Nov 10, 1996 - between long-term and short-term precision to system- atic errors in ..... measured deformation in Long Valley caldera, eastern. California ...
JOURNALOF GEOPHYSICALRESEARCH,VOL. 101,NO. Bll, PAGES25,547-25,552, NOVEMBER10, 1996
Observed discrepancybetweenGeodoliteand GPS distancemeasurements J. C. Savage,M. Lisowski,andW. H. Prescott U.S. GeologicalSurvey,Menlo Park, California
Abstract.
Comparisonof contemporaneous measurementsof 84 distancesin the
rangeof 10 to 50 km by both GlobalPositioningSystem(GPS) and Geodolite (an electro-optical dista.nce-mea, suringinstrument)indicatesthat the Geodolite measurementsare systematicallylongerby 0.283 :l: 0.100 parts per million of the measured distance. Quoted uncertainty is 1 standard deviation. This amounts
to 11.3-I-4.0 mm at 40 kin, whichis near the maximumGeodoliterange. The systematicdifferenceis within the random uncertaintyof an individual GPSGeodolitecomparison a,nd•vasdetectedonly from an analysisof a large number (84) of suchcomparisons. The sourceof the systematicdifferencehas not been identified.
Introduction
Prescott[1973]. We will discuss SOllieof the data re-
The U.S. GeologicalSurvey changedproceduresfor measuring tectonic deformation in about 1987, and comparisonsof measurementsmade before and after that date may involvean offset. From 1971 to 1987,deformationwas inferredfrom changesin distancesmeasuredwith a Geodolite,a preciseelectro-opticaldistance-
measuring instrument[Savage andPrescott, 1973].The reft'activitycorrectionsfor thesemeasurements werededucedfrom endpoint pressuremeasurementsand temperature and humidity profilesmeasuredfrom a sinall aircraftflyingalongthe lineof sightat the time of ranging. After 1987, deformationwas generallydeduced from changesin geodeticpositionsmeasuredby the
duction proceduresin more detail later. Two different
Geodolites,both of the salliedesign,wereusedin the surveysreported here. Side-by-sidecomparisonof the two instrulnentsh• not revealedany systematicdifferencein the measurements.The most likely source of systematicerror in the Geodolitesurveysis in the measurementof the reft'activitycorrection. The GPS measurements are more complicatedbecausethe technologyevolvedrapidly over the years 1987-1994
when the lneasurements were made.
Al-
thoughall receiversin any singlesurveywere of the same model, two different modelsof GPS receiverswere
used.In the earliestsurveys(Hebgen,Montana,in 1987 and Farallon,California,in 1988),TexasInstruments GlobalPositioning System(GPS) [Daviset al., 1989]. TI-4100 receiverswere used,but the subsequent surEither measuringsystemby itself is adequateto mea- veysusedAshtechLM-XII codelessreceivers.All GPS sure tectonic deformation. tIowever, a problemmay surveyswere reduced with Berneseversion 3 software. arise when GPS is used to extend the record of deformation in a network that had earlier been monitored
by Geodolite:a systematicbias in either systemwould produce an apparent offset in the deformation record at the time of the changefi'omGeodoliteto GPS measurements.To detect whetherthere is a systematicbias between GPS and Geodolite distance measurements, we have compared84 contemporaneous measurements of distance by both Geodolite and GPS. We conclude that there is a systematicbias betweenmeasurements of the two systems,with the Geodolitedistancebeing 0.2834- 0.100 ppm longerthan the GPS measurement. The proceduresused in making and reducingthe Geodolitemeasurements weredescribed by Savageand
The proceduresused in GPS observationsand data re-
ductionarethosedescribed by Daviset al. [1989].The critical details are as follows: GPS stations were occu-
pied continuouslyfor at least 6 hours. Satellite orbits were calculated from data from a network of fiducial
trackingstationsin NorthAmericaandItawaiioperated as part of the CooperativeInternational GPS Network
(CIGNET). Data wereanalyzeddownto 15* elevation usinga mappingfunction;the zenith delayin the troposphericcorrection was solved for at each station as part of the reduction.
