上地幔密度异常驱动小尺度对流及实验模型
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摘要
建立了由密度异常驱动上地幔小尺度对流的数学 物理模型, 发展了利用地震层析成像数据反演上地幔小尺度对流的基本理论和方法. 该模型建立在三维直角坐标系框架上, 假设地震层析成像所显示的地震波速度异常对应于上地幔物质密度异常, 而该密度异常反映了上地幔小尺度热对流系统的温度异常场. 模型首先将地震层析成像确定的地震波速度异常转换为密度异常, 并视其为对流的驱动力; 进而利用三维傅立叶变换, 在波数域内, 在给定的边界条件下, 求解控制流体行为的运动方程和连续性方程, 最后求得对流的流场. 为检验本研究提出的理论和方法的有效性, 本文使用了两个简单的实验模型: 热体和冷体模型; 俯冲断离( break off)板片模型, 计算了其驱动的地幔流场. 结果表明, 本文提供的理论和方法,可以直接应用于与区域岩石层构造动力学相关的上地幔小尺度对流的研究.
A mathematic physical convection model in upper mantle is established in this paper. This model is in a three dimensional frame. Assume that the density anomalies, which are mapped from the seismic tomography data, are responding to the temperature perturbation in the connective system. This model takes the density anomalies as the driving force for the mantle convection. We solve the basic equations with different boundary conditions in a domination of wave number by using the FFT arithmetic. In order to test the validity of our theory and method two simple models (higher lower density body and break off slab) are employed to calculate their flow patters in this paper. Results show that our method can be directly used to investigate the upper mantle convection patterns and its related problems of lithospheric dynamics.
A mathematic physical convection model in upper mantle is established in this paper. This model is in a three dimensional frame. Assume that the density anomalies, which are mapped from the seismic tomography data, are responding to the temperature perturbation in the connective system. This model takes the density anomalies as the driving force for the mantle convection. We solve the basic equations with different boundary conditions in a domination of wave number by using the FFT arithmetic. In order to test the validity of our theory and method two simple models (higher lower density body and break off slab) are employed to calculate their flow patters in this paper. Results show that our method can be directly used to investigate the upper mantle convection patterns and its related problems of lithospheric dynamics.
引文
傅容珊,常筱华,黄建华,等.1994a.区域重力异常和上地幔小尺度对流模型Ⅱ[J].地球物理学报,37(Supp):249~258
傅容珊,黄建华,刘文忠.1994b.区域重力异常和上地幔小尺度对流相关方程[J].地球物理学报,37(4):638~646
傅容珊,常筱华.1994.上地幔小尺度热对流及大陆岩石层动力学[A].见:陈运泰,阚荣举,滕吉文等编.中国地球物理学进展[M].北京:地震出版社,169~178
傅容珊,陈凌,黄建华,等.1995.全球地震层析地幔密度横向不均衡及大陆动力学[J].地球物理学进展,10(3):51~62
傅容珊,黄建华,徐耀民,等.1998.青藏高原天山地区岩石层构造运动的地幔动力学机制[J].地球物理学报,41(4):658~668
刘福田,曲克信,吴华,等.1989.中国大陆及其邻区的地震层析成像[J].地球物理学报,32(3):281~291
AndersonD L,SchreiberE,LiebermannR C, et al.1968.Some elastic constant data on minerals relevant to geophysics[J].RevGeophysSpacePhys,6:491~524
AndersonD L.1998.The scales of mantle convection[J].Tectonophysics,284:1~17
AtwaterT,SchlaterJ,SandwellD, et al.1993.Fracture zone traces across theN.PacificCretaceousQuietZone andtheir tectonic implications[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tec tonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,137~154
BaudryN,KroenkeL.1991.Intermediate wavelength(400~600 km),SouthPacific geoidal undulations:Their ralation ship of linear volcanic chains[J].EarthPlanetSciLett,102:430~443
CalcagnoP,CazenaveA.1993.Present and past regional ridge segmentation:Evidence in geoid data[J].GeophysResLett,20:1995~1998
ChandrasekharU.1961.Hydrodynamic andHydromagneticStabality[M].NewYork:OxfordClarendonPress,1~625
ChristensenU R.1989.Mantle rheology, constitution, and convection.Mantle convection[A].In:PeltierW R ed.PlateTectonics andGlobalDynamics[C].NewYork:Gordon andBreachSciPublish,595~655
