胶东蚀变岩型金矿成矿元素聚集分形研究
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摘要
成矿元素品位分布具有不规则性和自相似性,适于用分形理论来研究其聚散规律。在确定布朗运动与分数布朗运动作为描述元素迁移过程的物理模型基础上,系统运用简单分形与多重分形对胶东典型蚀变岩型大尹格庄和大磨曲家金矿的成矿元素品位分布规律进行了研究,并进一步建立和运用分形分布模型来刻画元素分布的整体规律,最后将分形模型与其它地质方法相结合,对矿床的资源量进行了估算与预测。
通过简单分形模型参数动态分析对分维值地质意义进行了探讨,将其视为描述元素分布均一性和复杂性的变量;大尹格庄金矿特定中段不同勘探线元素分形特征的比较,发现无矿化区分维>矿化连续区分维值>矿化间断区分维值,表明元素品位分维值是元素富集尺度的一种重要标志;对大尹格庄金矿Ag-Pb-Zn-S-Cu五种成矿元素的简单分形分析,显示元素分维值大小关系与其聚类分析相关系数吻合较好。对金元素自仿射简单分形统计和重标极差分析验证了矿化区成矿元素品位分布具有长程相关性,等同于分数布朗运动,而无矿化区属于布朗运动,元素分布具有随机性。证明了广义谱的单调性、多重分形谱的凸凹性和当q→±∞时的极限性质,进而为利用多重分形理论研究地质问题提供理论依据;对大尹格庄金矿不同中段与勘探线成矿元素多重分形谱及大磨曲家金矿不同地质体中多种成矿元素聚散规律的分析,发现其可以较好的刻画元素的富集强度,并指示地质体物质继承性和元素的溶解—混合—迁移—沉淀过程;多重分形的结论与简单分形分析结果相对应,但是多重分形对元素分布规律有更为精细的刻画。
通过最大熵原理,建立了Weibull模型描述元素品位整体分布,其分布函数包括两个参数:α>0为形状参数,是数据集分维值,μ>0为尺度参数,是数据集均值;进一步引入Stable模型作为描述元素品位分布的统计模型,其特征函数包括以下四个参数:α为特征指数,β为偏斜指数,σ是尺度指数,μ是位置指数,特征指数在一定范围内是数据集分维值。Weibull分布对描述成矿元素品位分布的峰值具有优势,而Stable模型则在刻画成矿元素的厚尾特征方面具有较好效果。但总体而言,后者比前者能更为准确地拟合元素品位的整体分布。Weibull模型与Stable模型内置分形性,可以有效刻画品位分布的不规则性与自相似性,比经典正态与对数正态等统计模型更具普适性。
根据蚀变岩型矿床特征,建立了理想资源量模型和极限资源量模型,估算了大尹格庄金矿理想金属资源量和极限资源量。利用成矿元素品位分布分形统计与矿化网络、原生晕、成矿系统数值模拟等其它方法的有机组合,建立了矿床预测模型,并在大尹格庄金矿的深部隐伏矿体预测中取得了较好的效果,成矿预测模型中的分形特征主要体现在同一尺度的近似周期性与多尺度间的相似性。
通过自相似简单分形、自仿射分形和多重分形的系统分形统计计算,对分形不同分支的数学性质、物理意义、相互关系与应用效果做了较为全面的探索;以分维值为内在参量,提出描述元素分布及预测矿床资源量的普适性统计模型。本文研究证实分形理论及方法是对蚀变岩型金矿成矿元素数据深度挖掘的有效工具;分形与其它经典数学方法的有机组合,不但有利于对成矿元素聚散规律的深入剖析,还有利于新数学方法的创新。
The fractal theory is suitable for the analysis of the abundance distribution irregularity with self-similarity of metallogenic element. Based on the confirming the Brown Motion(BM) or the fractional Brown Motion(FBM) as the physical mechanism of the transport of metallogenic element, the single fractal and multi-fractal are utilized systemically to study the distribution pattern of metallogenic element in the Dayin'gezhuang and Damoqujia ore deposits, the typical altered rock type deposits in Jiaodong Peninsula. And then, the fractal distributing models are set up or introduced to describe the whole discipline of element's abundance distribution. Additional, the fractal method in conjunction with other geological ones is used for the reserve estimation of the two deposits.By means of the dynamic analysis of the single fractal dimension, indicating the fractal dimension can reflect the uniform degree of the element's abundance distribution. In the example analysis of different prospect lines in the certain level in Dayin'gezhuang deposit, it is shown that the dimension in non-mineralized zone is bigger than that in continuously mineralized zone, which is also bigger than the dimension in discontinuously mineralized zone. Furthermore, the value difference of fractal dimension of Ag-Pb-Zn-S-Cu five elements is in agreement with the correlation coefficient in their cluster analysis. The self-affine and rescaled range analysis of the gold element reveal the element distribution in the mineralized zone is with long range correlation and accords to FBM, while the element distribution in the unmineralized zone is completely random and falls into the scope of BM. The monotonicity of generalized spectrum, the convex function property of multi-fractal spectrum and its limit property in the condition