成矿过程奇异性与矿床多重分形分布
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摘要
本文将成矿过程与地震、火山、滑坡、洪水、暴雨、森林火灾等一系列非线性地球系统过程称之为奇异性过程(Singular Processes)。奇异性过程的基本特征是在相对很小的时间间隔或者空间范围中产生巨大能量释放或者物质超常富集或堆积。探讨了奇异性过程的"资源"与"灾害"双重效应;从地幔对流、板块构造等自组织临界性系统探讨了成矿过程的奇异性以及成矿结果服从多重分形分布规律,如矿床规模与个数、矿床品位与个数等;介绍了可以刻画成矿域空间结构的不均匀性、尺度独立性和自组织临界性的多重分形模型,如度量元素富集强度的局部奇异性模型,度量成矿域结构各向异性的广义自相似性模型,以及度量分形结构序次的分形谱系模型。这些非线性模型为矿产资源定量预测提供了新的思路和工具。
According to the common non-linear property of several types of non-linear hazardous processes such as earthquakes,volcanos,landslides,cloud formation,rainfall,hurricanes,flooding,and mineralization that result in anomalous amounts of energy release or mass accumulation confined to narrow intervals in space or time,these types of processes can be termed as singular processes.The end products of these non-linear processes can be modeled as fractals or multifractals.Most types of hydrothermal mineral deposits are genetically associated with mantle events and plate tectonics which themselves shows self-orginazed creticility.Here we show that not only the relationships between mineral deposits size and the number of deposits(size and number model) and between ore grade and the number of deposits(grade and number model) may follow power-law models,but also the element concentrations in a mineral district and posterior probability of an unit area containg deposits calculated by weiths of evidence method for prediction of mineral deposits may also follow power-law distribution with area.The singularity theory and non-linear models proposed have provided useful ideas and powerful tools for quantitative assessment of mineral resources.
According to the common non-linear property of several types of non-linear hazardous processes such as earthquakes,volcanos,landslides,cloud formation,rainfall,hurricanes,flooding,and mineralization that result in anomalous amounts of energy release or mass accumulation confined to narrow intervals in space or time,these types of processes can be termed as singular processes.The end products of these non-linear processes can be modeled as fractals or multifractals.Most types of hydrothermal mineral deposits are genetically associated with mantle events and plate tectonics which themselves shows self-orginazed creticility.Here we show that not only the relationships between mineral deposits size and the number of deposits(size and number model) and between ore grade and the number of deposits(grade and number model) may follow power-law models,but also the element concentrations in a mineral district and posterior probability of an unit area containg deposits calculated by weiths of evidence method for prediction of mineral deposits may also follow power-law distribution with area.The singularity theory and non-linear models proposed have provided useful ideas and powerful tools for quantitative assessment of mineral resources.
引文
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[3]Cheng Q.Multifractal imaging filtering and decomposition methodsin space,fourier frequency,and egien domains[J].Non-LinearProcesses in Geophysics,2007,(14):293-303.
[4]Cheng Q.Mapping singularities with stream sediment geochemicaldata for prediction of undiscovered mineral deposits in Gejiu,Yun-nan Province,China[J].Ore Geology Reviews,2007,(32):314-324.
[5]Bak P,Chen K,Tang C.A forest-fire model and some thoughtson turbulence[J].Phys.Lett.,1992,(A14):297-300.
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[7]http://www.pnsn.org/HELENS/helensep_mo.html
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[13]赵鹏大.地质异常理论与矿床预测:现代矿产资源评价理论与方法[M].北京:地质出版社,1998.Zhao Pengda.Geological anomaly theory and mineral depositsprediction:Advanced mineral resources assessment theoryand methods[M].Beijing:Geological Publishing House,1998.(in Chinese)
[14]裴荣富,邱小平,尹冰川,熊群尧.成矿作用爆发异常及巨量金属推积[J].矿床地质,1999,(18):333-340.Pei Rongfu,Qiu Xiaoping,Yin Bingchuan,Xiong Qunrao.The explosive anomaly of ore-forming processes and superac-cumulation of metals[J].Mineral Deposits,1999,(18):333-340.(in Chinese with English abstract)
[15]成秋明.非线性成矿预测理论:多重分形奇异性-广义自相似性-分形谱系模型与方法[J].地球科学,2006,(31):337-348.Cheng Qiuming.New multifractal mineralization predictiontheory and singularity-generalized self-similarity-fractalspectrum(3S)models[J].Earth Science,2006,(31):337-348.(in Chinese with English abstract)
[16]Cheng Q.Non-linear theory and power-law models for infor-mation integration and mineral resources quantitative assess-ments[J].Mathematical Geosciences,10.1007/s11004-008-9172-6.
