成矿过程奇异性与矿产预测定量化的新理论与新方法
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摘要
在分析地震、滑坡、洪水、暴雨、森林火灾等一系列非线性地球系统过程共同特征的基础上,笔者提出了成矿过程作为奇异性过程的命题。探讨了成矿过程奇异性、广义自相似性、自组织临界性等基本非线性特征的内在联系。从多重分形理论出发给出了:(1)度量成矿域空间结构不均匀性的局部奇异性分析模型;(2)度量成矿多样性与自相似性关系的系列广义自相似性度量模型;(3)首次给出了奇异性指标作为度量控矿要素与矿床分布相关关系的非线性模型,提出了从奇异性出发计算成矿后验概率的新的对数概率模型;(4)介绍了成矿奇异性的动力学模拟过程。详细介绍了非线性矿产资源预测理论和方法的基本内容和模型。
Analyzing several types of non-linear hazardous processes such as earthquakes,clouds,landslides,rainfalls,floods,hurricanes and forest fires,the paper puts forward a proposition that mineralization processes can be considered as singular processes.The fundamental properties of singular processes including spatial heterogeneity and singularity,diversity and generalized self-similarity,and self organized criticality and fractal/multifractal distributions were discussed first and followed by an introduction to non-linear models for characterizing mineralization and for mineral deposit prediction.These models include a local singularity analysis model,generalized self-similarity models,and a log-probability model associating singularity of mineral deposit controlling factors(evidential layers)and posterior probability of mineral deposit.The contents of the newly proposed non-linear theories and methods for mineral resource prediction were introduced.
Analyzing several types of non-linear hazardous processes such as earthquakes,clouds,landslides,rainfalls,floods,hurricanes and forest fires,the paper puts forward a proposition that mineralization processes can be considered as singular processes.The fundamental properties of singular processes including spatial heterogeneity and singularity,diversity and generalized self-similarity,and self organized criticality and fractal/multifractal distributions were discussed first and followed by an introduction to non-linear models for characterizing mineralization and for mineral deposit prediction.These models include a local singularity analysis model,generalized self-similarity models,and a log-probability model associating singularity of mineral deposit controlling factors(evidential layers)and posterior probability of mineral deposit.The contents of the newly proposed non-linear theories and methods for mineral resource prediction were introduced.
引文
[1]Yu C.Fractal growth of mineral deposits at the edge of chaos[M].Hefei:Anhui Eduction Press,2007:705(in Chinese).
[2]Yu C.Complexity of geological systems—fundamental prob-lems of geosciences(I)[J].Earth Science,2002,27(5):509-519(in Chinese).
[3]Yu C.Chaos edge of large deposits and mineral districts[J].Earth Sciences Frontiers,1999,6(1):85-102(in Chinese).
[4]Feder J.Fractals[M].New York:PlenumPress,1988:283.
[5]Shore M,Fowler A D.The origin of spinifextexturein kom-atiites[J].Nature,1999,397:691-694.
[6]Cheng Q.The perimeter-area fractal model andits application in geology[J].Mathematical Geology,1995,27(7):64-77.
[7]Zhang Z,Mao H,Cheng Q.Fractal geometry of element dis-tribution on mineral surface[J].Mathematical Geology,2001,33(2):217-228.
[8]Wang Z,Cheng Q,Cao L,et al.Fractal modelling of the mi-crostructure property of quartz mylonite during deformation process[J].Mathematical Geology,2007,39(1):53-68.
[9]Mandelbrot B B.The fractal geometry of nature[M].Fran-cisco:W.H.Freeman San,1982:468.
[10]Cheng Q,Agterberg F P,Ballantyne S B.The separation of geochemical anomalies from background by fractal methods[J].Journal of Geochemical Exploration,1994,51:109-130.
[11]Turcotte D L.Fractals in petrology[J].Lithos,2002,65:261-271.