We distinguishbetweenthree typesof errors. Randomsurveyerror includesall errorsthat are not systematic. Errors in centeringall instrumentover the stationmonumentwouldbe an exampleof randomer-
aNow at HaxvaiianVolcanoObservatory,Hawaii National ror. Systematicsurveyerror includesall errorsthat are
Park.
This paper is not subject to U.S. copyright. Published in 1996 by the American Geophysical Union. Paper number 96JB02288.
systematicwithin onesurveybut onlyrandomlyrelated to those in a subsequentsurveyseverallnonthslater. An error in calibratinga pressuresensorin a Geodolite surveyor an error in satellite orbits in a GPS survey wouldbe an exampleof systematicsurveyerror. Fi-
25,547
25,548
SAVAGE ET AL'
GEODOLITE-GPS
na.lly,bias includesall systematicerrorsnot anticipated in designingthe measuringsystemor not properlycorrected for in the data reduction. Tha.t is, bias is a.fundamentalerror reflectingan incompleteunderstanding of the measuringsystem. Our interestin this paper is in detectingbias by compa. ring two differentmeasuring systems.
The precisionof the Geodolite measurementshas
DISCREPANCY
systematicsurveyerror. That systematicsurveyerror occursis convincinglydemonstratedwhere GPS dis-
tancesare measureddaily oversevera.1 yea.rs[Dragerr and Hyndman.,1995;King et al., 1995]. There coherent, intermediate-term (weeksor months)fluctuations in the distances are observed.
Equation(2) probablyoverestimates the errorat relativelyshortdistances (L < 10 km). Both the iono-
beendiscussed by Savageet al. [1986]. The measure- sphereand tropospherecorrectionsfor two receiversa ment precisionis thought to be describedby a norma.1 shortdistanceapart are highlycorrelated,and the cordistribution with zero mean and standard deviation rectionscancelout in differencing. As the distancebe-
O'- (a2q-b'*2)•/2 ,
(1)
tween receiversis increased,the correlationsdecrease
and commonmoderejectionno longerapplies. Thus the ionosphereand troposphereerrorsincreasewith reb - 0.2 x 10-6 (dimensionless). This errorcanbe re- ceiverseparationout to somecorrelationdistancecharsolvedinto random and systema. tic components,both acteristicof the troposphere-ionosphere combination. of which a.re describedby standard deviationsof the Beyondthat separationthe correctionsat the receivers form (1). For the ra.ndom component, a - 3 mm and areuncorrelated andthe errorbecomes almostindepenwhere L is the distance measured, a -
3 ram, and
b = 0.14 x 10-6, and for the systematic component,dentof distance.Thusthe estimateof uncertainty (2) a = 0.5 mm and b - 0.14 x 10-6 . The systcma.ticis probablytoo largefor L < 10 km.
componentis principally due to imperfect calibration of the probesused to measurepressure,temperature, and humidity for the reft'activity correction. Because the meteorologica. l probesare replacedor recalibra.ted betweensurveys,the systematiccomponentis systematic only within a.singlesurvey;it is only ra.ndomlyrelated to a.systematicerror in a subsequentsurvey.That is, the error is what we have calledsystematicsurvey error in the precedingparagraph. Finally, becausethe Geodolitemeasurementsha.vebeen comparedto absolute measurements (i.e., taped distances)only at short
Estimates of the standa.rd deviations of the random
and systematicsurveyerrorsfollow immediatelyfrom the estimatesof short-term and long-term precision
[Daviset al., 1989,p. 13,643].The short-term precision is taken to representrandom error, and thus the stan-
darddeviation of therandomerroris s (equation (2)). That estimate of random error does not allow for mon-
umentinstability. The long-termprecisionis a combi-
nation(squareroot of the sumof the squares)of the ra.ndomerror and the systematicsurveyerror. Given that the standarddeviationfor the long-termprecision
ranges(< 15 m), theremay be an undetected biasin
is 2s, one finds that the standard deviation asociated
the measurement.
withthesystematic survey erroris(4s•-s•) •/"'= 3•/2s.
