Author name used in this publication: 宁津生Author name used in this publication: 罗志才Author name used in this publication: 杨沾吉Author name used in this publication: 陈永奇Author name used in this publication: 张天纪Title in Traditional Chinese: 深圳市1km高分辨率厘米級高精度大地水準面的確定Journal title in Traditional Chinese: 測繪通報2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Chen, YQ

Luo, ZC

Ning, JS

Yang, ZJ

Zhang, TJ

PolyU Institutional Repository

? 32 ?  ? 2 ? ?  ?  ?  ? Vol. 32, No. 2 2003 ? 5 ? ACTA GEODAET ICA et CARTOGRAPHICA SINICA May, 2003  ????: 10011595( 2003) 02010206 ?????: P223+ . 0     ?????: A??? 1 km??????????????????宁津生1,罗志才1, 3,杨沾吉2,陈永奇3,张天纪2( 1. ???? ???????????????????, ?? ?? 430079; 2. ????????????????,?? ?? 518028; 3. ?????? ???????????,??)Determination of Shenzhen Geoid with 1 km Resolution andCentimeter AccuracyNING Jinsheng1, LU O Zhicai1, 3, YANG Zhanji2, CHEN Yongqi3, ZHANG T ianji2( 1. T he K ey Laboratory of Geospace Environment and Geodesy , M inistr y of Education, Wuhan Univer sity ,Wuhan 430079, China; 2. Land Planning Depar tment of Shenzhen , Shenzhen 518028, China; 3. Depar tment of Land Sur veying and GeoI nf ormatics , T he H ong K ong Polytechnic University , Hong K ong, China)Abstract: The geoid of Shenzhen with onekilometer resolution, has been constructed with remover estor e technique, using 65 GPS/ leveling data wit h accuracy better than 2 cm, 5 213 discrete g ravity data, dig ital terrain modelw ith 100 m resolutions and g lobal earth s g ravity field model WDM94. The modeled geoid heights were comparedw ith the observ ed ones derived from 29 GPS/ leveling data that not applied to the construction of Shenzhen geoid.T he test results show that t he standard deviation of the differences is  1. 4 cm.Key words: geo id; gravity ; GPS/ leveling ; earth s gr av ity field model; digital terrain model?  ?: 利用 65个精度优于2 cm的 GPS 水准数据?5 213个实测重力点数据?100 m 分辨率的数字地形模型和WDM94地球重力场模型,采用移去恢复技术计算了深圳市 1 km 分辨率的大地水准面模型?将该模型大地水准面高与由 29 个 GPS 水准得到的大地水准面高进行比较,其差值的标准差为  1. 4 cm?  ????: 20020928; ????: 20030128????:???????????????;???????( RGC)????( B. 34. 37. Q328)????:???( 1932 ) ,?,?????,??,???????,?????????????????:大地水准面;重力; GPS水准;地球重力场模型; 数字地形模型1  引  言???????????????????????????????????????????????????????????,???????????????????????????????????????????????,???????????? 2000???????? 1 km ????????????,??????:????????, ????8 km ? 60 km, ???? 79 km ? 179 km,??????????????????????,??????????????????????????,??????????????????????????????????? 8???? 2001??????????? GPS?????1 km????????????????????????????????????????????, ???????????????????????,??????????(???????????)??? GPS?????????????????2  数据资料及其处理2. 1  ?????????????????: ( 1) ?? Lacoste &Romberg G? D??????????????3 608??????, ?????1 km,?????????????? 0. 1 mGal; ( 2)?? Lacoste & Romberg S????????? 1 262?????????, ?????? 1 km, ????1. 6 mGal; ( 3)?????????????? 298???????? 45???????,??????? 2 km ? 2 km ? 4km?? 1??? 5 213??????????? 1  ??????????????Fig . 1 Distribution of discrete grav ity po ints over Shenzhen and its surrounding area??? Stokes??,???????????????????, ???????????1956???????????????, ?gFA = g- + FA (1)??, g ????????; ?????; FA?????,??= 978 032. 68(1+ 0. 005 302 4sin2 B-0. 000 005 8sin2 2B) (2)FA = 0. 308 6(1+ 0. 000 7cos 2B) h-0. 7210- 7h2 (3)??, B ??WGS84 ??????????; h???????????????????(1)??????????????,?C= - 0. 086 1h (4)2. 2  GPS????????????????????????,???? 73????? GPS ?????,?????? GPS ??? 14 ?, ??????10 km,?????????????????????????????????????? 5??(???????????????????)?????????????, ??????GPS?????? GPS????????( GPS??)???????N = H - h (5)??, ??? H ??? WGS84 ??, ????ITRF931 996. 365; ??? h ??? 1956 ??????????????????????,???????????????? 2 cm?? 2??? GPS ?????????? 2  ???? 65???? GPS ??????F ig. 2  Distr ibution of 65 high quality GPS/ leveling stations in Shenzhen2. 