外文翻译跨越式精确三角高程测量.docx

外文翻译跨越式精确三角高程测量.docx

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外文翻译跨越式精确三角高程测量

附录A外文翻译

PreciseHeightDeterminationUsingLeap-Frog

TrigonometricLeveling

AyhanCeylan1andOrhanBaykal2

Abstract:

Preciselevelinghasbeenusedforthedeterminationofaccurateheightsformanyyears.Theapplicationofthistechniqueisdifficult,timeconsuming,andexpensive,especiallyinroughterrain.Thesedifficultieshaveforcedresearcherstoexaminealternativemethodsofheightdetermination.Asaresultofmodernhigh-techinstrumentdevelopments,researchhasagainbeenfocusedonprecisiontrigonometricleveling.Inthisstudy,aleap-frogtrigonometricleveling（LFTL）isappliedwithdifferentsightdistancesonasampletestnetworkattheSelcukUniversityCampusinKonya,Turkey,inordertodeterminetheoptimumsightdistances.Theresultswerecomparedwithprecisegeometriclevelingintermsofprecision,cost,andfeasibility.Leap-frogtrigonometriclevelingforthesightdistanceS=150mresultedinastandarddeviationof±1.87mm/

andwithaproductionspeedof5.6km/day.

CEDatabasesubjectheadings:

Leveling;Height;Surveys.

Introduction

Thedevelopmentoftotalstationshasledtoaninvestigationofprecisetrigonometriclevelingasanalternatetechniquetoconventionalgeometricleveling（Kratzsch1978;RuegerandBrunner1981,1982;KuntzandSchmitt1986;Hirschetal.1990;Whalen1984;Chrzanowskietal.1985;KellieandYoung1987;Youngetal.1987;Haojian1990;Aksoyetal.1993）.Mostofthesepapersgivemorepracticalresults,ratherthantheoretical.

Inthisstudy,wetreatthesubjectmoretheoretically,withcurrentinstruments.Wealsodiscusstheoreticalaspectssuchaslimitsofthetechniques,errors,andaccuraciesinleap-frogtrigonometricleveling.

Slopedistancesandzenithanglesaremeasuredusingeitheraunidirectionalorareciprocalorleap-frogmethodoffieldoperationintrigonometricleveling.Bothofthetargetsinleap-frogtrigonometriclevelingcanalwaysbeplacedatthesameheightabovetheground.Thus,sightlengthsarenotlimitedbytheinclinationoftheterrain,andsystematicrefractionerrorsareexpectedtobecomerandombecausetheback-andforesightlinespassthroughthesameorsimilarlayersofair.Thenumberofsetupsperkilometercanbeminimizedbyextendingthesight

lengthstoafewhundredmeters.Thisreducestheaccumulationoferrorsduetoinstrumentsettlementthatisanothersignificantsourceofsystematicerror.

1AssistantProfessor,EngineeringandArchitectureFaculty,KonyaSelcukUniv.,42031Konya,Turkey.E-mail:

aceylan@selcuk.edu.tr

2Professor,CivilEngineeringFaculty,IstanbulTechnicalUniv.,80626Istanbul,Turkey.

Note.DiscussionopenuntilJanuary1,2007.Separatediscussionsmustbesubmittedforindividualpapers.Toextendtheclosingdatebyonemonth,awrittenrequestmustbefiledwiththeASCEManagingEditor.Themanuscriptforthispaperwassubmittedforreviewandpossible

publicationonAugust6,2003;approvedonAugust25,2005.

PrincipleofUnidirectionalTrigonometricLeveling

Trigonometriclevelingisthedeterminationofheightdifferencesbymeansofthemeasuredzenithanglesandtheslopedistance.Similartogeometricleveling,theheightdifferencebetweentwoturningpoints（benchmarks）iscomputedasthesumofseveralsingleheightdifferencesobtainedfromeachsettlement.

Themeasurementmodeloftheunidirectionaltrigonometricleveling（UDTL）isillustratedinFig.1.Thetotalstationissetupatonlyonepointandtheobservationsareperformedonlyinonedirection.

InFig.1,

=geodetic（ellipsoidal）zenithanglefrom

to

;

=observedzenithanglefrom

to

;

=modelerrorduetotherefractioneffect;Ƹij=modelerrorduetothedeviationoftheplumbline;Sij=slopedistancebetweenPiandPj;hiandhj=ellipsoidalheightsofPiandPj,respectively;Rm=meanradiusoftheearth（≈6,370km）and∆hij=heightdifferencefromPitoPj.

Theheightdifference∆hijisformulatedas

（1）

wherethefirsttermisthenominalheightdifference,thesecondtermisthesphericaleffectoftheearth,andthethirdtermisthetotaleffectduetothedeviationoftheplumblineandtheverticalrefraction（CoskunandBaykal2002）.

Thecoefficientofrefraction,kij,isdefinedastheratiobetweentherefractionangledZriandhalfofthecenterangle

（RuegerandBrunner1982）;i.e.

（2）

and

（3）

Thecenterangle,

canbecomputedas

（4）

If

isintroducedintoEq.（3）,themodelerrorduetotherefractioneffect,dZri

isobtainedasfollows:

（5）

TheheightdifferencebetweenthestationpointsPiandPjviaunidirectionalzenithangleobservationisobtainedfromEqs.