of g→±∞ are proved for the more reliable application of multi-fractal theory. It is suggested that the shapes of the element's multi-fractal spectrums of the different prospect lines and levels in Dayin'gezhuang deposit and those of the different geologic bodies in Damoqujia deposit can reflect more accurate and comprehensive information of the element's concentration intensity than the simple fractal, such as the material inheriting of various geologic bodies and the process of dissolution-mixing-transport-deposition of metallogenic element.Via the maximum entropy analysis, the Weibull model is set up to describe the whole distribution of the elements and the distribution function of the model depicted by the two parameters, e.g. shape parameter (β ) and scale parameter(μ). The shape parameter (α > 0) and scale parameter( μ > 0) represent the fractal dimension and mean value of the data set respectively. Then, the Stable model, with four parameters including α (stable exponent or characteristic exponent, representing the fractal dimension of data set), β (decline exponent), α (scale exponent) and μ(position exponent), is introduced. The Weibull model is more predominant in describing the peak of density distribution of the data set than the Stable model, while the Stable model is more accurate in expressing the whole distribution, especially in the thick-tail part, than the other model. Since the Weibull and Stable models contain fractal property, they can describe the irregularity of element distribution much more efficiently than the traditional Normal distribution, Lognormal distribution etc..According to the fractal features of the abundance distribution of elements and the reserve distribution of orebodies in altered rock type deposits, the Ideal Reserve Model and the Ultimate Reserve Model are built, then the ideal metal reserve and the ultimate metal reserve in the Dayin'gezhuang deposit is properly estimated by means of the new models. Moreover, the exploration model is established on the basis of the combination of fractal method with the ones including the primary halo, the mineralized network, the numerical simulation of metallogenic system, etc., resulting in the successful detection of concealed orebodies in Dayin'gezhuang deposit. The fractal characteristic in the exploration model is manifested on the semi-periodicity in same scale and the similarity among different scales.In virtue of the systematic calculation of the self-similar simple fractal, self-affine fractal and multi-fractal, the mathematic property, physical sense, mutual relationship and application effect of these branched methods are clarified, and the fractal distribution models with fractal dimension as their core parameter are put forward for the universal statistical model describing the element's abundance distribution and estimating the reserve scale of the deposit. Through the study in this paper, it is suggested that the fractal theory is efficient in extracting deep-seated metallogenic information hidden in element data and that the joint application of the fractal methods with traditional geo-mathematic ones is favorable for the method's improvement and creation.
