近地表密度估计的重力贝叶斯分析方法及在云南地区的应用
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摘要
基于布格重力异常相对于地形起伏光滑分布的约束条件,从一维自由空气重力异常数据出发,采用贝叶斯方法估算近地表岩石密度,同时采用三次B样条函数拟合布格重力异常,获取光滑分布的布格重力异常.数据拟合和光滑约束之间的权重采用Akaike贝叶斯准则(ABIC准则)自动确定.均匀剖分模型和不均匀剖分模型数据试验都验证了该方法的有效性.相关参数评价表明,足够多的样条系数可以提高估计结果的准确性,样条系数的个数接近测点数时可获得较稳定的估计结果.增大异常的噪声水平时,ABIC准则可有效地自动增大先验光滑约束的权重.云南地区两条重力剖面应用结果表明,剖面沿线的近地表密度值起伏变化明显(达2.45～2.8g·cm~(-3)),前寒武纪和古生代地层密度相对较高(主要为2.53～2.75g·cm~(-3)),而中生代密度较低(2.45～2.73g·cm~(-3));本文估计的近地表密度结果与区域物性资料及地表地质特征较吻合;估计的剖面布格重力异常具有光滑性;红河断裂两侧近地表密度差异较大,可达0.4g·cm~(-3).本文获得的两条剖面近地表密度结构和布格重力异常为该区深部结构与构造研究提供更可靠的重力基础数据.
Bouguer gravity anomalies are calculated by terrain correction and Bouguer correction to free-air gravity anomaly data.Near-surface density is an important parameter in these two corrections.Assuming that Bouguer gravity anomalies vary smoothly with surficial topography,we estimate the near-surface density from 1-D free-air gravity anomalies by using the Bayesianmethod and simultaneously obtain the smooth Bouguer anomalies fitted by the cubic B-spline function.We determine the trade-off parameters between the data misfit and prior constraints automatically by the Akaike′s Bayesian Information Criterion(ABIC).Synthetic data tests by using uniform and non-uniform subdivisions verify the effectiveness of the presented method.Relevant parameter evaluations show that more of the spline coefficients are involved in the method,better results will be produced.When the number of spline coefficients are close to the number of observed stations,a more stable estimation can be obtained.More noise in the data,higher weight for smooth constraints will be determined automatically by the ABIC algorithm.The application of this method to two gravity profiles in the Yunnan area shows that near-surface density along the profiles varies significantly(2.45～2.80 g·cm~(-3)).The Proterozoic and Paleozoic strata have relatively high density(mainly 2.53～2.75 g·cm~(-3)),and the Mesozoic strata have relatively low density(2.45～2.73 g·cm~(-3)).The estimated near-surface density in this paper is in a good agreement with regional physical data and surface geological characteristics,and the estimated Bouguer gravity anomalies have good smoothness.The density differences between both sides of the Honghe fault are as large as 0.4 g·cm~(-3).The near-surface density structure and Bouguer gravity anomalies obtained in this paper provide reliable basic data for the study of deep structure in this area.
Bouguer gravity anomalies are calculated by terrain correction and Bouguer correction to free-air gravity anomaly data.Near-surface density is an important parameter in these two corrections.Assuming that Bouguer gravity anomalies vary smoothly with surficial topography,we estimate the near-surface density from 1-D free-air gravity anomalies by using the Bayesianmethod and simultaneously obtain the smooth Bouguer anomalies fitted by the cubic B-spline function.We determine the trade-off parameters between the data misfit and prior constraints automatically by the Akaike′s Bayesian Information Criterion(ABIC).Synthetic data tests by using uniform and non-uniform subdivisions verify the effectiveness of the presented method.Relevant parameter evaluations show that more of the spline coefficients are involved in the method,better results will be produced.When the number of spline coefficients are close to the number of observed stations,a more stable estimation can be obtained.More noise in the data,higher weight for smooth constraints will be determined automatically by the ABIC algorithm.The application of this method to two gravity profiles in the Yunnan area shows that near-surface density along the profiles varies significantly(2.45～2.80 g·cm~(-3)).The Proterozoic and Paleozoic strata have relatively high density(mainly 2.53～2.75 g·cm~(-3)),and the Mesozoic strata have relatively low density(2.45～2.73 g·cm~(-3)).The estimated near-surface density in this paper is in a good agreement with regional physical data and surface geological characteristics,and the estimated Bouguer gravity anomalies have good smoothness.The density differences between both sides of the Honghe fault are as large as 0.4 g·cm~(-3).The near-surface density structure and Bouguer gravity anomalies obtained in this paper provide reliable basic data for the study of deep structure in this area.