（1）and（5）

（6）

Inpractice,theeffectofdeviationofplumblineisverysmallbecausethezenithanglesobservedalongthesightlengthsarenotlongerthan500m.Thus,thesecondterminEq.（6）canbeignored（RuegerandBrunner1982）.Asaresult,theheightdifferencebetweenthestationpoints,PiandPj,iscomputedfromUDTLobservationsas

PrincipleofLeap-FrogTrigonometricLeveling

Observationofleap-frogtrigonometricleveling（LFTL）wasperformedinbackandforesightreadingatonesetupofthetotalstationbetweentwoturningpoints,thesamemethodusedingeometricleveling.ThemeasurementmodeloftheLFTLisshowninFig.2.

Fig.2.MeasurementmodelofLFTL

AccordingtoFig.2andEq.（7）,theheightdifferencebetweenthestationpoints,PiandPj,isobtainedfromLFTLobservationsas

Considering

wherethefirsttermisthenominalheightdifference,thesecondtermisthesphericaleffectoftheearth,thethirdtermistheeffectduetotheverticalrefraction,andthefourthtermisthetotalinfluenceofallotherrandomerrors,namely,sinkingoftargetrods,verticalityandcalibrationofrods,anduncertaintiesinthedeviationsofplumblines.Ifweusethefollowingassumptions:

thesecondterminEq.（9）willbezero.Asaresult,theheightdifferencebetweenthestationpoints,PiandPj,iscomputedas

ItisobviousthattheheightdifferenceobtainedfromEq.（11）isaffectedbythedifferenceintheactualrefractioncoefficientsandotherrandomerrorsintheleap-frogtrigonometricleveling（LFTL）.Therefractiontermrequiresfurtherinvestigation.TheuncertaintyintherefractiontermofEq.（11）canbeminimizedbymakingthelengthsoftheback-andforesightsequal.However,inequalitiesoftenexistbetweentherefractioncoefficientsofthebacksightandforesight,evenifthesedistancesareequal.Inanycase,themethodofLFTLwillmakethedifferenceinthecoefficientsofrefractiontolerablysmall.Foraspecialcase,themeancoefficientofrefractionkofalengthcanbecomputedfromreciprocalzenithangleobservations

TheaccuracyofLFTLcanbeobtainedbyapplyingthelawofvariancepropagationtoEq.（11）underthefollowingassumptions:

Afterpropagatingerrors,anexpressionforthevarianceinheightdifferencebetweenPiandPjcanbederivedas

Standarddeviationsofthedistances,thezenithangles,therefractioncoefficients,andotherrandomerrorsaredenotedby

respectively.Thevarianceofa1kmlevellineiscomputedas

Thecomputedstandarddeviationsofa1kmLFTLline,basedonstandarddeviationsof±1.0″,±2.0″,and±3.5mmforzenithanglesandslopedistances,respectively,aresummarizedinTable

1.Theuncertaintyinthecoefficientofrefractionistakenas±0.05and±0.10for（nonsimultaneous）reciprocalzenithangleobservations.Thevalueof

hasbeenarbitrarilyacceptedas±0.30mmfortotalinfluenceofallotherrandomerrors.

Table1.StandardDeviations_inmm_ofa1kmLFTLLinewithSightDistancesof100,150,200,and300mandAverageZenithAnglesof80,85,and90°

Applications

Thepreciseleveling（PL）andLFTLmeasurementswereperformedonalevelingnetworkwitheightpointsestablishedonhillyterrainattheCampusAreaofSelcukUniversityinKonya,Turkey（Fig.3）.

DesignandCalibrationofSurveyingInstruments

PLmeasurementswerecarriedoutbyameasurementteamofsixpeople（oneobserver,onerecorder,tworodmen,andtwoauxiliary）usingapreciselevelinginstrument（WildN3）equipped

withaparallelglassmicrometerandapairof3minvarrods（Wild）.

LFTLmeasurementswereperformedbyateamoffourpeopleusingapairoftargetrodsandatotalstation.Theaccuracyofzenithanglemeasurementwithsixseriesis±1″usingthetotalstationSokkiaSET2[telescopemagnification:

30x;minimumreading:

1″;accuracyofhorizontalandzenithanglemeasurement:

±2″;accuracyofdistancemeasurement:

±（3mm+2ppm·S）].Targetrodswereformedbytwoparts,abottomone,whichwasaninvarrodof2m,andatopone,whichwasanironbar1minlengthand2cmindiameter.Thesetwopartswereattachedtogether.Areflectorwasmountedontargetrodataheightof1.70mfromthebottominordertoimplementdistancemeasurementsandtwotargetplatesforverticalangleobservationsatlevelsof2.20and3.00m,respectively.Acircularspiritbubble（with10′precision）andatripodwereusedtoplumbthetargetrod（Fig.4）.

Severaltargetplateswithdifferentpatternsofvariousdimensionswereinvestigatedfortargetingaccuracyofsightdistancesof200and300m.AredandwhitecoloredcircletargetwaspreferredforLFTL.Ithasbeenproventhattheaccuracyofsingletargetingisbetterthan30″/M（M=telescopemagnification）inaverageatmosphericconditions（Chrzanowski1989）.Consequently,thetargetplateinFig.5ispreferred.

BecauseapairoftargetrodsisusedcommonlyinLFTL,theheightdifferencesbetweenthetargetplatesonbackwardandforwardrodsshouldbedeterminedwiththehighes