[12]Cheng Q.Non-linear mineral resources assessment models and unconventional mineral resources[J].Earth Science—Journal of China University of Geosciences,2003,28(4):445-454(in Chinese).
[13]Zhai Y.Earth system,metallogenic system to exploration system[J].Earth Science Frontiers,2007,14(1):173-181(in Chinese).
[14]Teng J.Dynamic process of substance and energy exchanges in depths of the Earth andformation of mineral resources[J].Geotectonica and Metallogenia,2003,27(1):3-21(in Chi-nese).
[15]Ottino J M,Muzzio F J,Tjahjadi M,et al.Chaos,symme-try,and self-similarity—exploiting order and disorder in mix-ing processes[J].Science,1992,257:754-760.
[16]Lovejoy S,Schertzer D,Ladoy P.Fractal characterization of inhomogeneous geophysical measuring networks[J].Nature,1987,319:43-44.
[17]Cheng Q,Xu Y,Grunsky E C.Integrated spatial and spec-trumanalysis for geochemical anomaly separation[J].Natu-ral Resources Research,2001,9:43-51.
[18]Cheng Q.A new model for quantifying anisotropic scale in-variance andfor decomposition of mixing patterns[J].Mathe-matical Geology,2004,36(3):345-360.
[19]Li Q,Cheng Q.Fractal singular-value(eigen-value)decom-position method for geophysical and geochemical anomaly re-construction[J].Earth Science,2004,29(1):109-118.
[20]Cheng Q.Multifractal modeling of eigenvalues and eigenvec-tors of2-D maps[J].Mathematical Geology,2005,37(8):915-927.
[21]Cheng Q.Generalized self-similarity analysis of spatial pat-terns and mineral resources assessments[J].Earth Science—Journal of China University of Geosciences,2004,29(6):733-744(in Chinese).
[22]Cheng Q.Mapping singularities with stream sediment geo-chemical data for prediction of undiscovered mineral deposits in Gejiu,Yunnan Province,China[J].Ore Geology Reviews,2007,32(1-2):314-324.
[23]Turcotte D L.Fractals and chaos in geology and geophysics[M].2nd edition.Cambridge:Cambridge University Press,1997.
[24]Schertzer D,Lovejoy S.Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative proces-ses[J].Journal of Geophysical Research,1987,92:9693-9714.
[25]Veneziano D.Multifractality of rainfall and scaling of intensi-ty-duration-frequency curves[J].Water Resources Research,2002,38(1):1-12.
[26]Sornette D.Critical phenomena in natural sciences:chaos,fractals,selforganization and disorder[M].2nd edition.New York:Springer,2004.
[27]Malamud B D,Turcotte D L,Barton C C.The1993Missis-sippi river flood:a one hundred or a one thousand year event[J]?Environmental&Engineering Geosciences,1996,2(4):479-486.
[28]Malamud B D,Turcotte D L,Guzzetti F,et al.Landslidein-ventories and their statistical properties[J].Earth Surface Processes Landforms,2004,29:687-711.
[29]Bak P,Chen K,Tang C.A forest-fire model and some thoughts on turbulence[J].Phys Let,1992,A14:297-300.
[30]Cheng Q.Multifractality and spatial statistics[J].Computers&Geosciences,1999,25:949-961.
[31]Cheng Q,Agterberg F P.Singularity analysis of ore-mineral and toxic trace elements in streamsediments[J].Computers&Geosciences(in press).
[32]Cheng Q.Modeling local scaling properties for multi-scale mapping[J].Vadose Zone Journal(in press).
[33]Cheng Q.Multifractal imaging filtering and decomposition methods in space,Fourier frequency,and eigen domains[J].Non-Linear Processes in Geophysics,2007,14:293-303.
[34]Pei R,Qiu X,Yin B,et al.The explosive anomaly of ore-forming processes and superaccumulation of metals[J].Min-eral Deposits,1999,18(4):333-340(in Chinese).