引文
Akaike H.1980.Likelihood and the Bayes Procedure(with Discussion),Bayesian Statistics.Valencia,Spain:University Press.
Cui Z Z,Lu D Y,Chen J P,et al.1987.The deep structural and tectonic features of the crust in panxi area.Chinese Journal of Geophysics(in Chinese),30(6):566-580.
Davidon W C.1975.Optimally conditioned optimization algorithms without line searches.Mathematical Programming,9(1):1-30,doi:10.1007/BF01681328.
Eshaghzadeh A,Kalantari R S,Hekmat Z M.2015.Optimum density determination for bouguer correction using statistical methods:a case study from north of Iran.International Journal of Advanced Geosciences,3(2):25-29,doi:10.14419/ijag.v3i2.4988.
Fukao Y,Yamamoto A,Nozaki K.1981.A method of density determination for gravity correction.Journal of Physics of the Earth,29(2):163-166,doi:10.4294/jpe1952.29.163.
Ge B R,Yang K Y.1990.Mesozoic-cenozoic tectonic features in panzhihua-xichang area.Acta Geoghysics Sinica(in Chinese),33(1):64-69,125-126.
Gibb R A,Thomas M D.1980.Density determinations of basic volcanic rocks of the Yellowknife supergroup by gravity measurements in mine shafts-Yellowknife,Northwest Territories.Geophysics,45(1):18-31,doi:10.1190/1.1441036.
Grant F S,Elsaharty A F.1962.Bouguer gravity corrections using a variable density.Geophysics,27(5):616-626,doi:10.1190/1.1439071.
Hammer S.1965.Density determinations by underground gravity measurements-Sequel.Geophysics,30(6):1133-1134,doi:10.1190/1.1439698.
Hou T,Zhang Z C,Encarnacion J,et al.2013.The role of recycled oceanic crust in magmatism and metallogeny:Os-Sr-Nd isotopes,U-Pb geochronology and geochemistry of picritic dykes in the Panzhihua giant Fe-Ti oxide deposit,central Emeishan large igneous province,SW China.Contributions to Mineralogy and Petrology,165(4):805-822.
Inoue H.2012.A least-squares smooth fitting for irregularly spaced data:finite-element approach using the cubic B-spline basis.Geophysics,51(11):2051-2066,doi:10.1190/1.1442060.
Jian P,Liu D Y,Kr9ner A,et al.2009.Devonian to Permian plate tectonic cycle of the Paleo-Tethys Orogen in southwest China(II):insights from zircon ages of ophiolites,arc/back-arc assemblages and within-plate igneous rocks and generation of the Emeishan CFB province.Lithos,113(3-4):767-784.
Jilinski P,Fontes S L,Meju M A.2013.Estimating optimum density for regional Bouguer reduction by morphological correlation of gravity and bathymetric maps:examples from offshore south-eastern Brazil.Geo-Marine Letters,33(1):67-73,doi:10.1007/s00367-012-0312-0.
Kane M F.1962.A comprehensive system of terrain corrections using a digital computer.Geophysics,27(4):455-462,doi:10.1190/1.1439044.
Kirkpatrick S,Gelatt C D Jr,Vecchi M P.1983.Optimization by simulated annealing.Science,220(4598):671-680,doi:10.1126/science.220.4598.671.
Kowalik J S,Osborne M R.1968.Methods of unconstrained optimization problems.Mathematics of Computation,8(24):425-427,doi:10.2307/2004893.
LaFehr T R.1983.Rock density from borehole gravity surveys.Geophysics,48(3):341-356,doi:10.1190/1.1441472.
Marc B,Jacques L.1983.Determination directe des densites du sol et de remblais a partir de mesures gravimetriques.Bulletin of the International Association of Engineering Geology,26(1):171-173,doi:10.1007/BF02594213.
Miao Y K,Ren Z D,Chen X Y,et al.1986.Tectonic environment and tectonic development of Panxi Rift in Sichuan.Earth ScienceJournal of Wuhan College of Geology(in Chinese),11(6):631-637.