3  ??????( DTM)????????????????????????,????????????????????,??,?????? 11???????????????????? 100 m ???? DTM ????? 100 m ???? DT M, ???????????????100 m ?DTM ,?103? 2 ?        ????: ??? 1 km ??????????????????DTM ??????: ??????????- 1 km? 69 km,???? 70 km ? 190 km???????? 969. 1 m,????- 137. 5 m, ????? 57. 2 m?2. 4  ???????????????????????????????, ????????????????????????????EGM96[ 1]??????????????? ( 360 ?) ????,WDM94[ 2]???????????????360????????,? GPM98CR[ 3]? 720????????,??,????????????,???????????? GPS ?????? 3?????????????????????, ????????????WDM94??? EGM96? GPM98CR,????WDM94??????????????????????[ 4]?3  大地水准面的计算3. 1  ???????????????????????????? DTM ??????????????????,?????????????????,???????????, ??, ??????????????, ?[ 5- 9, 12] N ( P, P) = N GM ( P, P )+ N RES( P, P )+N T ( P, P) (6)??, NGM?? WDM94 ???????? 360???????,?[ 10]N GM =GMrnmaxn= 2(ar)n nm= 0( C nm cos m+Snmsin m) Pnm( sin ) (7)??, GM ???????; ?????????; a ?????????; , ? r ?????????????????; Cnm? S nm?????????; Pnm ( sin )???????? Legendre??; n max= 360?NT ? DTM ?????,?????[ 11]N T ( P , P )= - G h2P - G6Eh3- h3Pr3 dx dy +3G40Eh5- h2Pr5 dx dy+  (8)??, h ?hP ??????????????N RES????????,????????Stokes??????,?[ 10]N RES( P , P )= R4Eg( , ) S ( P, P, , )cos dd (9)??, S ( P , P, , )? Stokes???, g( , )???????,??????g = gFA - gGM+ T C (10)??, gFA?????????; gGM????????????????; ???? TC ?????[ 10, 12]T C( i , j )= - GM Ehxyhij( x , y , z ) ( hij - z )r3( x i- x , yj - y , h ij - z )dx dydz (11)??, GM ???????; ( x , y , z )?????????; h ij????( x i , y i )???; E ??????; r ( x , y , z )= x 2+ y 2+ z 2?Stokes??????????????, ???????????????????,????????????? 1DFFT ????, ??????[ 12~ 14] N RES( P, P) = R4 Nn = 0F- 1{ F{g( n)cos n} F { S ( P , n ) , } }(12)??????? DTM ?????????????????, ??????? 100 m ????DTM ? 1 km ?????????????3. 2  ?????????,??????????? 1 km ??????????????? 1 km ????????????? 65? GPS???????????,?????????????,? 1????????????????, ???????? GPS????????????????,?????????????????????,?[ 5, 8] N obs( x , y )= N G ( x , y )+ a0+ a1 x + a2y +a3 xy+ a4 x2+ a5y2+  (13)??, a i ( i= 0, 1, 2, 3, )?????; x ? y ???????; N obs? N G ??????????????????????????????104 ?  ?  ?  ?                   ? 32 ????(13)??????,????????????????, ???( 13)??? a0, a1, a2,a3 ? a5 ??????????????????????????????????, ???????????????????? GPS????,?????????????? GPS????, ???????????????????????????, ?? 1 km ?????????????, ????????????????????????? 1 km ????????????,? 3????????????,??????????????????, ?????????????? 4. 5 m, ??????????????????????????????N ( i , j )= nk= 1N ( k , k)( 1r k)m/ nk= 1(1r k)m,  r k 0N ( k , k)         ,  r k= 0(14)??, i , j ????????; r k???????????; m ?????,??????? 1 ?????????? GPS??????????????????Tab. 1  Statistics of the differences between gravimetricgeoid heights and those from GPS/ leveling m??? ??? ??? ??? ???0. 955 0. 303 0. 529 0. 539  0. 107? 3  ??? 1 km ????????????F ig. 3 Combined geoid of Shenzhen w ith 1 km g rid4  大地水准面的外部检核?????? 1 km ????????????????,?????????? GPS B????????????????? 29? GPS???,????? 4?????????,???????????? 2 cm ,?????? 1 km???????????????? 1 km ??????????? 29?GPS????????????, ?????????,? 2?? 3 ????????????????????????????????????, ??? 1 km ???????????????????(???)???  0. 014 m? 0. 019 m, ?????????? 1  10- 6 D????????? ( CJJ 899)??????????????, ??? 3?????, ???1 km?????????????????????????? 4 29 ? GPS ????????Fig. 4 Distribution of 29 GPS/ leveling check points? 2 ?????????? GPS??????????????????Tab. 2 Statistics of the differences between modeled geoidheights and those from GPS/ leveling m??? ??? ??? ??? ???0. 026 - 0. 022 - 0. 001 0. 014  0. 0145  结论与建议???? 65???? GPS ?????5 213?????????100 m ??????????? WDM94???????, ?????????????? 1 km ??????????????????, ??? 1 km ????????????????????