通过简单分形模型参数动态分析对分维值地质意义进行了探讨,将其视为描述元素分布均一性和复杂性的变量;大尹格庄金矿特定中段不同勘探线元素分形特征的比较,发现无矿化区分维>矿化连续区分维值>矿化间断区分维值,表明元素品位分维值是元素富集尺度的一种重要标志;对大尹格庄金矿Ag-Pb-Zn-S-Cu五种成矿元素的简单分形分析,显示元素分维值大小关系与其聚类分析相关系数吻合较好。对金元素自仿射简单分形统计和重标极差分析验证了矿化区成矿元素品位分布具有长程相关性,等同于分数布朗运动,而无矿化区属于布朗运动,元素分布具有随机性。证明了广义谱的单调性、多重分形谱的凸凹性和当q→±∞时的极限性质,进而为利用多重分形理论研究地质问题提供理论依据;对大尹格庄金矿不同中段与勘探线成矿元素多重分形谱及大磨曲家金矿不同地质体中多种成矿元素聚散规律的分析,发现其可以较好的刻画元素的富集强度,并指示地质体物质继承性和元素的溶解—混合—迁移—沉淀过程;多重分形的结论与简单分形分析结果相对应,但是多重分形对元素分布规律有更为精细的刻画。
通过最大熵原理,建立了Weibull模型描述元素品位整体分布,其分布函数包括两个参数:α>0为形状参数,是数据集分维值,μ>0为尺度参数,是数据集均值;进一步引入Stable模型作为描述元素品位分布的统计模型,其特征函数包括以下四个参数:α为特征指数,β为偏斜指数,σ是尺度指数,μ是位置指数,特征指数在一定范围内是数据集分维值。Weibull分布对描述成矿元素品位分布的峰值具有优势,而Stable模型则在刻画成矿元素的厚尾特征方面具有较好效果。但总体而言,后者比前者能更为准确地拟合元素品位的整体分布。Weibull模型与Stable模型内置分形性,可以有效刻画品位分布的不规则性与自相似性,比经典正态与对数正态等统计模型更具普适性。
根据蚀变岩型矿床特征,建立了理想资源量模型和极限资源量模型,估算了大尹格庄金矿理想金属资源量和极限资源量。利用成矿元素品位分布分形统计与矿化网络、原生晕、成矿系统数值模拟等其它方法的有机组合,建立了矿床预测模型,并在大尹格庄金矿的深部隐伏矿体预测中取得了较好的效果,成矿预测模型中的分形特征主要体现在同一尺度的近似周期性与多尺度间的相似性。
通过自相似简单分形、自仿射分形和多重分形的系统分形统计计算,对分形不同分支的数学性质、物理意义、相互关系与应用效果做了较为全面的探索;以分维值为内在参量,提出描述元素分布及预测矿床资源量的普适性统计模型。本文研究证实分形理论及方法是对蚀变岩型金矿成矿元素数据深度挖掘的有效工具;分形与其它经典数学方法的有机组合,不但有利于对成矿元素聚散规律的深入剖析,还有利于新数学方法的创新。
The fractal theory is suitable for the analysis of the abundance distribution irregularity with self-similarity of metallogenic element. Based on the confirming the Brown Motion(BM) or the fractional Brown Motion(FBM) as the physical mechanism of the transport of metallogenic element, the single fractal and multi-fractal are utilized systemically to study the distribution pattern of metallogenic element in the Dayin'gezhuang and Damoqujia ore deposits, the typical altered rock type deposits in Jiaodong Peninsula. And then, the fractal distributing models are set up or introduced to describe the whole discipline of element's abundance distribution. Additional, the fractal method in conjunction with other geological ones is used for the reserve estimation of the two deposits.By means of the dynamic analysis of the single fractal dimension, indicating the fractal dimension can reflect the uniform degree of the element's abundance distribution. In the example analysis of different prospect lines in the certain level in Dayin'gezhuang deposit, it is shown that the dimension in non-mineralized zone is bigger than that in continuously mineralized zone, which is also bigger than the dimension in discontinuously mineralized zone. Furthermore, the value difference of fractal dimension of Ag-Pb-Zn-S-Cu five elements is in agreement with the correlation coefficient in their cluster analysis. The self-affine and rescaled range analysis of the gold element reveal the element distribution in the mineralized zone is with long range correlation and accords to FBM, while the element distribution in the unmineralized zone is completely random and falls into the scope of BM. The monotonicity of generalized spectrum, the convex function property of multi-fractal spectrum and its limit property in the condition of g→±∞ are proved for the more reliable application of multi-fractal theory. It is suggested that the shapes of the element's multi-fractal spectrums of the different prospect lines and levels in Dayin'gezhuang deposit and those of the different geologic bodies in Damoqujia deposit can reflect more accurate and comprehensive information of the element's concentration intensity than the simple fractal, such as the material inheriting of various geologic bodies and the process of dissolution-mixing-transport-deposition of metallogenic element.Via the maximum entropy analysis, the Weibull model is set up to describe the whole distribution of the elements and the distribution function of the model depicted by the two parameters, e.g. shape parameter (β ) and scale parameter(μ). The shape parameter (α > 0) and scale parameter( μ > 0) represent the fractal dimension and mean value of the data set respectively. Then, the Stable model, with four parameters including α (stable exponent or