Moribayashi S.1990.A new method for variable density correction of gravity data.BUTSURI-TANSA(Geophys.Explor.),43,97-106(in Japanese with English abstract).
Munteanu M,Yao Y,Wilson A H,et al.2013.Panxi region(South-West China):Tectonics,magmatism and metallogenesis.Areview.Tectonophysics,608:51-71.
Murata Y.1993.Estimation of optimum average surficial density from gravity data-an objective bayesian approach.Journal of Geophysical Research:Solid Earth,98(B7):12097-12109,doi:10.1029/93jb00192.
Nagy D.1966.The gravitational attraction of a right rectangular prism.Geophysics,31(2):362-371,doi:10.1190/1.1439779.
Nawa K,Fukao Y,Shichi R,et al.1997.Inversion of gravity data to determine the terrain density distribution in southwest Japan.Journal of Geophysical Research:Solid Earth,102(B12):27703-27719,doi:10.1029/97jb02543.
Nettleton L L.1939.Determination of density for reduction of gravimeter observations.Geophysics,4(3):176-183,doi:10.1190/1.0403176.
Parasnis D S.1979.Principles of Applied Geophysics.3rd ed.London:Chapman and Hall.
Rikitake T,Tajima H,Izutuya S,et al.1965.Gravimetric and geomagnetic studies of Onikobe area.Bul Earthq Res Inst,43:241-267.
Rimbert F,Erling J C,Lakshmanan J.1987.Variable density Bouguer processing of gravity data from Herault,France.First Break,5(1):9-13,doi:10.3997/1365-2397.1987001.
Saha D,Chatterjee S M,Baruah B N.2006.Determination of optimum average density for bouguer correction-a case study in Tirasujanpur Area,Himachal Pradesh,India.∥6th International Conference&Exposition on Petroleum Geophysics.Kolkata:Society of Petroleum Geophysicists India,89-93.
Sastry R G,Chaudhary N,Israil M.2005.Is there a need for variable density option in making combined mass correction to gravity data acquired over high relief?Current Science,88(2):269-273.
Shellnutt J G,Zhou M F.2007.Permian peralkaline,peraluminous and metaluminous A-type granites in the Panxi district,SWChina:Their relationship to the Emeishan mantle plume.Chemical Geology,243(3-4):286-316.
Shi L,Lou H,Wang Q S,et al.2015.Gravity field characteristics and crust density structure in the Panxi region,China.Chinese Journal of Geophysics(in Chinese),58(7):2402-2412,doi:10.6038/cjg20150717.
Singh P,Pandey R S,Gupta S K,et al.2006.Bouguer reduction with lateral variable surface densities-a model based case study in geologically complex frontier area.∥6th International Conference&Exposition on Petroleum Geophysics.Kolkata:Society of Petroleum Geophysicists India,72-77.
Sissons B A.1981.Densities determined from surface and subsurface gravity measurements.Geophysics,46(11):1568-1571,doi:10.1190/1.1441163.
Tarantola A.1987.Inverse Problem Theory:Methods for Data Fitting and Model Parameter Estimation.Amsterdam:Elsevier Science Publishing Co.
Tontini F C,Graziano F,Cocchi L,et al.2007.Determining the optimal Bouguer density for a gravity data set:implications for the isostatic setting of the Mediterranean Sea.Geophysical Journal International,169(2):380-388,doi:10.1111/j.1365-246X.2007.03340.x.
Vajk R.1956.Bouguer corrections with varying surface density.Geophysics,21(4):1004-1020,doi:10.1190/1.1438292.
Wang Q S.2003.Gravitology(in Chinese).Beijing:Seismological Press.
Zeng H L.2005.Gravity Field and Gravity Exploration(in Chinese).Beijing:Geological Publishing House.
崔作舟,卢德源,陈纪平等.1987.攀西地区的深部地壳结构与构造.地球物理学报,30(6):566-580.
葛碧如,杨科佑.1990.攀西地区中、新生代构造特征.地球物理学报,33(1):64-69,125-126.
缪以琨,任祖德,陈小源等.1986.四川攀西裂谷的构造环境及构造发展.地球科学-武汉地质学院学报,11(6):631-637.
