorangedata, 10 line and ti is the time of the ith measurement. The reduced and 250 mm, respectively. These data weights Were deter- X2 statisticfor S•i,½is mined empirically in the followingmanner. For each sta- N tion, we multipliedthe RMS post-fitscatter by the quantity V/N/(N- P), whereN isthe number of data points and P Xu.•2 = N I- 2 • (Yi' (a ai-]- bti)) 2 (4) is the number of parameters we have estimated. This data i----1 noiseis then approximately what is required to make x 2 one. These formulae are correct if we can assume that each es- 16,552 LARSONAND AONEW:GLOBAL POSITIONINO SYSTEM PRECISION AND ACCURACY timate of an interstation vector is independent. In general, •N our data were collected several days in succession,separated by 6-12 months, and thus were not evenly distributed in time. Even thou.gh we have analyzedeach day of GPS data 315o•••"•-90• 45o independently,Davis et al. [1989] have pointed out that estimates only a few days apart will be correlated, due to common error sources. Therefore, Davis et al. attempted to separateshort- and long-term error statistics. The short- term error was determined by the scatter about the mean for a single3-5 day experiment, and the long-term error Was w/ / E computed from the RMS of these means about the best fit- ting line. The total error was then computedassuming the long- and short-termerrors were independent.One problem with this formulation is that it ignores the formal errors, with all estimatesbeing treated equally. When we usedthe Davis et al. technique, we found that measurements from the M89a and M89b experiments were the largest contribu- S tors to the long-term error. We know there were systematic errors in that particular experiment, causedby the fiducial Fig. 2. GPS sky tracks over California for. the six block I GPS satellitesobserved during the December1986 campaign (modified network we were forced to use. Since this paper is a sum- from Dong and Bock[1989]).The anisotropyof thesesky tracks mary of a large quantity of data, we would like to leave gives measurements of north-south components greater inherent discussionof known systematic errors to papers 2 and 3. If precision than those of east-west components. one adapts the method of Davis et al. to incorporate the for- mal errors, one is then computing nearly the same quantity lengthwhich is about I/•aorb/L, where L is the distance from as if equation(3) were used. We thereforeuse the simplest the GPS receiverto GPS satellites(about 20,000km), formulationwe have for long-termprecision, equation (3), is the orbit error, and f• is a constant that depends on net- although we recognizethat we have not solvedfor the long- work geometry;it is about 0.2 for continentalscale networks versus short-term error sources. [Lichten,1990]. The GPS constellationobserved during the While much of the information about precision is best experiments used here consistedof seven block I satellites. obtained from the plots of scatter, we also wish to summarize Figure 2 showsthe sky paths of six of thesesatellites as seen the resultsin a compact way. One way of summarizingerrors from California; since the satellites cover a wider range of of distancemeasurements is the expression[Savage, 1983] elevationsalong a north-south azimuth than to the east or west, we might expect the baselineerror to be larger for east- tr2 = A2 -{-B212 (15) west componentsthan north-south ones. Similarly, because where a is the standard deviation and I is the baseline the data come only from satellites above the horizon, the length. This equation derivesfrom the nature of EDM mea- vertical component precision Can be expected to be much surementstRueget, 1990], where the measuringinstrument worse than either horizontal precision. has a constant error A, a proportional error B being in- Because of the varied nature of errors in GPS baselines, troduced by errors in the estimated atmosphericrefraction. there seemsto be no good reasonto adopt the form of equa- Equation(5) then followsfrom the usuallaw for the combi- tion (5) for the errors. However,some acknowledgment of nation of independent errors. the existence of proportional errors is appropriate; we have The dependenceof error on distance might be expected therefore adopted the simple law to be more complicated for GPS measurements. Over very short baselines(<100 m) the intrinsic precisionand accu- (6) racy of the measurementare 2 mm or less [Davis et al., to summarizethe changeof precisionwith distance. We do 1989], though in many surveyconditions we might expect not believe this relation truly reflects the underlying error the errors of locating the antenna relative to the geodetic structure of GPS; inste&d we use this relation as a means of monument to be several times this. Another source of error summarizingthe precisionestimates we have made. Since that is independent of length is the effect of antenna mul- our analysis is restricted to baselinesfrom 50 to 450 km in tipath: the signal receivedis the sum of the direct-arriving length, we will incorporate the long-term precisionresults radio wave and waves that have been reflected off nearby of Davis et al. [1989]for baselinesless than 50 km in order objects(such as the ground). As the positionin the sky of to extend this assessmentof GPS precision. Further stud- a satellite changesthe relative contributions of these waves ies will be required to determine the long-term precisionof will vary,causing the apparentlocation of the antennato continental- and global-scaleinterstations vectors measured wander about its true one. Becauseof the long duration of withGPs. At thattime, it willbe appropriate to investigate tracking during these measurementswe expect this error to be small. in a moresystematic fashion whether equation (5), (6), or a more complicated expressionadequately describeslong-term Over longer distancesother error sourcesenter in. For precision. distancesof more than the tropospherescale height (a few kilometers),differences in wet anddry delaycease to cancel, Results at least relative to other error sources;at larger distancesthe same becomestrue for the ionosphere. One well-understood Short-term precision. The most successfulexperiment of error scaleswith baselinelength' errorsin the estimatedor- the 11 listed in Table 2, in terms of high data yield, was the bits of the satellites. This contributes to an error in baseline March 1988central California campaign (designated M88b). LARSONAND AGNEW:GLOBAL POSITIONING SYSTEM PRECISION AND ACCURACY 16,553