The precisionof GPS measurementshas been dis-
cussed by Blewtit,[1993],whoconcludes that a.tranges Data
shorter tha.n about 400 km the precisionin distance measurementis severalmillimeters. Larson and Agnew
To compa.reGPS and Geodolitemeasurements,distances betweenpairs of geodeticmonumentsin a tri[1991]differentiate between theshort-term (1 dayto the lateration network were measuredby both GPS and next) andlong-term(yearto year)precision.Theyfind Geodolite within a period of about i week. The netthat short-termprecisionis describedby a standarddeworksfor whichsuchdata are availableare Hebgen, viation
s = 2 mm q-10-SL,
(2) Montana [Savageet al., 1993]; Fairweather,Alaska.
whereasthe standarddeviationthat describes the longterm precisionis about twiceas large. The largerstandard deviationfor the long-termprecisioncouldbe due simplyto monumentinstability[Johnsonand Agnew, 1995]but morelikelyimpliesthat someerrorsare systematic over the durationof singlesurveys.The short-
[Lisowskiet al., 1987];Mammoth,easternCalifornia [Savage, 1988];Shoshone, Nevada[Savage et al., 1994]; LomaPrieta, California[Savageand Lisowski,1995];
and Farallon,Ca.lifornia(a networkextendingfromthe California coast near San Francisco to the Farallon Is-
lands,about 35 km offshore,surveyedin both 1988and 1990). The distancemeasuredby Geodoliteminusthat term precisionis associatedwith random errorsin satelmeasuredby GPS is plotted as a function of distance lite orbits, satellite and receiverclockcorrections,ionofor ea.ch line in eachnetworkin Figure 1. sphereand tropospheredela.ys,and in positioningof the We postulatethat the systematicbiasbetweenGeodoGPS antennaoverthe station monument[Larsonand lite and GPS measurements of distanceL canbe repreAgnew,1991]. Blewill [1993]emphasizes the imporsentedby the linear relation tanceof tropospherevaria.bilityin the short-termpreci-
sion.LarsonandAgnew[1991]attributethe difference betweenlong-termand short-termprecisionto systematic errors in satellite orbits, unresolvedphase ambiguities, systematicerrors in modelingthe ionosphere and troposphere,and blunders,all peculiar to a particular survey. That is, the differenceis attributed to
AL - L•od - Laps - a +/•L.
(3)
Comparisonof short-range(< 15 m) Geodolitea.nd GPS measurements with directly taped distancesindicatesthat c•= 0.0 4- 1.0 mm. We then estimate/• from the data in Figure 1.
SAVAGE ET AL.: GEODOLITE-GPS DISCREPANCY
Hebgen
40
root of the sum of the squares)of the standarddevia-
Fairweather
40
tionof theslopeandthestandarddeviation(0.14ppm) of the systematicsurveyerror for the Geodolite(Table 1). That is, eachslopeestimateis contaminated by
2O
20
the Geodolitesystematicsurveyerror for that survey.
0
o
Notice that the standard deviations for all seven esti-20
-20 0
25,549
10
20
30
40
mates of/? are about equal. Thus the best estimate of
50
/?is the meanof the sevenestimates (/?- 0.2834.0.100 ppm), and the scatterof thoseestimatesabout that mean suggestsa standard deviation of an individual ob-
servationof about0.246ppm, onlyslightlylargerthan theformallyestimated standa. rd deviations (lastcolumn in Table 1). 0
10
20
30
40
50
0
40
40
20
20
0
0
-20
10
20
30
40
50
were rejected, the discrepancywould be 0.225 + 0.093 ppm, which is significantat the 94% confidencelevel. Thusthe observedGeodolite-GPSdiscrepancy appears
-20
0
10
20
30
40
50
Student's t test indicates that the observed Geodolite-
GPS discrepancy (0.283-4-0.100 ppm) is significant (greaterthan 0) at the 97% confidence level. Even if the Farallon1990discrepancy (the largestvalueof
0
10
20 Distance,
30
40
50
km
to be rea.1.