DubuffetF,RabinowiczM,MonnereauM.2000.Multiple scales in mantle convection[J].EarthPlanetSciLett,178:351~366
DuncanR A,StoreyM.1992.The life cycle ofIndianOcean hotspots[A].In:DuncanR A ed.Synthesis ofResultsfromScientificDrilling in theIndianOcean[C].WashingtonD C:AmericanGeophysicalUnion,91~103
FuR S.1995.The applications ofGPS network for monitoring the crustal deformations inChina[A].MilitaryApplica tions ofGPS andGIS Technology[C].Seoul:KoreaMilitaryAcademy,121~139
FuR S,HuangJ H,WeiZ X.1996.The upper mantle flow beneath theNorthChina platform[J].PureApplGeophys,146(3/4):649~659
HaxbyW F,WeisselJ K.1986.Evidence for small scale mantle convection fromSEASAT altimeter data[J].J GeophysRes,91:3507~3520
HayesD E,KaneK A.1994.Long lived mid ocean ridge segmentation of thePacificAntarctic ridge and the southeastIndian ridge[J].J GeophysRes,99:19679~19692
HondaS,BalachandarS,YuenD A, et al.1993.Three dimensional mantle dynamics with an endothermic phase transi tion[J].GeophysResLett,20:221~224
HoernleK,SchminckeH U.1993.The role of partial melting in the15Ma geochemical evolution ofGranCanaria—Ablob model for theCanaryHotspot[J].J Petrol,34:599~626
HumphreysE,ClaytonR W,HagerB H.1984.A tomographic image of mantle structure beneath southernCalifornia[J].GeophysResLett,11:625~627
ItoG,McNuttM,GibsonR L.1995.Crustal structure of theTuamotuPlateau,15°S, and mplications for its origin[J].J GeophysRes,100:8097~8114
JosephD,TaylorB,ShorA, et al.1993.TheNovaCantonTrough and theLateCretaceous evolution of the centalPa cific[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,171~185
LiuF T,LiuJ H,ZhongD L, et al.2000.The subducted slab ofYangtze continental block beneath theTethyan orogenin westernYunnan[J].ChineseSciBull,45(5):466~471
MachetelP,WeberP.1991.Intermittent layered convection on a normal mantle with an endothermic phase change at670km[J].Nature,350:55~57
MacdonaldK C Jr,FoxP J,PerramL J, et al.1988.A new view of the mid ocean ridge from the behaviour of ridge axisdiscontinuities[J].Nature,335:217~225
MaiaM,DiamentM.1991.An analysis of the altimetric geoid in various wave bands in theCentralPacificOcean:con straints on the origin of intraplate features[J].Tectonophysics,190:133~153
MastersG,JordanT H,SilverP G, et al.1982.A spherical earth structure from fundamental spherical mode data[J].Nature,298:609~613
MüllerR T,RoyerJ,LawverA L.1991.Evidence for hotspot group motion in theLateCretaceous,EarlyTertiary[A].Abstracts withPrograms[C].GeolSocAmer,A318
PetronotisK E,JurdyD M.1990.Pacific plate reconstructions and uncertainties[J].Tectonophysics,182:383~391
PringleM S.1993.Age progressive volcanism in theMusiciansSeamounts:A test of the hotspot hypothesis for theLateCretaceousPacific[A].In:PringleM,SagerW,SliterWet al, eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,187~215
PringleM S,DalrympleG B.1993.HessRise,WentworthSeamountChain[A].In:PringleM,SagerW,SliterW, etal eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMono graph77[C].WashingtonD C:AGU,263
RichterF M,McKenzieD P.1978.Simple plate models and mantle convection[J].J Geophys,44:441~471
SagerR A,DuncanR A,HandschumacherD.1993.Japanese,MarcusWake seamounts; westPacificOcean[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,401
SchillingJ G.1991.Fluxes and excess temperatures of mantle plumes inferred from their interaction with migratingmidocean ridges[J].Nature,352:397
SmithS W,KnappJ S,McPhersomR C.1993.Seismicity of theGordaPlate, structure of the continental margin, andan eastward jump of theMendocinoTripleJunction[J].J GeophysRes,98:8153~8171
SmithR B,BraileL W.1994.TheYellowstoneHotspot[J].J VolcanolGeothermRes,61:121~187