Four days of data were collected at 18 sites in North Amer- •0 ica, 13 in California. The short-term precision for the north- (a) south, east-west, and vertical componentsfor this experi- mentis plotted,as a functionof baselinelength, in Figures 8 3a-3c and is listed in Table 4. The most prominent feature of these plots is the absence E of significantbaseline dependence for the north-south corn- • ponent.This has errors of1.9.4.0.6 parts in 10 s. In the east- • west component, the precision is described by 2.1 mm+l.3 • partsin 10s. The constantterm for both componentsis in •:• 4 ß goodagreement with the precision of100-m baselines [Davis "• et al.,1989]. The difference in baseline dependence forthe • two componentsis easily explainedby the satellite geometry [] D [] D [] of the block I constellation discussedin the previous section. [] [] This is a similar network to the one studied by Dong and ß i ß i ß Bock[1989] ß By fitting a lineto their baseline scatter, Dong 00 •00 200 300 400 and Bockreported precision of 6 mm + 0.5 partsin 10s in Baseline Length (km) the east-westcomponent and 2.5 mm + 0.9 partsin 10s in the north- south component. •0 The vertical component is nearly an order of magnitude less precise than horizontal components. The scatter has (b) a mean value of 17 mm, with no length dependence.Using 8 data collected during the June 1986 southern California GPS ß experiment(see J86 in Table2), Blewitt[1989] reported a • mean RMS of 29 mm on baselinesranging from 50 to 650 v 6 km, which is in good agreementwith formal errors from • ß 1 Ill O his analysis. Inspectionof scatter plots in Blewitt's paper :• shows no baseline dependence. In contrast, Dong and Bock • a [1989]reported a slightdependence on baseline length for .• their verticalcomponent precision, 12 mm -4-6 partsin 10s. •: D The differencesbetween our results and those of Dong and 2 Bock may be due to the difference in fiducial networks we used. We leave this discussionto paper 2. Discussion. Our primary objective is to use the scatter in 0 the interstationvector estimates to determineGPS system 0 400 Baseline Length (km) precision. Another important question we address is the va- lidity of the formal errors. It has long been recognizedthat formal errors underestimate the scatter in actual data. This •0 is generally attributed to unmodeled systematic effects and (c) to mismodelingof certain parameters. One technique com- monly used to produce more reasonable errors is to scale 3O formalerrors so that the reduced X2 is I [Clarket al., 1987]. • •.,ß ß[] ß In theirstudy of GPSprecision, Davis et al. [1989]discarded • [] [] their formal errors and used an ad hoc technique,deriving a • [] standarddeviation from the actualscatter. While it is dif- • 20 ficult to determine how the systematic errors impact on the • [] precision,it is fairly simpleto determinehow representative •: the formal errors are of the actual scatter in the data. In '• [] otherwords, wecompare thepredicted standard deviation •: 10• D and the actual standard deviation. Included with short-term precisionin Figures 3a-3c are the formalerror (the meanof the foursingle-day formal er- 0 i i ' I ' rots) as a functionof basehnelength. The north-southcom- 0 100 200 300 400 ponent indicates that the actual scatter is less than that Baseline Length (km) predicted by the formal errors. The formal error predicts Fig. 3. The open squares are the short-term precision, defined by a scatterof 2.4 mm .4.0.4 partsin 10s whereasthe actual equation (1) as the weighted RMS about the mean, of different components of the baselines measured in March 1988, plotted scatteris 1.9 mm -4-0.6 partsin 10s. For the east-westcom- as a function of line length. The solid squares are the mean of ponent,the formalerror is 2.4 mm -4-1.5 partsin 10s, which the formal 1-•r errors for the same quantities, as computed from is also close to the actual scatter of 2.1 mm .4. 1.3 parts in the size of the residuals and the covariances of the least squares 10s. For the verticalcomponent, formal errors overpredict adjustment. Figure 3a is for the north-south component of the the scatter by a factor of 1.5. The vertical component formal baseline; Figure 3b is for the east-west component, and Figure 3c for the vertical component. (The directionsare those of a errors are heavily dependent on the random walk parame- Cartesian coordinate system located at one end of the baseline, terization we have chosen for the wet troposphere zenith whose north is coincident with the local north, and vertical with delay. Thus, we leave discussionof vertical formal errors to the normal to the ellipsoid.) 16,554 LARSONAND AONEW: OLOBAL l:"OSlTIONINO SYSTEM PRECISION AND ACCURACY

TABLE 4. Short-Term Precision

InterstationVector Length, East, X2 North, X2 Vertical, X2 km mm mm mm

Blackhill-Blancas 53 4.9 2.25 1.2 0.20 25.4 0.78 Lospe- Madre 53 3.8 1.29 2.1 0.68 20.6 0.52 Center-Lacumbre 55 1.6 0.22 2.1 0.64 16.4 0.33 Blackhill-Lospe 55 1.8 0.32 0.5 0.03 9.6 0.12 Buttonwillow-Madre 71 3.8 1.14 3.2 1.25 12.8 0.18 Madre- Lacumbre 72 3.4 0.96 3.0 1.13 27.0 0.82 Blackhill-Madre 76 3.9 1.25 1.8 0.46 24.7 0.73 Center-Nicholas 88 3.3 0.91 3.8 2.11 14.8 0.29 Lospe- Lacumbre 93 1.7 0.22 2.0 0.54 31.5 1.19 But tonwillow- Lacumbre 105 4.2 1.13 0.4 0.02 31.2 1.06 Blancas-Lospe 105 3.8 1.01 1.2 0.18 19.9 0.48 Palos Verdes-Nicholas 115 3.5 0.80 3.1 1.30 16.0 0.34 Madre-Center 123 4.4 1.32 2.1 0.55 15.0 0.27 Lospe-Buttonwillow 123 3.8 0.80 2.4 0.74 27.4 0.89 Lospe-Center 127 2.7 0.52 2.5 0.86 22.2 0.64 Blancas-Madre 128 3.5 0.80 2.3 0.60 5.7 0.04 Palos Verdes-Center 128 2.5 0.43 0.9 0.11 11.3 0.18 Blackhill- But tonwillow 131 2.8 0.45 2.2 0.60 27.6 0.88 Blackhill-Lacumbre 140 1.4 0.13 1.9 0.41 36.7 1.57 Nicholas-Lacumbre 142 2.8 0.48 3.0 1.00 30.4 1.07 Palos Verdes-Lacumbre 146 3.8 0.90 1.4 0.24 23.2 0.65 Buttonwillow-Center 160 4.5 0.98 1.8 0.31 24.6 0.70 Blancas-Buttonwillow 174 4.5 0.88 1.0 0.10 16.5 0.30 Blackhill-Center 180 1.3 0.08 2.2 0.50 29.9 1.14 Blancas- Lacumbre 193 4.6 0.95 0.7 0.05 22.0 0.52 Palos Verdes-Buttonwillow 204 6.8 2.00 1.3 0.16 22.7 0.60 Madre-Nicholas 211 4.4 0.80 3.0 0.74 11.1 0.14 Lospe-Nicholas 211 4.5 0.87 1.7 0.28 16.8 0.35 Palos Verdes-Madre 212 6.6 1.96 2.2 0.48 13.1 0.20 Blancas-Center 232 5.8 1.29 1.6 0.20 9.5 0.11 Palos Verdes-Lospe 239 5.3 1.11 2.1 0.45 29.0 1.09 Buttonwillow-Nicholas 240 6.3 1.29 3.3 0.77 23.1 0.58 Blackhill-Nicholas 267 3.7 0.44 2.0 0.31 23.9 0.67 Palos Verdes-Blackhill 286 4.2 0.55 1.9 0.32 35.3 1.53 Blancas-Nicholas 316 6.8 1.15 2.6 0.40 11.1 0.13 Palos Verdes-Blancas 339 8.1 1.60 0.6 0.02 10.2 0.12