Notice that the a priori error estimatesin the Geodolite and GPS distance measurenmnts are consistent with
=
the scatterof the observations. For example,in Table 1 the two estima, tesof the standarddeviationof the slope, one derived from a priori estimatesof random error in
20
O -20 0
10
20
30
40
50
Distance, km
GeodoliteandGPSsurveys andtheother(in parentheses)fromthescatterof the data aboutthelinearfits, are consistent. Moreover, the a priori standard deviations
(la.stcolumnof Table 1) of the individualestimatesof Figure 1. Plots of the Geodolite-measured distance /? a.re in reasonableagreementwith the standard delessthe Global PositioningSystem-measureddistance for lines in sevennetworks. The error bars represent1 viation (0.246ppm) estimatedfrom the scatterof the standarddeviation(randomerror only) on eitherside estimatesof/? about its mean. This consistencyindiof the plotted point. The straightlinesare linear fits to cates that the a priori estimatesof both the random the data, subject to the constraintthat the zero distance and systematicsurveyerrors are reasonable.
interceptbe 0.0 -4-4.0 mm (standarddeviation). Discussion
Recall that the data for each network in Figure 1 are contaminatedwith systematicsurvey errors from both the Geodoliteand GPS measuringsystems. For
The precedinganalysisde]nonstratesa 0.2834-0.100 ppm bias between measure]•.,:•ts of the same distance by Geodolite and GPS, the Gcodolite measurementbe-
the ranges(10 to 50 kin) involvedin the Geodolite- ing the longer. Becausethe G PS measurementshave GPS comparisonsthe Geodolitesystematicsurveyerror beenshownto be generallyconsistent with very long is approximately 0.0 4- bL, where b - 0.14 ppm and baselineinterferometry(VLBI) measurements on a the GPS systematicsurveyerror is approximately0.0 4- globalscale[Blewlitet al., 1992],GPS andVLBI scales 4.0 mm (quoteduncertainties arestandarddeviations). appearto be identical.Nevertheless, recentdata [GipThe formervaluefollowsfrom (1) with a = 0.5 1rimand son, 1996, p. 54] demonstrateVLBI-GPS agreement b - 0.!4 ppm, and the latter followsfrom the standard
only at the level of 6 mm rms. Tha,t limited precisionis due in part to the difficultyin locatingthe phasecenOne can estimate/3in (3) from the slopesof linear ter of the VLBI antennapreciselywith respectto the fits in Figure1 to the data for eachnetwork.To take ac- GPS monument. Moreover,procedures(e.g., depencount of the systematicsurveyerror in GPS, a pseudo- denceuponfiducialnetworks,useof ]nappingfunctions observation,AL - 0.0 =k4.0 mm at L - 0, is included to calculatetropospheric delays)employed in analyzing
deviaton 3•/•s,wheres isgivenby(2).
in the data for ea.ch network[Sungand Jackson,1985, the olderGPS data.in our measurements (i.e., particupp. 25-26]. That is, the systematicerror in GPS data larly data before1992, whenInternational GPS Service could shift all data up or down by that amount in the orbitsbecameavailable)]nay introducesystematicloplot for any network. The linear fit then givesa slope cal errorsin surveys.Nevertheless, it seemsmorelikely and its standarddevia,tion for eachnetwork(Table1). that a discrepancybetween GPS and Geodolite meaEach slope is an estimate of/?, but the standard devi- surements of the magnitudeobservedoriginatedin the ation of that estimateof/3 is the combination(square Geodolite,rather than GPS, measurements.