[35]Turcotte D L.Self-organized criticality:doesit have anythingto do with criticality andis it useful[J]?Nonlinear Processes in Geophysics,2001(8):193-196.
[36]Cheng Q.Multiplicative cascade mineralization processes and singular distribution of mineral deposit associated geochemical anomalies[M]∥Cheng Q,Bonham-Carter G.Proceedings of Annual Conference of the International Associationfor Math-ematical Geology(I AMG’05),GIS and Spatial Analysis,2005(1):297-302.
[37]Cheng Q.Fractal and multifractal modeling of hydrothermal mineral deposit spectrum:application to gold deposits in the Abitibi Area,Canada[J].Earth Science—Journal of China University of Geosciences,2003,14(3):199-206.
[38]Zhao P.Geological anomaly theory and mineral deposits pre-diction:advanced mineral resources assessment theory and methods[M].Beijing:Geological Publishing House,1998(in Chinese).
[39]Cheng Q.Discrete multifractals[J].Mathematical Geology,1997,29:245-266.
[40]Rudin W.Real and complex analysis[M].3rd edition.New York:McGraw-Hill Book Company,1987:434.
[41]Nottal L.Fractal space-time and microphysics-towards a the-ory of scale relativity[M].Singapore:World Scientific,1993:1-333.
[42]Mallet S,Hwang WL.Singularity detection and processing with wavelets,IEEE Trans[J].Information Theory,1992,38:617-643.
[43]Arneodo A,Argoul F,Bacry E,et al.Wavelet transformof fractals[C]∥Meyer Y,Marseille.Wavelets and applica-tions:Proceedings of the International Conference.Paris:Springer-Verlag,1992:287-352.
[44]Cheng Q,Agterberg F P,Bonham-Carter G F.Fractal pat-tern integration method for mineral potential mapping[J].Nonrenewable Resources,1996,5(2):117-130.
[45]Cheng Q.GIS based fractal/multifractal anomaly analysis for modeling and prediction of mineralization and mineral deposits[M]∥Jeff Harris.GIS applications in Earth Sciences.Geo-logical Association of Canada Special Book,2006:289-300.
[46]Schertzer D,Lovejoy S,Schmitt F,et al.Multifractal cas-cade dynamics and turbulent intermittency[J].Fractals,1997,5:427-471.
[47]Chao L,Cheng Q.Atentative integrated model of scale in-variant generator technique(SIG)and spectrum-area(S-A)technique[M]∥Cheng Q,Bonham-Cater G.Proceedings of I AMG’05:GIS and Spatial Analysis.International Associa-tion for Mathematical Geology.Wuhan:China University of Geosciences Press,2005:303-309.
[48]Li Q,Cheng Q.Fractal singular decomposition method and anomaly reconstruction[J].Earth Science—Journal of ChinaUniversity of Geosciences,2004,29(1):109-118(in Chi-nese).
[49]Cheng Q.New multifractal mineralization prediction theory and singularity-generalized self-similarity—fractal spectrum(3s)models[J].Earth Science—Journal of China University of Geosciences,2006,31(3):337-348(in Chinese).
[50]Agterberg F P.Multifractal simulation of geochemical map patterns[M]∥Merriam D F,Davis J C.Geologic modeling and simulation:sedimentary systems.New York:Kluwer,2001:327-346.
[51]Agterberg F P.New applications of the model of de Wijs in regional geochemistry[J].Mathematical Geology,2007,39(1):1-26.
[52]Zhao P.“Three components”mineral resources prediction and assessment—digital mineral deposit prospecting theory and practice[J].Earth Science—Journal of China University of Geosciences,2002,27(5):482-489(in Chinese).
[53]Bonham-Carter G F.Geographicinformation systems for geo-scientists:modelling with GIS[M].Oxford:Pergamon,1994:398.
[1]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.