paper3. Comparably,plots of X2 as a functionof baseline in geodetic measurementsof crustal deformation. The con- length, as shownin Figures 4a-4c, indicate that over the stant terms for both horizontal components indicate that short term, the formal errors are comparableto the scatter. centering errors are no greater than 2 mm. It should be The outliersin the X2 plots,in both senses,those that are noted that over the courseof these 11 experiments, no effort too small and those that are too large, are often for a single was made to send the same field crews and the same equip- baseline. As an example, the interstation vector between mentto the samesites. Therefore long-term centering errors PalosVetdes and Buttonwillow(204 km) hasa X2 of 2.0 may be larger, since precisecentering may not be accurate in the east-westcomponent and a X• of 0.16 in the north- centering. south component. Noting the location of these stationsin Long-term precision. Although our objective is to sum- Figure 1, it is apparentthat this baselineis alignednearly marize long-term precisionof interstation vectors from 50 north-south. The geometryof ground stationsand satellites to 450 km in length, it is appropriate to show a few, repre- degradesthe east-westcomponent (and improvesthe north- sentative time series of estimates from these networks. We south component),in a way that is not predictedby the discuss results for two interstation vectors in detail and sub- formal errors. sequentlytabulate statistics using estimatesfrom all 11 ex- The observed short-term precision is a function of our periments. More time seriesof interstation vectors will be ability to remove error sourcesassociated with satellite or- discussedin the accuracy section. bits, satellite and receiver clocks, and propagationdelays; The baselinefrom Mojave to the Owens Valley Radio Ob- to precisely center the GPS antenna over the monument; servatory(OVRO) is frequentlyused for engineeringtests and to measure the distance between the antenna base and [Ware et al., 1986]. The baselineis approximately240 km monument. Precise orbits are not necessarily accurate or- east of the San Andreas fault and is oriented N30*W. The bits. Since the accuracy of GPS orbits will influence the north-south, east-west, and vertical componentsfor this 245- accuracyof interstation vectors,we leave that discussionto km interstation vector are shownin Figure 5. Mojave-OVRO the next section. Mismeasurement and miscenteringof the solutionsfrom the March 1989 experiment are not displayed GPS antennaover the monumentare a significantlimitation or used in this calculation of long-term precision because LARSONAND AGNEW:GLOBAL POSITIONING SYSTEM PRECISION AND ACCURACY 16,555 both sites were tightly constrained to their VLBI wlues for mm. There have been 62 VLBI observations of these sites that experiment. Ignoring this experiment limits the c•l- between1983 and 1988 [Ma et al., 1990]. VLBI estimates culation of long-term precision to a temporal span of 14 the displacement rate between the sites to be 0.14-2.0 and months, with nine data points measuredover four epochs. -2.64-1.4 mm/yr in the north-southand east-westcompo- In the north-south component,the long-term precisionis 2 nents, respectively. The very precise GPS north-south com- mm. In the east-westcomponent, it is significantly worse, 9 ponent is additional evidence that the VLBI measurement

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TABLE 5. Long-Term Precision

InterstationVector Length, East? X2 North? X2 Vertical,b X2 Years Number of kla Illnl mm Illnl Observations

Losp e-Vandenberg 37 4 2.2 4 2.4 16 0.3 2.2 8 Blancas-Blackhill 53 7 4.0 1 0.1 36 1.6 2.2 8 Clembluf-Brush 54 5 0.7 4 0.8 30 0.8 2.2 8 Lacumbre-Center 55 3 0.8 3 0.8 26 0.7 2.2 11 Madre-But t onwillow 71 4 1.0 4 3.0 35 1.3 2.2 11 Vandenberg-Madre 76 4 0.9 4 2.0 22 0.6 2.2 10 Madre-B lackhill 76 4 1.0 2 0.4 27 0.8 2.2 11 Blackhill-Vandenberg 91 6 2.2 5 3.1 29 1.1 2.2 13 PalosVerdes- Clembluf 91 10 1.6 5 0.9 39 1.1 2.7 9 VandenbergCenter 101 5 1.4 4 2.5 25 0.8 2.2 16 PalosVerdes-Nicholas 115 8 1.9 4 1.1 29 0.9 2.7 10 Soledad-Clembluf 119 7 1.1 7 3.1 45 1.6 2.7 9 Madre-Center 123 4 1.0 2 0.4 30 1.0 2.2 11 Center-PalosVerdes 127 4 0.6 5 2.2 31 1.1 2.2 16 Butt onwillow-Blackhill 131 3 0.5 5 2.5 32 1.1 2.2 11 Butt onwillow-Blancas 173 6 1.2 5 2.0 42 1.7 2.2 9 Vandenberg-Nicholas 180 6 0.8 9 3.2 26 1.1 2.7 8 Blackhill-Center 181 6 1.5 3 0.6 39 1.5 2.2 16 PalosVerdes-Vandenberg 223 5 0.8 7 3.1 41 1.7 2.2 14 Mojave-PalosVerdes 224 9 1.4 6 1.4 38 1.2 2.2 18 Mojave- Ovro 245 9 1.9 2 0.4 57 4.3 1.2 9 PalosVerdes-Blackhill 286 7 0.9 4 1.0 41 1.6 2.2 12 Ovro- Blackhill 308 13 2.9 5 1.2 34 1.1 2.2 14 Mojave-Vandenberg 351 10 1.5 6 2.4 42 1.8 2.2 18 Moj ave- Blackhill 358 6 0.9 4 1.3 46 2.0 2.2 12 Ovro-Vandenberg 363 14 3.0 5 1.2 33 0.9 1.2 11 Ovro-Center 382 14 2.6 5 0.9 47 2.0 2.2 15

USGS Results c Mojave-NCMN1 1 2 2 5 2.0 4 10JDG-33JDG 7 6 3 12 3.0 27 10JDG-Joaquin 11 6 5 13 3.0 27 10JDG-Oquin 12 5 4 18 3.0 26 LomaPrieta-Eagle d 31 8 4 16 0.9 7 Loma Prieta-Allisond 43 8 4 21 0.9 8 PalosVerdes-Vandenberg 223 11 6 40 2.2 6