25,550
SAVAGE ET AL.: GEODOLITE-GPS DISCREPANCY
Table 1. Slopesof WeightedLinear Fits in Figure 1 Network
Slope,
Standard Deviation Slope,a
ppm
Hebgen
ppm
-0.171
Standard Deviation •,a ppm
0.182(0.154)
0.230(0.208)
Fairweather
0.211
0.172(0.156)
0.222(0.210)
Mammoth
0.348
0.163(0.154)
0.215(0.208)
Shoshone
0.250
0.186(0.160)
0.233(0.213)
Farallon1988
0.280
0.135(0.110)
0.194(0.178)
Farallon1990
0.636
0.139(0.132)
0.197(0.192)
LomaPx'ieta
0.430
0.120(0.103)
0.184(0.174)
aEstimates of standard deviations are the a priori estimates, whereasthose
in parenthesesare derived from the scatter of the data in Figure 1 about the linear fit.
The reduction of the Geodolite data involves correct-
Frictional heating of the thermistorused to measure air temperature amountsto about 1øC at that speed. The temperature indicatedby a thermistor is corrected as follows:wind tunnelexperiments [Hilton,1938]indicate that the temperature on a cylindrical probe in clude a correction to the humidity factor found more an airstreamis greaterthan the air temperatureby an recentlyby Birch and Downs[1988]. That correction amount proportionalto the squareof the air velocity: increasesthe Owensreft'activity by
ing for the refractivityof the air. The dependence of refractivity upon pressure,temperatureand humidity usedin past Geodolitereductionswastakenfrom Owens [1967].However,the reductions usedin this paperin-
AT = 7v2
An = h(3.7+0.23t+7.1x 10-3t 2
(5)
where h is the relative humidity in percent and t is the
where v is the correctedairspeed.We have determined 7 by flying along the same line a.t differentairspeeds, allowingfor a linear drift with time of the temperature along the line. We have repeated this calibration six
temperature in degrees Celsius.For 100%humiditythis correctionamountsto a reductionin line lengthof 0.04
ent weather conditionsand find a weightedmean value
+2.2 x 10-4ta) x 10-•ø
(4)
ppm at 0øC, 0.13 ppm at 20øC, and 0.38 ppm at 40øC. The correctedrefractivity shouldthen be in error by no
times(Table 2) at differentlocationsand underdiffer-
7 = 2574-32øC/(km/s) •'. In the lasttwo determinations of 7 shownin Table 2 one passin each appeared
morethan 0.03 ppm [Birchand Downs,1988],which anomalous.If thosetwo passes (onein the calibration impliesthe sameuncertainty in distancemeasurement. Inaccuratemeasurement of air temperaturealongthe line appears to be a likely sourceof the GeodoliteGPS discrepancy.Ideally, air telnperatureshouldbe measured with a thermometer
that is at rest with re-
spectto the air, whereasour measurements are made froin an airplaneflyingat an airspeednear 220 km/hr.
of October 1, 1974, and the other in the calibration
of January 8, 1976) are omitted, the weightedmean
valuebecomes 7 = 2754- 28øC/(km/s) 2 The value 7 = 300øC/(km/s) •' usedin the data reduction was based on the first three calibrations
Table 2. Coefficient • in Equation(5) Date
Number
of Passes
oC (km/s)-•Nov. 12, 1972
6
332 _+38
March 24, 1973
5
339 _+57
March 20, 1974
in Table 2. That
value of 7 was checkedin early 1996 by measuringa 15-kmlongline repeatedly(6 passesat eachairspeed)
øC (km/s)-2
8
243 4. 49
April 4, 1924
12
1844-35
Oct. 1, 1974
6
492 4-284
330 -+ 38
Jan. 8, 1976
8
181 4-70
256 4- 46
* Here 'v was recomputedwith one passrejected.
SAVAGE ET AL.: GEODOLITE-GPS
at two different airspeeds,130 and 260 km/hr. The measurementsagreedwithin 0.9 4- 1.2 min. Another correctionin the Geodolitedata processing that is not completely satisfactoryis the reduction of distancemeasuredalongthe curvedlaser trajectory to the rectilinear
distance from monument
to monument.