石磊,楼海,王谦身等.2015.攀西地区重力场特征及地壳密度结构.地球物理学报,58(7):2402-2412,doi:10.6038/cjg20150717.
王谦身.2003.重力学.北京:地震出版社.
曾华霖.2005.重力场与重力勘探.北京:地质出版社.
Cui Z Z,Lu D Y,Chen J P,et al.1987.The deep structural and tectonic features of the crust in panxi area.Chinese Journal of Geophysics(in Chinese),30(6):566-580.
Davidon W C.1975.Optimally conditioned optimization algorithms without line searches.Mathematical Programming,9(1):1-30,doi:10.1007/BF01681328.
Eshaghzadeh A,Kalantari R S,Hekmat Z M.2015.Optimum density determination for bouguer correction using statistical methods:a case study from north of Iran.International Journal of Advanced Geosciences,3(2):25-29,doi:10.14419/ijag.v3i2.4988.
Fukao Y,Yamamoto A,Nozaki K.1981.A method of density determination for gravity correction.Journal of Physics of the Earth,29(2):163-166,doi:10.4294/jpe1952.29.163.
Ge B R,Yang K Y.1990.Mesozoic-cenozoic tectonic features in panzhihua-xichang area.Acta Geoghysics Sinica(in Chinese),33(1):64-69,125-126.
Gibb R A,Thomas M D.1980.Density determinations of basic volcanic rocks of the Yellowknife supergroup by gravity measurements in mine shafts-Yellowknife,Northwest Territories.Geophysics,45(1):18-31,doi:10.1190/1.1441036.
Grant F S,Elsaharty A F.1962.Bouguer gravity corrections using a variable density.Geophysics,27(5):616-626,doi:10.1190/1.1439071.
Hammer S.1965.Density determinations by underground gravity measurements-Sequel.Geophysics,30(6):1133-1134,doi:10.1190/1.1439698.
Hou T,Zhang Z C,Encarnacion J,et al.2013.The role of recycled oceanic crust in magmatism and metallogeny:Os-Sr-Nd isotopes,U-Pb geochronology and geochemistry of picritic dykes in the Panzhihua giant Fe-Ti oxide deposit,central Emeishan large igneous province,SW China.Contributions to Mineralogy and Petrology,165(4):805-822.
Inoue H.2012.A least-squares smooth fitting for irregularly spaced data:finite-element approach using the cubic B-spline basis.Geophysics,51(11):2051-2066,doi:10.1190/1.1442060.
Jian P,Liu D Y,Kr9ner A,et al.2009.Devonian to Permian plate tectonic cycle of the Paleo-Tethys Orogen in southwest China(II):insights from zircon ages of ophiolites,arc/back-arc assemblages and within-plate igneous rocks and generation of the Emeishan CFB province.Lithos,113(3-4):767-784.
Jilinski P,Fontes S L,Meju M A.2013.Estimating optimum density for regional Bouguer reduction by morphological correlation of gravity and bathymetric maps:examples from offshore south-eastern Brazil.Geo-Marine Letters,33(1):67-73,doi:10.1007/s00367-012-0312-0.
Kane M F.1962.A comprehensive system of terrain corrections using a digital computer.Geophysics,27(4):455-462,doi:10.1190/1.1439044.
Kirkpatrick S,Gelatt C D Jr,Vecchi M P.1983.Optimization by simulated annealing.Science,220(4598):671-680,doi:10.1126/science.220.4598.671.
Kowalik J S,Osborne M R.1968.Methods of unconstrained optimization problems.Mathematics of Computation,8(24):425-427,doi:10.2307/2004893.
LaFehr T R.1983.Rock density from borehole gravity surveys.Geophysics,48(3):341-356,doi:10.1190/1.1441472.
Marc B,Jacques L.1983.Determination directe des densites du sol et de remblais a partir de mesures gravimetriques.Bulletin of the International Association of Engineering Geology,26(1):171-173,doi:10.1007/BF02594213.
Miao Y K,Ren Z D,Chen X Y,et al.1986.Tectonic environment and tectonic development of Panxi Rift in Sichuan.Earth ScienceJournal of Wuhan College of Geology(in Chinese),11(6):631-637.
Moribayashi S.1990.A new method for variable density correction of gravity data.BUTSURI-TANSA(Geophys.Explor.),43,97-106(in Japanese with English abstract).