characteristic exponent, representing the fractal dimension of data set), β (decline exponent), α (scale exponent) and μ(position exponent), is introduced. The Weibull model is more predominant in describing the peak of density distribution of the data set than the Stable model, while the Stable model is more accurate in expressing the whole distribution, especially in the thick-tail part, than the other model. Since the Weibull and Stable models contain fractal property, they can describe the irregularity of element distribution much more efficiently than the traditional Normal distribution, Lognormal distribution etc..According to the fractal features of the abundance distribution of elements and the reserve distribution of orebodies in altered rock type deposits, the Ideal Reserve Model and the Ultimate Reserve Model are built, then the ideal metal reserve and the ultimate metal reserve in the Dayin'gezhuang deposit is properly estimated by means of the new models. Moreover, the exploration model is established on the basis of the combination of fractal method with the ones including the primary halo, the mineralized network, the numerical simulation of metallogenic system, etc., resulting in the successful detection of concealed orebodies in Dayin'gezhuang deposit. The fractal characteristic in the exploration model is manifested on the semi-periodicity in same scale and the similarity among different scales.In virtue of the systematic calculation of the self-similar simple fractal, self-affine fractal and multi-fractal, the mathematic property, physical sense, mutual relationship and application effect of these branched methods are clarified, and the fractal distribution models with fractal dimension as their core parameter are put forward for the universal statistical model describing the element's abundance distribution and estimating the reserve scale of the deposit. Through the study in this paper, it is suggested that the fractal theory is efficient in extracting deep-seated metallogenic information hidden in element data and that the joint application of the fractal methods with traditional geo-mathematic ones is favorable for the method's improvement and creation.
引文
[1] Akpinar E.K, Akpinar S. Statistical analysis of wind energy potential on the basis of the Weibull and Rayleigh distributions for Agin-Elazig, Turkey[J]. Proc.Instn Mech.Engrs 2004, 218(A): 557-564.
[2] Balankin A.S, Susarrey O.H. A new statistical distribution function for self-affine crack roughness parameters[J]. Philosopcal Magazine Letters, 1999, 79(8): 629-637.
[3] Bening V.E, Korolev V Y, Kolokol'tsov V N. Estimation of Parameters of Fractional Stable Distributions[J].Journal of Mathematical Sciences, 2004, 123(1): 3722-3732.
[4] Caniego F.J, Espejo R, Mart in M A et al. Multifractal scaling of soil spatial variability[J].Ecological Modelling 2005, 182 291-303.
[5] Cargill S.M, Root D. H., Bailey E.H et al. Resource estimation from historical data: Mercury, a test case[J]. Math.Geol., 1980, 12: 489-522.
[6] Castroa J.J, Carsteanu A.A, Flores C G. Intensity-duration-area-frequency functions for precipitation in a multifractal framework [J]. Physiea A 2004, 338: 206-210.
[7] Chaudhari A, Yan C.S, Lee S.L. Multifraetal scaling analysis of autopoisoning reactions over a rough surfaee[J].Journal of Physics A: Mathematical and General, 2003, 36: 3757-3772.
[8] Cheng Q.M, Agterberg F.P, Ballantyne S.B. The Separation of Geochemical Anomalies from Background by Fractal Methods[J].J.Geoehem.Explor., 1994, 51(2): 109-130.
[9] Cheng Q.M.Agterberg F P. Multifraetal modeling and spatial point processes[J]. Math.Geol., 1995, 27: 831-845.
[10] Cheng Q.M. Discrete multifraetals[J]. Math Geol, 1997a, 9(2): 245-266.
[11] Cheng Q.M. Multifractal modeling and lacunarity analysis [J]. Math Geol, 1997b, 29: 919-932.
[12] Cheng Q.M. Multifractality and spatial statistics[J]. Computer & Geoseiences, 1999a, 25(9): 949-962.