[2]於崇文.地质系统的复杂性——地质科学的基本问题(Ⅰ)[J].地球科学,2002,27(5):509-519.
[3]於崇文.大型矿床和成矿区(带)在混沌边缘[J].地学前缘,1999,6(1):85-102.
[12]成秋明.非线性矿床模型与非常规矿产资源评价[J].地球科学,2003,28(4):445-454.
[13]翟裕生.地球系统、成矿系统到勘查系统[J].地学前缘,2007,14(1):173-181.
[14]滕吉文.地球深部物质与能量交换的动力过程与矿产资源的形成[J].大地构造与成矿学,2003,27(1):3-21.
[21]成秋明.空间模式的广义自相似性分析和矿产资源评价[J].地球科学,2004,29(6):733-744.
[33]裴荣富,邱小平,尹冰川,等.成矿作用爆发异常及巨量金属堆积[J].矿床地质,1999,18(4):333-340.
[38]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.
[48]李庆谋,成秋明.分形奇异值分解方法与异常重建[J].地球科学,2004,29(1):109-118.
[49]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(3):337-348.
[52]赵鹏大.“三联式”资源定量预测与评价——数字找矿理论与实践探讨[J].地球科学,2002,27(5):482-489.
[2]Yu C.Complexity of geological systems—fundamental prob-lems of geosciences(I)[J].Earth Science,2002,27(5):509-519(in Chinese).
[3]Yu C.Chaos edge of large deposits and mineral districts[J].Earth Sciences Frontiers,1999,6(1):85-102(in Chinese).
[4]Feder J.Fractals[M].New York:PlenumPress,1988:283.
[5]Shore M,Fowler A D.The origin of spinifextexturein kom-atiites[J].Nature,1999,397:691-694.
[6]Cheng Q.The perimeter-area fractal model andits application in geology[J].Mathematical Geology,1995,27(7):64-77.
[7]Zhang Z,Mao H,Cheng Q.Fractal geometry of element dis-tribution on mineral surface[J].Mathematical Geology,2001,33(2):217-228.
[8]Wang Z,Cheng Q,Cao L,et al.Fractal modelling of the mi-crostructure property of quartz mylonite during deformation process[J].Mathematical Geology,2007,39(1):53-68.
[9]Mandelbrot B B.The fractal geometry of nature[M].Fran-cisco:W.H.Freeman San,1982:468.
[10]Cheng Q,Agterberg F P,Ballantyne S B.The separation of geochemical anomalies from background by fractal methods[J].Journal of Geochemical Exploration,1994,51:109-130.
[11]Turcotte D L.Fractals in petrology[J].Lithos,2002,65:261-271.
[12]Cheng Q.Non-linear mineral resources assessment models and unconventional mineral resources[J].Earth Science—Journal of China University of Geosciences,2003,28(4):445-454(in Chinese).
[13]Zhai Y.Earth system,metallogenic system to exploration system[J].Earth Science Frontiers,2007,14(1):173-181(in Chinese).
[14]Teng J.Dynamic process of substance and energy exchanges in depths of the Earth andformation of mineral resources[J].Geotectonica and Metallogenia,2003,27(1):3-21(in Chi-nese).
[15]Ottino J M,Muzzio F J,Tjahjadi M,et al.Chaos,symme-try,and self-similarity—exploiting order and disorder in mix-ing processes[J].Science,1992,257:754-760.
[16]Lovejoy S,Schertzer D,Ladoy P.Fractal characterization of inhomogeneous geophysical measuring networks[J].Nature,1987,319:43-44.
[17]Cheng Q,Xu Y,Grunsky E C.Integrated spatial and spec-trumanalysis for geochemical anomaly separation[J].Natu-ral Resources Research,2001,9:43-51.
[18]Cheng Q.A new model for quantifying anisotropic scale in-variance andfor decomposition of mixing patterns[J].Mathe-matical Geology,2004,36(3):345-360.