(???)???105? 2 ?        ????: ??? 1 km ??????????????????? 3  1 km??????????????Tab. 3 Relative accuracy of geoid height diff erences????/ km???/ m???/ m???/ m???/ m???/ m????????( 1 10- 6 D )12 LL( 1  10- 6 D)20 LL(1  10- 6 D)0~ 5 0. 031 - 0. 010 0. 008 0. 017  0. 015 5 3. 57 7. 59 12. 655~ 10 0. 048 - 0. 038 0. 003 0. 019  0. 019 47 2. 45 4. 38 7. 3010~ 15 0. 035 - 0. 039 0. 005 0. 019  0. 019 54 1. 51 3. 39 5. 6615~ 20 0. 042 - 0. 044 0. 000 0. 019  0. 019 60 1. 10 2. 87 4. 7820~ 25 0. 039 - 0. 036 0. 002 0. 018  0. 018 55 0. 81 2. 53 4. 2225~ 30 0. 045 - 0. 042 0. 003 0. 018  0. 018 49 0. 66 2. 29 3. 8130~ 35 0. 030 - 0. 046 - 0. 005  0. 019  0. 018 43 0. 58 2. 11 3. 5135~ 40 0. 037 - 0. 039 0. 002 0. 020  0. 020 31 0. 53 1. 96 3. 2740~ 45 0. 034 - 0. 022 0. 009 0. 017  0. 014 25 0. 39 1. 84 3. 0745~ 50 0. 029 - 0. 022 0. 001 0. 015  0. 015 16 0. 33 1. 74 2. 90> 50 0. 043 - 0. 038 0. 012 0. 026  0. 024 21 0. 49 1. 66 2. 76???? 0. 048 - 0. 046 0. 003 0. 019  0. 019 406 0. 76 ???????????? 0. 014 m?  0. 019 m ,??????????1  10- 6 D????????? GPS????????????????????, ?????????????????????(?????????) ,?????????????????????, ?????? GPS ???????????????????,?????? 2 km ?????????(??????)?????? 2 km ????????,?????????????????????????  0. 019 m ?  0. 026 m,?????? 1 km ????????????? 2 km ???????????, ????????????????,???????????????, ?????????????????????, ???????? GPS ????????????????????, ? GPS????????????????????????,??????????????参考文献:[ 1]  PAVLIS N K . EGM96: The NASA GSFC and NIMA Joint Geopotent ial Model[ R ] . [ s. l. ] : [ s. n. ] ,1996.[ 2]  NING Jinsheng , LI Jiancheng, CHAO DingBo, etal . The Research on the Earth s Grav ity F ield ModelWDM94 Complete to Degree 360 [ J ] . Journal ofWuhan Technical University of Surv ey ing and Mapping , 1994, 19( 4) : 283291. ( in Chinese)[ 3]  WENZEL G. U ltr a High Degree Geopotential ModelsGPM98A, GPM98B and GPM98C to Degree 1800[ R] . [ s. l. ] : [ s. n. ] , 1998.[ 4]  LUO Zhicai, CHEN Yongqi. Evaluation of Geopotential Models EGM96, WDM94 and GPM98CR inHong Kong and Shenzhen [ J] . Journal of GeospatialEng ineering, 2002, 4( 1) : 2130.[ 5]  LUO Zhicai, CHEN Yongqi. Precise Determinationof Hong Kong Geo id Using Heterogeneous Data [ A ] .Pr oceeding of F IG XXII International Congr ess [ C] .Washington, D C: [ s. n. ] , 2002.[ 6]  MORITZ H. Local Geoid Determination in Mountainous Areas[ R ] . Columbus: The Ohio State Univ ersity,1983.[ 7]  L I Jiancheng . The Spectral Methods in PhysicalGeodesy[ D] . Wuhan: Wuhan Technical University ofSurveying and Mapping , 1993. ( in Chinese)[ 8]  YANG Zhanji. Precise Determination of Local Geoidand I ts Geophysical Interpretation[ D ] . Hong Kong:The Hong Kong Po lytechnic University, 1999.[ 9]  SIDERIS M G, FORSBERG R. Review of Geoid Prediction Methods in Mountainous Reg ions[ A ] . Determination of the Geoid, Pr esent and Futur e[ C] . NewYork: SpringerVerlag , 1990.[ 10]  HEISKANEN W A, MORITZ H. Physical Geodesy[ M ] . Graz: Institut e of Physical Geodesy, TechnicalUniversit y, 1967.106 ?  ?  ?  ?                   ? 32 ?[ 11]  WICH IENCHAROEN C. The Indirect Effects on theComputat ion of Geoid Undulations[ R ] . Columbus:The Ohio State Universit y, 1982.[ 12]  L I Yecai. Optimized Spectral Geoid Determination[ R] . [ s. l. ] : The University of Calg ar y, 1993.[ 13]  HAAGMANS R R N , de MIN E, van GELDERENM. Fast Evaluation of Convolution Integr als on theSphere Using 1DFFT , and a Comparison wit h Existing Methods for Stokes s Integral [ J] . ManuscrGeod, 1993, 18, 227241.[14]  SIDERIS M G, SHE Binbin. A New Highr esolution Geoid for Canada and Part of the U . S. by 1DFFT Method [ J] . 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深圳市1km高分辨率厘米级高精度大地水准面的确定

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