The correctionis based upon approximatingthe laser trajectory by a circular arc of radius p in the vertical planecontainingthe two endpointmonulnents.The differencebetweenthe arc lengthL and lengthof the chord
joiningthe monuments is L3/(24 p2)for L 35 km. To avoidthis possibility,Geodolitelinesare generally kept to distancesL < 35 kin. However,longerlines
L3/(1176R2), whereR is the Earthradius,to correct for curvature
of the laser beam.
That
correction was
not includedin the originalreduction.(3) All lengths L shouldbe reducedby subtractingAn x L (whereAn (Farallonand LomaPrietanetworks)wererequiredin is givenby (4)) to accountfor the correctionproposed this study to accentuatethe Geodolite-GPSdifference. by BirchandDowns[1988]to the refractivityformulas for the We are particularly concernedabout the curvaturecor- of Owens[1967]. Noticethat the corrections new velocity of light and for curvature can be made given only the line lengthsfrom the USGS files. The lon Islands. There the laser trajectoriesgenerallyare Birch and Downs[1988]correctionto the refractivity only 100 or 200 m abovethe ocea. n surface. The ver- (4) requiresin additionthe temperatureand the relatical temperaturegradient set up by the combination tive humidity measuredalong the line, data which are of warm air over cold water causes the beam curvature availablein the line-lengthfilesfor mostlines. rection for the Farallon network, a network that ex-
tends from the California
coast to the offshore Faral-
to increase (K to decrease) [Bomford, 1971,Table1.1]. Thus the curvature correction may be underestimated for the long lines in the Farallon network. This would References cause/3to be overestimated,a possibleexplanationfor the large value of/3 measuredin 1990 in the Fara.llon Birch, K. P., and M. J. Downs,The resultsof a comparison
network(Farallon1990in Table 1).
between calculated
and measured value of the refractive
We have also investigatedthe possibility that the Geodolitemeasurementis perturbed by contamination from exhaustfroin the aircraft engine. Recall that a small airplaneis flown along the laser trajectory at the tinheof rangingto measureair temperatureand humidity. The probesare mountedon the front of the aircraft and do not sample the air behind the aircraft, which is contaminatedby engineexhaust.The laserbeam,however, doestraversethat contaminatedair. The exhaust
nologyfor geodynamicinvestigations1978-1992, in Con. tributionso• SpaceGeodesyto GeodynamicsTechnology, Geodyn. Set., vol. 25, edited by D. E. Smith and D. L. Turcotte,pp. 195-213, AGU, Washington,D.C., 1993. Blewitt, G., M. B. Heftin, F. H. Webb, U. J. Lindqwister,
both heats and moistens
Bornford,G., Geodesy,3rd ed., Oxford Univ. Press,New
the column
of air traversed
by the laser beam. Thus we underestimateboth the temperatureand humidity of the air and thereforeunderestimatethe line length. Accountingfor this effect would then increase,not decrease,the Geodolite-GPS discrepancy.However,the effectmust be very minor as can be seenby comparingthe massof the fuel burned in flying betweenstationswith the massof the column of air over which the exhaust is dispersed. The
secular increase of carbon
dioxide
in the at-
mosphere,which is thought to causeglobal warming, should be associated with a secular increase in refrac-
tivity. In the Geodolite data reduction the proportion of carbon dioxide in the air is taken to be 300 ppm
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M. Lisowski,Hawaiian Volcano Observatory,P.O. Box 51, Hawaii National Park, HI 96718.
W. H. Prescott and J. C. Savage (correspondingau-
thor), U.S. GeologicalSurvey, MS/977, 345 Middlefield Road, Menlo Park, CA 94025. (e-mail:jsavage@isdnml. wr.usgs.gov)
(ReceivedMarch 5, 1996;revisedJuly 3, 1996; 759-762, 1995. Savage,J. C., andW. H. Prescott,Precision of Geodolite acceptedJuly 11, 1996.)