Munteanu M,Yao Y,Wilson A H,et al.2013.Panxi region(South-West China):Tectonics,magmatism and metallogenesis.Areview.Tectonophysics,608:51-71.
Murata Y.1993.Estimation of optimum average surficial density from gravity data-an objective bayesian approach.Journal of Geophysical Research:Solid Earth,98(B7):12097-12109,doi:10.1029/93jb00192.
Nagy D.1966.The gravitational attraction of a right rectangular prism.Geophysics,31(2):362-371,doi:10.1190/1.1439779.
Nawa K,Fukao Y,Shichi R,et al.1997.Inversion of gravity data to determine the terrain density distribution in southwest Japan.Journal of Geophysical Research:Solid Earth,102(B12):27703-27719,doi:10.1029/97jb02543.
Nettleton L L.1939.Determination of density for reduction of gravimeter observations.Geophysics,4(3):176-183,doi:10.1190/1.0403176.
Parasnis D S.1979.Principles of Applied Geophysics.3rd ed.London:Chapman and Hall.
Rikitake T,Tajima H,Izutuya S,et al.1965.Gravimetric and geomagnetic studies of Onikobe area.Bul Earthq Res Inst,43:241-267.
Rimbert F,Erling J C,Lakshmanan J.1987.Variable density Bouguer processing of gravity data from Herault,France.First Break,5(1):9-13,doi:10.3997/1365-2397.1987001.
Saha D,Chatterjee S M,Baruah B N.2006.Determination of optimum average density for bouguer correction-a case study in Tirasujanpur Area,Himachal Pradesh,India.∥6th International Conference&Exposition on Petroleum Geophysics.Kolkata:Society of Petroleum Geophysicists India,89-93.
Sastry R G,Chaudhary N,Israil M.2005.Is there a need for variable density option in making combined mass correction to gravity data acquired over high relief?Current Science,88(2):269-273.
Shellnutt J G,Zhou M F.2007.Permian peralkaline,peraluminous and metaluminous A-type granites in the Panxi district,SWChina:Their relationship to the Emeishan mantle plume.Chemical Geology,243(3-4):286-316.
Shi L,Lou H,Wang Q S,et al.2015.Gravity field characteristics and crust density structure in the Panxi region,China.Chinese Journal of Geophysics(in Chinese),58(7):2402-2412,doi:10.6038/cjg20150717.
Singh P,Pandey R S,Gupta S K,et al.2006.Bouguer reduction with lateral variable surface densities-a model based case study in geologically complex frontier area.∥6th International Conference&Exposition on Petroleum Geophysics.Kolkata:Society of Petroleum Geophysicists India,72-77.
Sissons B A.1981.Densities determined from surface and subsurface gravity measurements.Geophysics,46(11):1568-1571,doi:10.1190/1.1441163.
Tarantola A.1987.Inverse Problem Theory:Methods for Data Fitting and Model Parameter Estimation.Amsterdam:Elsevier Science Publishing Co.
Tontini F C,Graziano F,Cocchi L,et al.2007.Determining the optimal Bouguer density for a gravity data set:implications for the isostatic setting of the Mediterranean Sea.Geophysical Journal International,169(2):380-388,doi:10.1111/j.1365-246X.2007.03340.x.
Vajk R.1956.Bouguer corrections with varying surface density.Geophysics,21(4):1004-1020,doi:10.1190/1.1438292.
Wang Q S.2003.Gravitology(in Chinese).Beijing:Seismological Press.
Zeng H L.2005.Gravity Field and Gravity Exploration(in Chinese).Beijing:Geological Publishing House.
崔作舟,卢德源,陈纪平等.1987.攀西地区的深部地壳结构与构造.地球物理学报,30(6):566-580.
葛碧如,杨科佑.1990.攀西地区中、新生代构造特征.地球物理学报,33(1):64-69,125-126.
缪以琨,任祖德,陈小源等.1986.四川攀西裂谷的构造环境及构造发展.地球科学-武汉地质学院学报,11(6):631-637.
石磊,楼海,王谦身等.2015.攀西地区重力场特征及地壳密度结构.地球物理学报,58(7):2402-2412,doi:10.6038/cjg20150717.
王谦身.2003.重力学.北京:地震出版社.
曾华霖.2005.重力场与重力勘探.北京:地质出版社.