TackleyP J,StevensonD J,GlatzmaierG A, et al.1994.Effects of multiple phase transitions in a3 dimensional spheri cal model of convection inEarth′s mantle[J].J GeophysRes,99:15877~15901
TardunoJ A,GeeJ.1995.Large scale motion betweenPacific andAtlantic hotspots[J].Nature,378:477~480
TurcottD L,SchubertG.1982.Geodynamics,Applications ofContinuumPhysics toGeologicalProblems[M].NewYork:JohnWiley&SonsPress,449
VogtP R.1972.Evidence for global synchronism in mantle plume convection, and possible significance for geology[J].Nature,240:338~342
WoodhouseJ H,DziewonskiA M.1984.Mapping the upper mantle:Three dimensional modeling of earth structure byinvertion of seismic waveforms[J].J GeophysRes,89:5953~5986
YamajiA.1992.Periodic hotspot distribution and small scale convetion in the upper mentle[J].EarthPlanetSciLett,109,107~116
ZobackM L,McKeeE H,BlakelyR J.1994.The northernNevada rift regional tectonomagmatic relations and middleMiocene stress direction[J].GeolSocAmerBull,106(3):371~382
傅容珊,黄建华,刘文忠.1994b.区域重力异常和上地幔小尺度对流相关方程[J].地球物理学报,37(4):638~646
傅容珊,常筱华.1994.上地幔小尺度热对流及大陆岩石层动力学[A].见:陈运泰,阚荣举,滕吉文等编.中国地球物理学进展[M].北京:地震出版社,169~178
傅容珊,陈凌,黄建华,等.1995.全球地震层析地幔密度横向不均衡及大陆动力学[J].地球物理学进展,10(3):51~62
傅容珊,黄建华,徐耀民,等.1998.青藏高原天山地区岩石层构造运动的地幔动力学机制[J].地球物理学报,41(4):658~668
刘福田,曲克信,吴华,等.1989.中国大陆及其邻区的地震层析成像[J].地球物理学报,32(3):281~291
AndersonD L,SchreiberE,LiebermannR C, et al.1968.Some elastic constant data on minerals relevant to geophysics[J].RevGeophysSpacePhys,6:491~524
AndersonD L.1998.The scales of mantle convection[J].Tectonophysics,284:1~17
AtwaterT,SchlaterJ,SandwellD, et al.1993.Fracture zone traces across theN.PacificCretaceousQuietZone andtheir tectonic implications[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tec tonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,137~154
BaudryN,KroenkeL.1991.Intermediate wavelength(400~600 km),SouthPacific geoidal undulations:Their ralation ship of linear volcanic chains[J].EarthPlanetSciLett,102:430~443
CalcagnoP,CazenaveA.1993.Present and past regional ridge segmentation:Evidence in geoid data[J].GeophysResLett,20:1995~1998
ChandrasekharU.1961.Hydrodynamic andHydromagneticStabality[M].NewYork:OxfordClarendonPress,1~625
ChristensenU R.1989.Mantle rheology, constitution, and convection.Mantle convection[A].In:PeltierW R ed.PlateTectonics andGlobalDynamics[C].NewYork:Gordon andBreachSciPublish,595~655
DubuffetF,RabinowiczM,MonnereauM.2000.Multiple scales in mantle convection[J].EarthPlanetSciLett,178:351~366
DuncanR A,StoreyM.1992.The life cycle ofIndianOcean hotspots[A].In:DuncanR A ed.Synthesis ofResultsfromScientificDrilling in theIndianOcean[C].WashingtonD C:AmericanGeophysicalUnion,91~103
FuR S.1995.The applications ofGPS network for monitoring the crustal deformations inChina[A].MilitaryApplica tions ofGPS andGIS Technology[C].Seoul:KoreaMilitaryAcademy,121~139
FuR S,HuangJ H,WeiZ X.1996.The upper mantle flow beneath theNorthChina platform[J].PureApplGeophys,146(3/4):649~659
HaxbyW F,WeisselJ K.1986.Evidence for small scale mantle convection fromSEASAT altimeter data[J].J GeophysRes,91:3507~3520
HayesD E,KaneK A.1994.Long lived mid ocean ridge segmentation of thePacificAntarctic ridge and the southeastIndian ridge[J].J GeophysRes,99:19679~19692
HondaS,BalachandarS,YuenD A, et al.1993.Three dimensional mantle dynamics with an endothermic phase transi tion[J].GeophysResLett,20:221~224
HoernleK,SchminckeH U.1993.The role of partial melting in the15Ma geochemical evolution ofGranCanaria—Ablob model for theCanaryHotspot[J].J Petrol,34:599~626