[17]Bonham-Carter G F.Geographic Information Systems for Ge-oscientists:Modelling with GIS[M].Oxford:Pergamon,1994:398.
[2]Cheng Q.Multifractality and spatial statistics[J].Computers&Geosciences,1999,(25):949-961.
[3]Cheng Q.Multifractal imaging filtering and decomposition methodsin space,fourier frequency,and egien domains[J].Non-LinearProcesses in Geophysics,2007,(14):293-303.
[4]Cheng Q.Mapping singularities with stream sediment geochemicaldata for prediction of undiscovered mineral deposits in Gejiu,Yun-nan Province,China[J].Ore Geology Reviews,2007,(32):314-324.
[5]Bak P,Chen K,Tang C.A forest-fire model and some thoughtson turbulence[J].Phys.Lett.,1992,(A14):297-300.
[6]於崇文.矿床在混沌边缘分形生长(上卷)[M].合肥:安徽教育出版社,2007:705.Yu Chongwen.Fractal growth of mineral deposits at the edgeof chaos[M].Hefei:Anhui Eduction Press,2007:705.(inChinese)
[7]http://www.pnsn.org/HELENS/helensep_mo.html
[8]Singer D,Berger V I,Moring B C.Porphyry copper depositsof the world:Database,map,and grade and tonnage models[R].U.S.Geological Survey Open-File Report 02-268,2005.
[9]翟裕生.地球系统、成矿系统到勘查系统[J].地学前缘,2007,(14):173-181.Zhai Yusheng.Earth,metallogenic to exploration system[J].Earth Science Frontier,2007,(14):173-181.(in Chinesewith English abstract)
[10]Turcotte D L.Self-organized criticality:Does it have anything todo with criticality and is it useful?[J].Non-linear Processes inGeophysics,2001,(8):193-196.
[11]Cheng Q.Discrete multifractals[J].Mathematical Geology,1997,(29):245-266.
[12]Cheng Q,Agterberg F P,Ballantyne S B.The separation of geo-chemical anomalies from background by fractal methods[J].Jour-nal of Geochemical Exploration,1994,(51):109-130.
[13]赵鹏大.地质异常理论与矿床预测:现代矿产资源评价理论与方法[M].北京:地质出版社,1998.Zhao Pengda.Geological anomaly theory and mineral depositsprediction:Advanced mineral resources assessment theoryand methods[M].Beijing:Geological Publishing House,1998.(in Chinese)
[14]裴荣富,邱小平,尹冰川,熊群尧.成矿作用爆发异常及巨量金属推积[J].矿床地质,1999,(18):333-340.Pei Rongfu,Qiu Xiaoping,Yin Bingchuan,Xiong Qunrao.The explosive anomaly of ore-forming processes and superac-cumulation of metals[J].Mineral Deposits,1999,(18):333-340.(in Chinese with English abstract)
[15]成秋明.非线性成矿预测理论:多重分形奇异性-广义自相似性-分形谱系模型与方法[J].地球科学,2006,(31):337-348.Cheng Qiuming.New multifractal mineralization predictiontheory and singularity-generalized self-similarity-fractalspectrum(3S)models[J].Earth Science,2006,(31):337-348.(in Chinese with English abstract)
[16]Cheng Q.Non-linear theory and power-law models for infor-mation integration and mineral resources quantitative assess-ments[J].Mathematical Geosciences,10.1007/s11004-008-9172-6.
[17]Bonham-Carter G F.Geographic Information Systems for Ge-oscientists:Modelling with GIS[M].Oxford:Pergamon,1994:398.
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