aWeightedRMS about best fitting line, as in equation(3). bWeighted RMS about weighted mean, as in equation(1). cUSGSresults are taken from Davis et al. [1989]. dj. Svarc(personal communication, 1990) of no significantmotion in thiscomponent is correct.The is 4 mmq- 0.3 partsin l0 s. In the east-westcomponent, the verticalprecision of 57 mm is the worsthsted in Table5. long-termprecision is comparableto the short-termresults Thelong-term precision for thebaseline from Vandenberg with a slightlylarger constant term, 3.4 mm + 2.0parts in to Center(located on SantaCruz Island)is shownin Fig- l0 s. As with our short-termprecision results, the vertical ure 6. A 101-km baselineoriented NNW, it is considerably componentis lessprecise than either horizontal components shorterthan Mojave-OVRObut hasbeen measured almost andis describedby 26 mm + 5 partsin l0s of the base- twice as often, with data spanning2.2 years. The scatter linelength. A morecareful inspection of Figure7c indicates about the best fit line is 5 and 4 mm for the east-westand that long-termvertical precision ranges from 30 to 40 mm, north-southcomponents, respectively. The verticalcompo- for baselineslonger than 50 km, and improvesrapidly for nent scatteris 24 mm. All experimentswere analyzed with smallervalues. Thus, for basehuesless than 50 km, vertical continental-scalefiducial networks, with the exceptionof the precisionis far betterthan the constantterm of our linear March 1989 data. fit, 26 m•n, would suggest. The long-termprecision statistics are hsted in Table5. Discussion. We have compiled the long-term precision For eachinterstation vector, we computedprecision, as de- statisticsfrom Davis et al. [1989]and list them in Table fined in the introduction of this section, and the reduced 5 alongwith our interstationvectors. The USGSbaselines X2 statistic.Our criteriafor selectionof theseinterstation rangefrom 200 m to 223km. Daviset al. definedprecision vectorswere that they be estimated during three or more as the RMS about the best fitting line for both horizontal experiments,over at least1.2 years,with eightor morein- and verticalcomponents {we compute the RMS aboutthe dependentestimates. The long-termprecision results have meanfor the verticalcomponent). By includingthe USGS beenplotted as a functionof baselinelength in Figures7a- results,we havea betterestimate of GPS precisionfor base- 7c. The long-termprecision for the north-southcomponent huesless than 450 km in length:3.4 mm + 1.2parts in l0s, LARSONAND AGNEW: GLOBALPOSITIONING SYSTEM PRECISION AND ACCURACY 16,557

5.2 mm + 2.8 parts in 10s, 11.7 mm + 13 parts in 10s in whereasDavis et al. did not attempt ambiguity resolution. the north-south, east-west, and vertical components. At 100 Resolvingambiguities has been shownto improve short-term km, this would yield subcentimeter horizontal precision, 25 precisionin the east-westcomponent [Dong and Dock,1989; mm in the vertical. Our study overlaps with Davis et al. on Blewitt, 1989], and results from paper 3 indicate that am- one baseline, Palos Vetdes to Vandenberg. Our long-ternt precision of 5, 7, and 41 mm in the north-south, east-west, and vertical only differs appreciably from that of Davis et (a) al. (6, 11, and 40 mm) in the east-westcomponent. We resolvedambiguities on nearly all estimates of this baseline,

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-5O i ß i ' i 100 200 300 400 Baseline Length (km) -100 Fig. 7. The solid squaresrepresent the long-term precisiondeter- mined from experiments described in Table 2. For the horizontal componentsthe precisionis defined(equation (3)) asthe weighted -150 . '. ' ß ' , ' 1986 19'87 19•88 1989 1990 RMS about the best fitting straight line; for the vertical, by the weightedRMS about the mean (equation(1)). The components Fig. 6. Change of relative coordinates for the Center to Van- are defined as in Figure 3. Also shown are long-term precision de- denbergvector (101 kin), with zero being the mean value. The terminations(open squares) from Davis et al. [1989]for baselines components shown are defined as in Figure 3. ranging from 200 m to 223 km in length. 16,558 LARSONAND AONEW: GLOBAL POSITIONINO SYSTEJV( PRECISION AND ACCURACY biguityresolution improves precision in the long term as requiredto discernthe seasonalvariations which may be well. This may alsoexplain the slightlyless precise USGS presentin thesedata. ContinousGPS networkswill Msore- east-westcomponehts for baselinesless than 50 km. duce the vertical scatter by ehminating the error associated Again,we address the questionof thevalidity of ourfor- with centeringand measuringthe heightof the antennaover mal errors.In Figures8a-8c, we plot Xe as a functionof the monument. Some of the scatter in the vertical compo- baselinelength. For the north-southcomponent, our formal nent may alsobe due to humanerror in translationof field errors underestimate the the actual scatter approximately notes into the site vector used in the analysis software. halfthe time,although X2 doesnot increase with baseline lengthßFor the east-west and vertical components, there is a slightincrease of X• withbaseline length. Long-term error (a) sourceswhich we think have contributed to the degraded long-termprecision are the accuracyof the GPSspacecraft orbit, the ability to resolvecarrier phase ambiguities, ade- quatemodeling ofthe ionosphere and atmosphere, and blun- ders. Sincesome of theseerrors (e.g., orbit accuracyand blunders)have not beenaccounted for in the formalerror, ß ß weexpect that this has inflated the long-term X• statistic. ß ß ß Wediscuss each of theseerror sources in turnß ß ß The orbit accuracyis primarily controlledby the accuracy ofthe fiducial coordinates, geometry ofthe fiducial network, and the numberof hoursof trackingdata that wereavailable. Experimentswhich suffered from failure or absenceof conti- nental fiducialsites were, in general,less precise. Addition- ally,mixing interstation vector estimates computed with dif- ferent fiducial networks undoubtedly inflates the long-term 100 2 0 30o 400 precisionstatistic. For the 11 experimentsin Table2, 10dif- Baseline Length (km) ferent fiducialnetworks were used (assuming the three mon- umentsat Mojaveto be independent.)Since the purposeof (b) fiducial networksis to provide a consistentreference frame in which to determine crustal deformation rates, their sta- bility is extremelyimportant. The influenceof the fiducial networkon GPSprecision and accuracy is discussedin pa-

per2 ß Theconsistency ofour long-term precision with that iI

of Daviset al. [1989]leads us to believethat highprecision ß canbe achievedwith a "single-day"arc, where each day of data yieldsan independentestimate of satelliteorbits and stationpositions. The precisionof single-dayarcs on these spatialscales may be dependent onthe sophistication ofthe orbit determinationsoftware. For continental-scale(2000- 3000km) baselines,a "multiday" arc solution, as discussed by [Lichtenand Border,1987], may be requiredto achieve comparable precision. The precisionresults that we and others(prominently 200 3O0 400 Dongand Bock[1989] and Blewitt[1989]) have presented Baseline Length (km) werefor experimentswhere a highpercentage of carrier phaseambiguities were resolved. The numberof hoursof (c) trackinginfluences the confidencestatistic used to decide whetherthe carrierphase ambiguity has been adequately resolved[Blewitt, 1989]. In general,we find that ambiguities canbe easily resolved with more than an hour of data, with oneadditional criterion: the interstationspacing should be lessthan 100 km. In the S88 experiment, the closestspacing

of two stations was 223 km ß We were only able to resolve 4 of 32 ambiguities. In experimentswith closerintersta- tion spacing,e.g., M88b, we wereable to resolve83 of 85 ambiguitiesin California. Experimentsconducted over a few daysdo not provide an adequatesampling of troposphericand ionosphericcon- ditions. This may explainwhy long-termvertical precision is degradedrelative to short-termprecision. With the other ! m - 400 error •sourcesin these data, it is difficult to isolate the at- 0 100 200 300 mosphericand ionosphericcontribution. Data that are col- Baseline Length (km) lectedcontinuously, with a stablefiducial network, will be Fig. 8. X2 for the baselinesshown in Figure 7. LARSONAND AGNEW: GLOBAL POSITIONINGSYSTEM PRECISIONAND ACCURACY 16,559