[13] Cheng Q .M. Spatial and scaling modeling for geochemical anomaly separation [J]. Geochem Explor,1999b, 65: 175-194.
[14] Cheng Q .M. Markov processes and discrete multifraetals [J]. Math. Geol., 1999c, 31(4): 455-469.
[15] Cheng Q.M. Multifractal theory and geochemical element distribution pattern[J].Earth Science, 2000, 25(3): 311-318~
[16] Cheng Q.M. Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum: Application Gold Deposits in Abitibi Area,Ontario,Canada [J].Joumal of China University of GeoscienceS, 2003, 14(3): 199-206.
[17] Cummings A, O'sullivan G, Hanan W G et al. Multifractal analysis of selected rare-earth elements[J] Physical Jouranal B: At.Mol.Opt.Phys., 2001, 34: 2547-2573.
[18] Deng J, Fang Y, Yang L. Numerical modelling of ore-forming dynamics of fractal dispersive fluid systems[J]. Acta geologica sinica, 2001, 75(2): 220-232.
[19] Deng J, Yang L.Q, Sun Z.S, et al. Metallogenie Model of Gold Deposits of the Jiaodong Granite-Greenstone Belt[J]. Acta Geologica Siniea, 2003,77(4).
[20] Deng J, Huang D, Wang Q. The Formation Mechanism of the Drag Depressions and the Irregular Boundaries in Intraplate Deformation[J]. Acta Geologica Sinica, 2004, 78(1): 267-272.
[21] Fedl M. Global and Local Multiscale Analysis of Magnetic Susceptibility Data[J].Pure and Applied Geophysics, 2003, 160: 2399-2417.
[22] Gao X, Dodds R.H. Loading rate effects on parameters of the Weibull stress model for ferritic steels[J].Engineering Fracture Mechanics 2005, 72: 2416-2425.
[23] Hippolyte F, Johnp N. Tail Behavior, Modes and other Characteristics of Stable Distributions[J].Extremes, 1999,2(1): 39-58.
[24] Huillet T, Raynaud H.F. Rare events in a log-Weibull scenario Application to earthquake magnitude data[J]. The Eurpean Physical Journal B, 1999, 12: 457-469.
[25] Jun D, Yun F, Li W. Fuzzy comprehensive appraisal of concealed ore deposit [J]. Journal of China University of Geosciences, 2000, 11(2): 134-139.
[26] Kanji G.K, Arif O.H. Median rankit control chart for Weibull distribution [J].Total Quality Management 2001, 12(5): 629- 642.
[27] Katsev S, L'heureux I. Are Hurst exponents estimated from short or irregular time series meaningful[J].Computers & Geosciences 2003,29: 1085-1089.
[28] Katsuragi H. Evidence of multi-affinity in the Japanese stock market[J].Physica A: Statistical Mechanics and its Applications, 2000,278(1-2): 275.
[29] Kentwell D. J, Bloom L .M, Comber G. A. Improvements in Grade Tonnage Curve Prediction via Sequential Gaussian Fractal Simulation [J]. Mathematical Geology, 1999,31(3): 311-325.
[30] Khue P.N, Huseby O, Saucier A et al. Application of generalized multifractal analysis for characterization of geological formations [J]. J. Phys.: Condens.Matter 2002, 14 2347-2352.
[31] Kim T. S, Kim S. Singularity spectra of fractional Brownian motions as a multi-fractal[J] .Chaos, Solitons and Fractals, 2004, 19:613-619.
[32] Kolokoltsov V, Korolev V, Uchaikin V. Fractional Stable distribution[J] Journal of Mathematical Sciences, 2001,105(6): 2569-2576.
[33] Krvavich Y.V, Mishura Y.S. Differentiability Of Fractional Integrals Whose Kernels Contain Fractional Brownian Motions[J].Ukrainian Mathematical Journal, 2001, 53(1): 35-47.
[34] Lee J. Constrained maximum-entropy sampling[J].Operations Research, 1998,46(5): 655-664.
[35] Li C, Ma T, Shi J. Application of a fractal method relating concentrations and distances for separation of geochemical anomalies from background[J].Journal of Geochemical Exploration 2003, 77: 167-175.
