磁偏角与磁倾角的公式推导与运算

29320096JOURNALOFGEODESYANDGEODYNAMICSVo.l29No.3June,2009:1671-5942(2009)03-0088-04*王解先{1,2)李浩军1)1),2000922),200092,,,;;;;:P212:ACALCULATIONANDFORMULADEDUCTIONOFMAGNETICDECLINATIONANDGEOMAGNETICINCLINATIONWangJiexian1,2)andLiHaojun1)1)DepartmentofSurveyingandGeomatics,TongjiUniversity,Shanghai2000922)KeyLaboratoryofModernEngineeringSurveying,StateBureauofSurveyingandMapping,Shanghai200092AbstractMagneticdeclinationistheanglebetweenmagneticnorthandtruenorth,theanglewillchangewiththevariationoflatitude,longitudeandheigh.tTherelationbetweenmagneticmeridianazimuthandtrueazimuthisdiscussed,andthecalculationformulaofmagneticdeclinationandgeomagenticinclinationarededucedwhenthelatitude,longitudeandheightareknown.Atthesametime,themagneticdeclinationandgeomagenticinclinationinChinaarecalculated,andtheirvariationruleswiththevariationoflatitude,longitudeandheightareanalyzed.Keywords:magneticdeclination;geomagenticinclination;trueazimuth;geodeticcoordinate;sphericalharmonicfunction1前言,(),,,,,,;,,,2方位角*:2009-01-25:,,1963,,.E-mai:[e-mail]3:,:1),;2),;3)(),,,,:,,:=+=+(1)(1),,11Fig.1Relationbetweenmagneticmeridianazimuthandtrueazimuth3磁偏角的求解3.1,B,:O,OX,OY,OZB;BHB,;XHOX,;YHOY,;ZFOZ,;DHOX,,H;IB,,B23.2(IGRF),IGRF,2Fig.2Relationsamongallgeomagneticessentials[1-3]:V(r,,)=akk=0km=0(ar)n+1(gmkcosm+hmksinm)Pmk()(2),a,r,gmkhmk(),Pmk(),,=90-(),k[4-6]XYZ:X=kmaxk=0km=0(ar)nk+1(gmkcosm+hmksinm)dPmnk(cos)dY=kmaxk=0km=1msin(ar)nk+1(gmksinm-hmkcosm)Pmnk(cos)Z=-kmaxk=0km=1(nk+1)(ar)nk+1(gmkcosm+hmksinm)Pmnk(cos)(3)(IAGA)5(IG-RF),8[3]IGRFDGRF[6,7](DefiniteGeomagneticRe-ferenceField),5,1945,13,,DGRF(2),[8]:D=arctan(Y/X)(4),:I=arctan(Z/X2+y2)(5),DGRF,89294算例,(4)(73~135E,4~53N),2000(),1(5),212,,,,;,,(12030),(4~104m),31(:)Tab.1Varietyrelationofmagneticdeclinationtothechangeoflatitudeandlongitude(unit:)7080901001101201301405-3.575-3.116-1.763-0.2800.4720.5531.0202.56715-1.602-1.526-0.913-0.395-0.550-1.148-1.1650.098250.122-0.092-0.147-0.593-1.764-3.227-3.929-3.116352.5261.9371.011-0.653-3.095-5.618-7.075-6.694456.3435.1542.936-0.436-4.547-8.283-10.38010.1945512.18910.2196.2230.431-5.96111.115-13.67513.3672(:)Tab.2Relationofgeomagneticinclinationtothechangeoflatitudeandlongitude(unit:)7080901001101201301405-6.902-7.988-8.490-7.952-6.810-6.135-6.223-6.1181517.14816.20615.73015.98816.51616.45015.62614.9172537.57636.99536.71936.82136.87036.26134.92033.5083552.94252.79652.79852.87152.63851.70050.06248.2224564.18364.50964.82764.94864.55263.41661.64759.6675572.60373.37274.00574.22773.77472.58070.86469.0073Tab.3Geomagneticinclinationandmagneticdeclination(m)5203550658095110()-4.385-4.385-4.385-4.385-4.385-4.385-4.385-4.385()44.51644.51644.51644.51644.51644.51644.51644.5163,,5m110m,5结论,,,,,;,:1ChapmanSandBartelsJ.Geomagnetism[M].London:Ox-fordUniversityPress,1940.2LangelRA.TheMainfield[A].In:JacobsJA(ed).Geo-magnetism[C].London:AcademicPress,1978.3.[J].,2003,46(6):774-184.(下转第94页)9029:1)GM(1,1),,,,,2),GM(1,1),-3.36mm-1.12mm,,3)GM(1,1)GM(1,1),,GM(1,1),,;,,5结论,GM(1,1),GM(1,1),,GM(1,1),,,,,GM(1,1),,,,1,.[J].,1990(2):20-26.2,.GPS[J].,2002,22(2):61-67.3,,.[M].:,2003.4,.[J].,2003,23(4):21-27.5,GM[J].,1985,5(2):23-32.6,.[J].,2007,32(4):121-123.7,.[J].,2008,28(1):41-44.8.[J].,2002.11:17-24.9,,.[J].,1997,26(4):365-372.10.[J].,1992,2(1):45-50.11.[J].,1997,25(1):25-27.12,,.()[M].:,2004.(上接第90页)4,.[J].,2005,48(1):84-95.5,.[J].,2005,47(1):1003-1008.6.[J].,1993,36(6):753-763.7BarracloughDR.Internationalgemagneticreferencefield:Thefourthgeneration[J].Phys.EarthPlanet.int.,1987,48:279-292.8.[J].(),2007,6(6):88-91.94