ACCURACY an accuracy of a millimeter at these distances. In practice, local surveys introduce uncertainty into the accuracy assess- Introduction ment. High precisionis necessaryfor, but not indicative of, ac- Measurements between the different monuments at these curacy. In order to assessaccuracy, we must compare GPS sites (local surveys) are of severaltypes and need to be vector estimates with vectors determined by an indepen- treated differently. There are conventional surveys, differen- dent measurement system. Comparisons are also useful for tial GPS determinations, and simple measurementsof height identifying systematic errors in GPS, becausedifferent tech- above a monument, which we discussin turn. Conventional niques presumably have different error sources. VLBI and surveyshave varying levels of redundancyand therefore ac- SLR are two systemsavailable to compare baselineslonger curacy. In many cases what are termed survey errors are than 50 km. No comparisons will be made between GPS actually errors in user understanding of the meaning of the and SLR measurements because there are few GPS occupa- coordinate differencescoming from ground surveysor blun- tions of SLR monuments in this data set. Unless otherwise dersin passingalong information and not measurementerror noted, the VLBI results are from the 1989 Crustal Dynamics (W. Strange,personal communication, 1990). The precision Project AnnumReport [Ma et al., 1990]and GLB223, the of differential GPS surveys on these scales is several mil- Goddard site velocity model that was used to determine the limeters in the horizontals but is twice that in the vertical. GPS fiducial coordinates. Davis et al. [1989]reported long-term vertical precisionof Most estimates of GPS accuracy have been restricted to 5 mm for a 240-mbaseline. This is considerablyless pre- singleepoch agreement with VLBI or SLR [Don9 and Bock, cise than the best conventional surveys. On the other hand, 1989; Blewitt, 1989; Bock et al., 1990], with the exception the accuracy of differential GPS surveys is not well under- of work by Davis et al. [1989]. Using data from six ex- stood or documented. The accuracy of these surveys may periments conducted in southern California, Davis et al. be dependent on which GPS receiverswere used and which compared GPS and VLBI length estimates of the 223-km software was used to analyze the measurements. Measure- baselinebetween Palos Vetdes and Vandenberg. Agreement mentsof heightabove the geodeticmonument are required was within the standard deviations of GPS and VLBI. They for both GPS and VLBI. For the TI-4100 GPS receiver, it alsocompared line lengthsfrom the HebgenLake (9-30 km) is assumed that the difference between the L• and L2 phase and Loma Prieta (30-50 km) networkswith the Geodolite, centers and the antenna base is well known, although dis- a laser measurement system, with agreement of 1-2 mrn at crepancieshave been reported (J. Svarc,personal commu- theselengths. At Parkfield,they compared the fault-parallel nication, 1990). Likewise,errors in VLBI site vector mea- motion to creep meters and alignmentarrays, where rates surements,for baselineswith very few data, will mkp into a agreedto within 1-2 mm/yr. While we cannot compare IGPS- VLBI I discrepancy. our interstation vectors with as many different kinds of sys- As an example of a typical situation in accuracy deter- tems, we have concentrated our efforts on the accuracy of minations, Figure 9 illustrates the number of vectors that "regional" scale baselines. We assessthe accuracy of GPS must be added to compare VLBI and GPS baseline vectors in two modes: agreement of interstation vectors and linear between Mojave and Vandenberg. Terms which are under- trends. lined are GPS sites, or antenna phase centers. The numbers As with our precision study, we would like to know if ac- refer to the Crustal Dynamics Project site catalog. Two lo- curacydegrades with baselinelehgth. The literature has cal surveyswere required to recoverthe vector from the main often referred to agreement with VLBI in terms of parts per baselinelength. This is usefulif thereis a true deterioration Mojave of accuracywlth baselinelength but is inappropriatewhere ?222 7228 errorsare not necessarilydependent on baselinelength. Cer- tainly, orbit estimationmay contributea baselinedependent VLBI , •/ error for comparisons at the continental baseline scale, but GPS__ / NCMN•. for baselines shorter than 500 km, there is no evidence to date that the IGPS- VLBI I discrepancyis length depen- dent. ß•-TI-4100 • FRPA Comparisonsbetween new and standard measurementsys- tems are essential for validation of the new measurement technique. The difficulty in comparison studies arises in de- termining the correct rotations which are required to com- Vandenberg/ / / pare vectors which were determined in different reference 7223• / frames. Even simple comparisonsof line lengths determined by EDM and GPS require that a scalingfactor be introduced to accountfor the differencein the speedof light value used Not drawn m scale in the two data analysis systems. Since GPS vectors are Fig. 9. Cartoon to show the vectorswhich must be measured referenced to a VLBI system of fiducial coordinates, GPS to compare GPS and VLBI measurementson a typical baseline. and VLBI comparisons are simplified somewhat. A more The bold vector between VLBI monuments at Vandenberg and mundane element of vector comparisonsis due to local site Mojave is 351 km long. The dashed line represents the Vector surveys.Different systems (VLBI, SLR, GPS) occupydif- between GPS monuments. GPS monuments/antennaeare un- derlined. Each segment with an arrow represents a local survey ferent geodeticmonuments at the same geographiclocation. which must be conducted to compare GPS and VLBI baseline Generally, these monuments are separated by only several solutions. This figure is not drawn to scale. Actual survey values hundred meters, and conventional surveyscan be done with are listed in Table 6. 16,560 LARSONAND AGNEW: GLOBALPOSITIONING SYSTEM PRECISION AND ACCURACY'

VLBI mark at Mojave to the VLBI referencemark, NCMN1. crustal delbrmation studies, becausethe fundamental mea- These surveys were done conventionally. The measurements surement that we seek is the time rate of changeof the vec- from NCMN1 to the three permanent antennae which were tor between two sites. Rate determinations are not immune placed at Mojave between mid-1988 through early 1989 were from local survey errors. If that station is used as a fiducial made with GPS. For completeness, in Table 6 we have listed site in some estimates but not for others, this will influence the relevant local survey information that we have used. In the computed rate. We discussonly a few interstation vec- addition to crustal deformation measurement sites in Cali- tors in detail. fornia, we also list local surveys at fiducial sites. Although it is important to compare interstation vectors Results at a singleepoch (we comparea few vectorsmeasured during Tl•e data collected in Table 2 were directed toward •nea- the J86 experiment),long-term monitoring of the intersta- sating crustal deformation rates in California. Therefore, tion vector will help to find probable local survey errors. We comparisons with VLBI are mostly limited to interstation feel that comparison of rates is ultimately more useful for vectors in California. Prominently featured in the available