HumphreysE,ClaytonR W,HagerB H.1984.A tomographic image of mantle structure beneath southernCalifornia[J].GeophysResLett,11:625~627
ItoG,McNuttM,GibsonR L.1995.Crustal structure of theTuamotuPlateau,15°S, and mplications for its origin[J].J GeophysRes,100:8097~8114
JosephD,TaylorB,ShorA, et al.1993.TheNovaCantonTrough and theLateCretaceous evolution of the centalPa cific[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,171~185
LiuF T,LiuJ H,ZhongD L, et al.2000.The subducted slab ofYangtze continental block beneath theTethyan orogenin westernYunnan[J].ChineseSciBull,45(5):466~471
MachetelP,WeberP.1991.Intermittent layered convection on a normal mantle with an endothermic phase change at670km[J].Nature,350:55~57
MacdonaldK C Jr,FoxP J,PerramL J, et al.1988.A new view of the mid ocean ridge from the behaviour of ridge axisdiscontinuities[J].Nature,335:217~225
MaiaM,DiamentM.1991.An analysis of the altimetric geoid in various wave bands in theCentralPacificOcean:con straints on the origin of intraplate features[J].Tectonophysics,190:133~153
MastersG,JordanT H,SilverP G, et al.1982.A spherical earth structure from fundamental spherical mode data[J].Nature,298:609~613
MüllerR T,RoyerJ,LawverA L.1991.Evidence for hotspot group motion in theLateCretaceous,EarlyTertiary[A].Abstracts withPrograms[C].GeolSocAmer,A318
PetronotisK E,JurdyD M.1990.Pacific plate reconstructions and uncertainties[J].Tectonophysics,182:383~391
PringleM S.1993.Age progressive volcanism in theMusiciansSeamounts:A test of the hotspot hypothesis for theLateCretaceousPacific[A].In:PringleM,SagerW,SliterWet al, eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,187~215
PringleM S,DalrympleG B.1993.HessRise,WentworthSeamountChain[A].In:PringleM,SagerW,SliterW, etal eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMono graph77[C].WashingtonD C:AGU,263
RichterF M,McKenzieD P.1978.Simple plate models and mantle convection[J].J Geophys,44:441~471
SagerR A,DuncanR A,HandschumacherD.1993.Japanese,MarcusWake seamounts; westPacificOcean[A].In:PringleM,SagerW,SliterW, et al eds.TheMesozoicPacific:Geology,Tectonics andVolcanism.AmericanGeophysicalUnionGeophysicsMonograph77[C].WashingtonD C:AGU,401
SchillingJ G.1991.Fluxes and excess temperatures of mantle plumes inferred from their interaction with migratingmidocean ridges[J].Nature,352:397
SmithS W,KnappJ S,McPhersomR C.1993.Seismicity of theGordaPlate, structure of the continental margin, andan eastward jump of theMendocinoTripleJunction[J].J GeophysRes,98:8153~8171
SmithR B,BraileL W.1994.TheYellowstoneHotspot[J].J VolcanolGeothermRes,61:121~187
TackleyP J,StevensonD J,GlatzmaierG A, et al.1994.Effects of multiple phase transitions in a3 dimensional spheri cal model of convection inEarth′s mantle[J].J GeophysRes,99:15877~15901
TardunoJ A,GeeJ.1995.Large scale motion betweenPacific andAtlantic hotspots[J].Nature,378:477~480
TurcottD L,SchubertG.1982.Geodynamics,Applications ofContinuumPhysics toGeologicalProblems[M].NewYork:JohnWiley&SonsPress,449
VogtP R.1972.Evidence for global synchronism in mantle plume convection, and possible significance for geology[J].Nature,240:338~342
WoodhouseJ H,DziewonskiA M.1984.Mapping the upper mantle:Three dimensional modeling of earth structure byinvertion of seismic waveforms[J].J GeophysRes,89:5953~5986
YamajiA.1992.Periodic hotspot distribution and small scale convetion in the upper mentle[J].EarthPlanetSciLett,109,107~116
ZobackM L,McKeeE H,BlakelyR J.1994.The northernNevada rift regional tectonomagmatic relations and middleMiocene stress direction[J].GeolSocAmerBull,106(3):371~382
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