[19]Li Q,Cheng Q.Fractal singular-value(eigen-value)decom-position method for geophysical and geochemical anomaly re-construction[J].Earth Science,2004,29(1):109-118.
[20]Cheng Q.Multifractal modeling of eigenvalues and eigenvec-tors of2-D maps[J].Mathematical Geology,2005,37(8):915-927.
[21]Cheng Q.Generalized self-similarity analysis of spatial pat-terns and mineral resources assessments[J].Earth Science—Journal of China University of Geosciences,2004,29(6):733-744(in Chinese).
[22]Cheng Q.Mapping singularities with stream sediment geo-chemical data for prediction of undiscovered mineral deposits in Gejiu,Yunnan Province,China[J].Ore Geology Reviews,2007,32(1-2):314-324.
[23]Turcotte D L.Fractals and chaos in geology and geophysics[M].2nd edition.Cambridge:Cambridge University Press,1997.
[24]Schertzer D,Lovejoy S.Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative proces-ses[J].Journal of Geophysical Research,1987,92:9693-9714.
[25]Veneziano D.Multifractality of rainfall and scaling of intensi-ty-duration-frequency curves[J].Water Resources Research,2002,38(1):1-12.
[26]Sornette D.Critical phenomena in natural sciences:chaos,fractals,selforganization and disorder[M].2nd edition.New York:Springer,2004.
[27]Malamud B D,Turcotte D L,Barton C C.The1993Missis-sippi river flood:a one hundred or a one thousand year event[J]?Environmental&Engineering Geosciences,1996,2(4):479-486.
[28]Malamud B D,Turcotte D L,Guzzetti F,et al.Landslidein-ventories and their statistical properties[J].Earth Surface Processes Landforms,2004,29:687-711.
[29]Bak P,Chen K,Tang C.A forest-fire model and some thoughts on turbulence[J].Phys Let,1992,A14:297-300.
[30]Cheng Q.Multifractality and spatial statistics[J].Computers&Geosciences,1999,25:949-961.
[31]Cheng Q,Agterberg F P.Singularity analysis of ore-mineral and toxic trace elements in streamsediments[J].Computers&Geosciences(in press).
[32]Cheng Q.Modeling local scaling properties for multi-scale mapping[J].Vadose Zone Journal(in press).
[33]Cheng Q.Multifractal imaging filtering and decomposition methods in space,Fourier frequency,and eigen domains[J].Non-Linear Processes in Geophysics,2007,14:293-303.
[34]Pei R,Qiu X,Yin B,et al.The explosive anomaly of ore-forming processes and superaccumulation of metals[J].Min-eral Deposits,1999,18(4):333-340(in Chinese).
[35]Turcotte D L.Self-organized criticality:doesit have anythingto do with criticality andis it useful[J]?Nonlinear Processes in Geophysics,2001(8):193-196.
[36]Cheng Q.Multiplicative cascade mineralization processes and singular distribution of mineral deposit associated geochemical anomalies[M]∥Cheng Q,Bonham-Carter G.Proceedings of Annual Conference of the International Associationfor Math-ematical Geology(I AMG’05),GIS and Spatial Analysis,2005(1):297-302.
[37]Cheng Q.Fractal and multifractal modeling of hydrothermal mineral deposit spectrum:application to gold deposits in the Abitibi Area,Canada[J].Earth Science—Journal of China University of Geosciences,2003,14(3):199-206.
[38]Zhao P.Geological anomaly theory and mineral deposits pre-diction:advanced mineral resources assessment theory and methods[M].Beijing:Geological Publishing House,1998(in Chinese).
[39]Cheng Q.Discrete multifractals[J].Mathematical Geology,1997,29:245-266.
[40]Rudin W.Real and complex analysis[M].3rd edition.New York:McGraw-Hill Book Company,1987:434.