TABLE 6. GPS-VLBI Local Survey Values

Station 1 Station 2 X, Y, Z, Survey Type Agency Reference m m m

Algonquin Park 6381 Algonquin(GPS) 92.760 70.280 13.066 conventional GSC I

Mojave 7222 7288 -323.1130 148.2132 -43.9926 conventional 2 7288 NCMN1 69.6589 -5.9415 35.6147 conventional 2 NCMN1 CIGNET-TI4100 -209.804 120.407 1.836 GPS, NGS a NGS 3 NCMN1 CIGNET-FRPA -209.7820 120.4134 1.8247 GPS, Berneseb USGS 3

Owens Valley Radio Observatory 7207 7853 -820.4891 549.1188 87.1157 conventional 3 7853 7114 (GPS) -1.2227 -2.2611 -3.6171 conventional 3

Richmond, Florida 7219 TIMER 1962 59.722 35.2121 29.920 conventional 3 TIMER 1962 CIGNET-FRPA 0.5483 -3.2420 1.5754 conventional 3

Westford Observatory 7209 MICRO 111.191 84.088 43.334 conventional 3 MICRO CIGNET-TI4100 -84.8933 -45.2645 -12.9246 GPS, NGS NGS 3

VandenbergAir Force Base 7223 RM1 (GPS) 23.105 -0.9629 17.253 conventional NGS I

Compilation of local survey information used, referenced to WGS84. Numbers are associated with the Crustal Dynamics Project VLBI marks. Full listings are given by Noll [1988]. For survey types, we distinguishbetween those done conventionally,and those done with GPS receivers. For GPS surveys, we indicate the software used. All GPS surveys were measured with TI-4100 GPS receivers. If known, the agency which conducted the survey and computed the survey values is listed. References: 1, M. Mum'ay, (personalcommunication, 1990); 2, J. Ray, (personalcommunication, 1990); and 3, Chin [1988]. aMader [1988]. bBeuileret al. [1987].

TABLE 7. GPS-VLBI Vector Differences

GPS VLBI

Interstation Vector Length, East, North, Vertical, Years Number of Years Number of km mm mm mm Observations Observations

Yuma a Monument Peak a 208 -10 5 -20 E 2 4.1 8 Mojave Palos Verdes 224 -15 -12 -80 2.3 18 4.1 5 Mojave Ovro 245 -8 10 -60 1.2 9 4.3 62 Fort Ord Vandenberg 256 -10 -15 0 1.2 10 4.2 7 Fort Ord Ovro 316 5 8 8 1.2 8 4.2 5 Mojave Vandenberg 351 -15 -13 -50 2.3 18 4.3 89 Ovro Vandenberg 364 -10 -30 -10 1.2 9 4.2 40 Monument Peak Vandenberg 430 10 -16 7 E 2 4.0 18

E: single epoch measurement. aSeeNoll [1988]for station description. LARSONAND AGNEW: GLOBAL POSITIONINGSYSTEM PRECISIONAND ACCURACY 16,561 data are VLBI sites at Fort Ord, Mojave, OVRO, Vanden- 100 berg, and Palos Vetdes. GPS and VLBI interstation vector changeswill be displayedin a standard form, with the north- south, east-west, and vertical components. Zero is the mean 5O value of the GPS estimates. The solid line in each figure is the VLBI baseline vector component which results from a simultaneousglobalestimate ofsite velocities (GLB223) ß •'E

Since this site velocity model was used to compute fiducial 0 locations for the GPS experiments, this is the most appro- •: priate measureof agreementwith VLBI. The error bars for • the GPS baselinecomponents are one standard deviation. = Based on our long-term precision study, these formal er- -50 rors underestimate the actual uncertainty. The differences between GPS and VLBI for all baselines are listed in Ta- ble 7. The interstation vectors compared at more than one -foo . epoch which we discussin greater detail are the vectors be- 1986 19 7 1988 1989 tween Mojave and Vandenberg, Mojave and Palos Vetdes, and OVRO and Fort Ord. 100 Mojave-Vandenberg-Palos Vetdes. In June 1986, the USGS began an effort to regularly measure the intersta- tion vectors between monuments at Mojave, Palos Verdes, s0 '• (b) and Vandenberg Air Force Base. Due to the commitment of both personneland receivertime, these are now the most fre- •' quentlyoccupied mobile GPS baselinesin Californialonger g than 200 km. For Vandenbergand Mojave there were eight • 0 experimentsover 33 months,spaced 4-6 monthsapart. Pa- • los Verdes was occupied simultaneously with Mojave and •5 Vandenberg in seven of those experiments. -50 Mojave to Vandenberg is the most frequently occupied VLBI baseline in California, with 89 observations between 1983 and 1988. This baselineis long enough to begin to show deterioration in the GPS east component due to poor orbit -100 determination in several of the seven epochs shown, partic- 1986 1987 1988 1989 ularly J88 and S88, where we were unable to resolvea large lS0 number of the carrier phase ambiguities. Figure 10 displays (c) the GPS vector componentsfrom 1986 through 1988. The offsetbetween GPS and VLBI coordinatesis 15 mm in the 100 east and 13 mm in the north. The GPS rates derived for the north-south and east-west componentsof the Vandenberg- so T Mojavevector are -25.5 + 2 and28.9 q- 4 mm/yr,respec- E tively. This agrees within one standard deviation of the v VLBIestimates of-28.14-2.0 and 27.64-1.6 mm/yr. The • 0 GPS east-westcomponent is significantlynoisier than the • ._ north-south component, as evidencedby the weighted RMS z -so about the best fitting line: 6 and 10 mm in the north-south and east-westcomponents, respectively. In the verticalcom- -100 ponent, GPS has a RMS of 41 mm and disagreeswith the VLBI mean by 50 mm. The VLBI vertical RMS about the -150 best fitting line is 37 mm. 1986 Palos Verdes was measured by VLBI only five times be- Fig. 10. The points with error bars are the GPS-derived relative tween 1983 and 1987. We have estimated 18 independent coordinatesfor the Mojave to Vandenbergvector (351 km), taken interstation vectors with the GPS data that were collected relative to the mean. The solid llne shows the coordinates given between 1986 and 1988, as shown in Figure 11. The VLBI by a model fit (GLB223) to the VLBI data. While the agreement and GPS monuments at Palos Vetdes are identical. The in rates is good, there is a persistent offset between the two types rates from VLBI are -194-3.7 and 204-3.4 mm/yr in the of measurement. Components are defined as in Figure 3. north-south and east-west components respectively. The GPS rates are similar: -20q-2.5 and 28q-4 mrn/yr. The O VRO-Fort Ord. The OVRO-Fort Ord baseline vector is horizontal components both exhibit an offset of approxi- 316 km long and oriented nearly east-west.OVRO requires mately 15 min. The weighted RMS about the best fitting a conventionalsurvey, but the Fort Ord monument is used line for G PS is 8 and 9 rnm for the east-west and north- by both VLBI and GPS. There have only been three GPS south components.In the vertical component,the•precision experimentsincluding Fort Ord, over the spaceof 1.2 years, is less than 50 mm for both VLBI and GPS, but their means whereas VLBI experiments span over 4 years. Agreement disagreeby 80 min. This is the largest differenceof eight between GPS and VLBI is shown in Figure 12. Agreement baselines listed in Table 7. of GPS to VLBI is 5 mm in the east and 10 mm in the 16,•62 LARSONAND AGNEW: GLOBAL POSITIONING SYSTEM PRECISION AND ACCURACY

lOO , lOO (.)

50 50

o •, o

-50 -50

-100 '. ' , ß ' - -100 ! 1986 1987 19•88 1989 1986.5 1987.5 1988.5

IO0 (b) (b)

0

-lOo -lOo ' ß , ß 1986 1987 1988 1989 1986.5 1987.5 1988.5

15o 150

(c) (c) lOO 100

ß

5O 50

• -5o

-lOO

-150-100 I -150 •1986 1986.5 1987.5 1988.5 Fig. 11. Change of relative coordinatesfor the Mojave to Palos Fig. 12. Change of relative coordinatesfor the OVRO to Fort Verdesvector (224 kin). SeeFigure 10 for details. Ord vector(316 km). SeeFigure 10 for details. north. The vertical agreement is within 20 mm for two ex- tion of baseline length. The error bar is determined from periments and 60 mm for the third. The computed rates for the weightedRMS about the best fitting line for VLBI and OVRO-Fort Ord agree with VLBI rates within one standard weightedRMS about the mean for GPS. The disagreement deviation, but the uncertainties on the GPS rate estimates is less than 80 mm on baselinevectors ranging from 200 to are quite large, due to the short time-span of occupations. 430 km. Dong and Bock[1989] compared single epoch ver- tical estimationsfor the Mojave-OVRO baselineand agreed within 22 mm of the VLBI solution. Results from Blewitt Comparison of Vertical Components [1989]are more comparableto Figure 13, where at a sin- The absolute value of the vertical component difference gle epoch, the agreement with VLBI was from 5 to 80 mm, betweenGPS and VLBI is shownin Figurd13 as a func- measuredon 15 baselinesranging from 100 to 1100 km. LA•SON AND AON•V: GLOBALPOSlTIONINO SYSTEM PRECISION AND ACCURACY 16,563

150 15 PaLos Vetdes- Vandenberg- 125 10 - Mojave Mojave 100 5 75

50

25 •10 - VLBI, 5 obs.4.1 yrs - - VLBL89 obs,4.3 yrs 0 -15 -25 -10 0 10 -10 0 10 -50 15 OVRO-Mojave Fort Oral-Mojave -75 -100 5 -125 0 , -150 ß i ß i - i - m - 0 100 200 300 400 500 -5

-10 - VLBI, 62 ohs,4.1 yrs - - VLBL7 obs,4.2 yrs Baseline Length (km) -15 Fig. 13. The GPS-VLBI vertical component difference, plotted -10 0 10 -10 0 10 as a function of length. The error bar is determined from the weightedRMS about the best fitting line for VLBI [Ms et •1., East Velocity, ram/jr 1990] and weightedRMS about the mean for GPS. More discus- sion can be found in the text and Table 7. Fig. 14. Difference in vector rates for GPS and VLBI derived mo- tion of Fort Ord, OVRO, Vandenberg, and Palos Verdes relative to Mojave. Zero, shown by the inverted triangle, is the VLBI Comparison of Rates horizontal rate, and the difference of the GPS rate is shown as a solid circle. Error ellipses are one standard deviation, including Finally, we compare rates for four baseline vectors in both GPS and VLBI. The number of observations and time span of measurements for each baseline are listed. southern and central California. Figure 14 showsthe GPS- VLBI rate difference vector for interstation vectors between Mojave and OVRO, Vandenberg, Palos Vetdes, and Fort Ord. The error ellipses were computed from the GPS and some of the interstation vectors listed in Table 7 are sugges- VLBI one standard deviations, and then projected onto the tive that a single"survey error" may, in fact, be responsible for a large portion of the GPS-VLBI horizontal discrepancy. horizontal plane. The GPS standard deviations would yield ellipsesoriented nearly alongthe north-south/east-westaxes. In order to test this hypothesis, we have taken solutionsfrom The addition of the VLBI standard deviations rotates the the four (D86, S87, M88a and M88b) experimentsthat in- clude the VLBI sites OVRO, Fort Ord, Mojave, and Vanden- ellipsesslightly, although in general, the GPS standard de- viationsdominate the error ellipses.The GPS rates for Fort berg. These experimentswere all analyzedwith continental- Ord and OVRO are determined from only 1.2 years; those scalefiducial networks but not necessarilythe sameones (as at Palos Vetdes and Vandenberg are determined from 2.3 indicatedin Table 2). Using the VLBI solutionsfor these years. The VLBI rates are determined from 4 or more years sites at each epoch, we adjusted the GPS interstation vec- tors and solved for the best fitting "discrepancy" vector at of data. The only significant difference between G PS and VLBI rates is for the east-west component of Palos Vetdes. OVRO, .Vandenberg,and Mojave. We did not adjust Fort The vertical rates of deformation for both VLBI and GPS Ord, as the GPS and VLBI monuments are identical. The are less than their formal uncertainties. formal errors from the G PS estimates were used to weight the fit. The results of this calculation are shown in Table

Discussion 8. The only offsets we consider to be significant are the discrepanciesin the north-south and east-west components There are several possible reasons that VLBI and GPS for Vandenberg,where the best fitting vector is -144-8 and vector componentsdisagree, at this level. The differenceson 134-4, and the north-south component at OVRO, 134-2. The