[41]Nottal L.Fractal space-time and microphysics-towards a the-ory of scale relativity[M].Singapore:World Scientific,1993:1-333.
[42]Mallet S,Hwang WL.Singularity detection and processing with wavelets,IEEE Trans[J].Information Theory,1992,38:617-643.
[43]Arneodo A,Argoul F,Bacry E,et al.Wavelet transformof fractals[C]∥Meyer Y,Marseille.Wavelets and applica-tions:Proceedings of the International Conference.Paris:Springer-Verlag,1992:287-352.
[44]Cheng Q,Agterberg F P,Bonham-Carter G F.Fractal pat-tern integration method for mineral potential mapping[J].Nonrenewable Resources,1996,5(2):117-130.
[45]Cheng Q.GIS based fractal/multifractal anomaly analysis for modeling and prediction of mineralization and mineral deposits[M]∥Jeff Harris.GIS applications in Earth Sciences.Geo-logical Association of Canada Special Book,2006:289-300.
[46]Schertzer D,Lovejoy S,Schmitt F,et al.Multifractal cas-cade dynamics and turbulent intermittency[J].Fractals,1997,5:427-471.
[47]Chao L,Cheng Q.Atentative integrated model of scale in-variant generator technique(SIG)and spectrum-area(S-A)technique[M]∥Cheng Q,Bonham-Cater G.Proceedings of I AMG’05:GIS and Spatial Analysis.International Associa-tion for Mathematical Geology.Wuhan:China University of Geosciences Press,2005:303-309.
[48]Li Q,Cheng Q.Fractal singular decomposition method and anomaly reconstruction[J].Earth Science—Journal of ChinaUniversity of Geosciences,2004,29(1):109-118(in Chi-nese).
[49]Cheng Q.New multifractal mineralization prediction theory and singularity-generalized self-similarity—fractal spectrum(3s)models[J].Earth Science—Journal of China University of Geosciences,2006,31(3):337-348(in Chinese).
[50]Agterberg F P.Multifractal simulation of geochemical map patterns[M]∥Merriam D F,Davis J C.Geologic modeling and simulation:sedimentary systems.New York:Kluwer,2001:327-346.
[51]Agterberg F P.New applications of the model of de Wijs in regional geochemistry[J].Mathematical Geology,2007,39(1):1-26.
[52]Zhao P.“Three components”mineral resources prediction and assessment—digital mineral deposit prospecting theory and practice[J].Earth Science—Journal of China University of Geosciences,2002,27(5):482-489(in Chinese).
[53]Bonham-Carter G F.Geographicinformation systems for geo-scientists:modelling with GIS[M].Oxford:Pergamon,1994:398.
[1]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.
[2]於崇文.地质系统的复杂性——地质科学的基本问题(Ⅰ)[J].地球科学,2002,27(5):509-519.
[3]於崇文.大型矿床和成矿区(带)在混沌边缘[J].地学前缘,1999,6(1):85-102.
[12]成秋明.非线性矿床模型与非常规矿产资源评价[J].地球科学,2003,28(4):445-454.
[13]翟裕生.地球系统、成矿系统到勘查系统[J].地学前缘,2007,14(1):173-181.
[14]滕吉文.地球深部物质与能量交换的动力过程与矿产资源的形成[J].大地构造与成矿学,2003,27(1):3-21.
[21]成秋明.空间模式的广义自相似性分析和矿产资源评价[J].地球科学,2004,29(6):733-744.
[33]裴荣富,邱小平,尹冰川,等.成矿作用爆发异常及巨量金属堆积[J].矿床地质,1999,18(4):333-340.
[38]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.
[48]李庆谋,成秋明.分形奇异值分解方法与异常重建[J].地球科学,2004,29(1):109-118.
[49]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(3):337-348.
[52]赵鹏大.“三联式”资源定量预测与评价——数字找矿理论与实践探讨[J].地球科学,2002,27(5):482-489.
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