TABLE 8. Estimated Survey Discrepancy Vectors

OVRO Mojave Vandenberg Experiment North East North East North East

D86 15•-10 -94- 8 54-14 -94- 11 -124-11 -94-9

S87 144- 7 -214- 6 64- 8 -174- 7 -74- 7 -164-6

M88a,b 11 4-8 94- 6 -64- 8 134- 7 -214- 7 -114-7

Weighted mean 134-2 -74-16 14- 7 -34-17 -144-8 -134-4

All values are in millimeters. 16,564 LARSONAND AONEW: GLOBAL POSITIONINGSYSTEM PRECISION AND ACCURACY latter is particularly surprising, given the energy which was that do not include these sites, agreement of horizontal com- expended to remeasure the line between Mojave and OVRO ponents is approximately 10 mm. The vertical discrepancies in the "MOTIES" experiment(J. Ray, personalcommunica- betweenVLBI and GPS are much larger, ranging from 0 to tion, 1989). The result is consistentwith the observeddis- 80 mm. There does not seem to be a systematic bias be- crepancy between Mojave and OVRO of 10 mm. Likewise, tween the two systems, which in any caseis unhkely because the discrepancyat Vandenberg would explain the long-term VLBI defines the orientation and scale of the GPS reference discrepancybetween Mojave and Vandenberg and would be system. For making crustal deformation measurements,the sufficient to create the largest discrepancy on these regional most important comparison may be between the vector rates baselines, between OVRO and Vandenberg determined by the two systems. The GPS-determined vector Another reason for horizontal component discrepanciesis rates agree well with those determined from VLBI measure- the robustness of the solution for the vector, either from GPS ments. or VLBI. Both systems will reduce the uncertainty in the in- These results confirm the study of Davis et al. [1989], terstation vectorwith additionaldata. Somevectors (such whichfound that precisionand accuracy(in rates) wassub- as OVRO-Fort Ord) are measuredby VLBI onceper year, centimeter on these spatial scales. In turn, this confirms whereas the VLBI Mojave-Vandenberg vector is based on that GPS geodeticmeasurements are appropriate for crustal 89 measurements. Both Mojave and Vandenberg are fixed deformation experiments, where signals range from several VLBI antennas, whereas Fort Ord is a mobile VLBI site. millimeters to hundreds of milhmeters per year. This pre- The interstationvectors between fixed antennas(which gen- cision and accuracy may not, of course always be achieved, erally are measuredmore often) are more preciselyknown and there are reasonswhy the data set we have studied may than those between mobile antennas. be better than most. Although we cannot prove this as- The vertical component discrepancies,while troubling for sertion, we feel that one of the most important factors in some baseline vectors, are based on very few data points. repeating high-accuracyGPS measurementsis keeping as We assumed that the GPS phase center, which varies with many factors common to all experiments as possible. Al- elevation angle to the GPS satellite, averaged to some mean though the tracking data for the different experiments have value. This phase center variation may in fact introduce not been homogeneous,most other factors were: the same a systematic bias, which could introduce the offset we see GPS receiver and data analysis software were used; the same between GPS and VLBI. GPS vertical components are par- type of GPS antenna was used at nearly all stations; and the ticularly sensitiveto poor fiducial networks(see paper 2). sameGPS satelhtes(which followed nearly the sameappar- Another possible source of vertical discrepancies is differ- ent sky paths) wereavailable. The challengeremains for the ences due to the estimation technique used to determine geodetic community to successfullymix different receivers, propagation delays of the atmosphere. We discussthis fur- antennas, block I and block II GPS satellites, and analy- ther in paper 3. sis software and to retain the high precision and accuracy The agreement between GPS and VLBI rates in all com- achieved with the block I GPS constellation. ponents is extremely encouraging, particularly considering the short time span of GPS data collection. We expect that Acknowledgments. Much of the GPS data usedin this paper the rate agreement will continue to improve as we collect were collected as part of a collaborative project to measure crus- tal. deformation in central and southern California by the Scripps more data and eliminate systematic errors. Institution of Oceanography, California Insititute of Technology, University of California, Los Angeles,.and MassachusettsInsitute CONCLUSIONS of Technology. We are particularly indebted to dozens of graduate students who contributed their time to this effort. The principal We have analyzed nearly 3 years of GPS data collected in investigators, Dave Jackson, Bob King, Tom Jordan, and Brad Hager, were instrumental in making these experiments possible. southern and central California between 1986 and 1989. On The scope of this study would not have been possible without time scalesof a few days, horizontal precision is 2 mm, with the cooperation and participation of the NGS and USGS, which an additionallength dependence of 0.6 and 1.3 partsin 10s were conducting their own surveys in the region. We thank Bill for the north-south and east-west components, respectively. Strange and Will Prescott for supervising the collection of high- Short-term precision in the vertical is length independent, quality GPS data in Cahfornia. Tracking data were provided by GIGNET. We thank Jerry Mader, Miranda Chin, and Linda with a mean value of 17 mm. Horizontal precision deter- Nussear for helping us acquire these data. Additional data and re- mined over several years, where we have included recent ceiverswere provided by JPL, CIGNET, DMA, PMTC, and the precisionestimates from the USGS [Daviset al., 1989],has GeodeticSquadron of Canada. Logistical(James Stowell) and a constant bias of 5 mm, with a length dependenceof I and archival(Judah Levine) supportwas provided by UNAVCO. One of the authors (K.M.L.) benefittedfrom numerousconversations 3 partsin 10s for the north-southand east-west components, with Jim Davis, Geoff Blewitt, Will Prescott, and Steve Lichten. respectively. These measurements were made when the GPS K.M.L. would also like to thank Mark Murray, Frank Webb, Kurt constellation was preferentially Migned north-south. Pre- Feigl, Jeff Freymueller, Jerry Svarc, and Shawn Larsen for helpful sumably, the precision of future GPS measurements will discussionson GPS data analysis techniques. Computing facili- ties and the GIPSY software were provided by the Jet Propulsion show less dependence on the direction of the interstation Laboratory. We particularly thank Tom Yunck and Tim Dixon vector. Vertical measurements are much less precise than and their groups for supporting this work. Written reviews by Jim horizontalmeasurements, 11.7 mm -4-13 parts in 10s. Davis, Bill Strange, Steve Lichten, and George Born improved the Accuracy(defined by agreementof horizontalcomponents quality and scope of this paper. The data collection was funded with thosefound from VLBI) is 5-30 mm for baselinesfrom (at UCSD) by NSF EAR-8618165. This researchwas supported by a NASA Graduate Student Research Fellowship awarded to 200 to 430 km long. The pattern of these discrepanciesis K.M.L. at Scripps Institution of Oceanography. The writing and consistent with a survey discrepancy at two VLBI sites in publication were completed at the Colorado Center for Astrody- California, Vandenberg and OVRO. For interstation vectors namics Research and supported by ONR N0001490J2010. LARSONAND AGNEW: GLOBAL POSITIONINGSYSTEM PRECISIONAND ACCUI•CY 16,565

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