[36] Liu H, Bodvarsson GS, Lu S. A Corrected and Generalized Successive Random Additions Algorithm for Simulating Fractional Levy Motions [J]. Mathematical Geology, 2004, 36(3): 361-378.
[37] Makeev M.A, Barabasi A.L. Effect of surface morphology on the sputtering yields. I. Ion sputtering from self-affine surfaces[J].Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2004,222(3-4): 316.
[38] Mandelbort B.B. Self-affine and fractal dimension [J]. Physica Scripta, 1985,32(4): 425-436.
[39] Mandelbort B.B. The fractals geometry of nature [M].New York: freeman, 1982.
[40] Marinelli C, Rachev S.T, Roll R. Subordinated Exchange Rate Models: Evidence for Heavy Tailed Distributions and Long-Range Dependence [J].Mathematical and Computer Modelling 2001, 34: 955-1001.
[41] Mcculloch J.H, Panton D.B. Precise tabulation of the maximally-skewed stable distributions and densities[J]. Computational Statistics & Data Analysis 1997,23:307-320.
[42] Mourzenko V. V, Thovert J. F, Adler P. M. Permeability of Self-Affine Fractures [J]. Transport in Porous Media 2001,45: 89-103.
[43] Nadarajah S. On the moments of the modified Weibull distribution [J]. Reliability Engineering and System Safety 2005,90: 114-117.
[44] Panahi A, Cheng Q.M, Bonham-Carter G F. Modelling lake sediment geochemical distribution using principal component, indicator kriging and multifractal power-spectrum analysis:a case study from Gowganda, Ontario [J]. Geochemistry: Exploration, Environment, Analysis, 2004,4: 59-70.
[45] Panas E. Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange [J]. Applied Financial Economics, 2001, 11: 395-402.
[46] Park H, Kima S, Chang H. Brownian dynamic simulation for the aggregation of charged particles [J].Aerosol Science 2001, 32:1369-1388.
[47] Pipiras V, Taqqu M. S. Decomposition of self-similar stable mixed moving averages[J]. Probab.Theory Relat. Fields 2002, 123: 412-452.
[48] Pocili S, Mendes R.S, Malacarne L C. q-exponential, Weibull, and q-Weibull distributions: an empirical analysis[J]. Physica A, 2003, 324:678-688.
[49] Rachev S, Han S. Portfolio management with stable distribution[J]. Math meth oper Res, 2000, 51: 341-352.
[50] Rao A .S. On joint Weibull probability density functions [J]. Applied Mathematics Letters 2005, 18: 1224-1227.
[51] Murad S. Taqqu. Stable non-Gaussian Random Processes [M].New York Chapman & Hall, 2000.
[52] Schmitt F.G. A causal multifractal stochastic equation and its statistical properties [J].The Eurpean Physical Jouranal B, 2003, 34: 85-98.
[53] Sengupta A, Roy S. Classification Rules for Stable Distfibutions[J].Mathematical and Computer Modelling.2001, 34:1073-1093.
[54] Shen W, Zhao P.D. The theoretical study of statistical fractal model and its application in mineral resource prediction [J]. computers & Geoscienees, 2002, 28(3): 369～376.
[55] Singh V.P. On Application of the Weibull Distribution in Hydrology[J]. Water Resources Managemenf 1987, 1: 33-43.
[56] Taleb A.A, Rao M.B, Zhang H. Periodic inspection plans: The case of Weibull distribution [J]. Metrika, 2003, 58: 15-30.
[57] Telesea L, Cuomo V, Lapenna V et al. Analysis of the time-scaling behaviour in the sequence of the aftershocks of the Bovec(?) Slovenia/April 12, 1998 earthquake[J].Physics of the Earth and Planetary Interiors 2000, 120:315-326.
[58] Tieling Z, Muqiao Z. Quantitative Study on Characteristics of the Weibull Distribution[J].Joumal of Beijing Institute of Technology[J].Journal of Beijing Institute of Technology, 1999, 8(4): 357-362.
[59] Voituriez R, Nechaev S. Multifraetality of entangled random walks and non-uniform hyperbolic spaces[J]. Joumal of Physics A: Mathematical and General, 2000, 33:5631-5652.
[60] Wang L.G., Qiu Y. M., McNaughton N.J.,et al. Constraints on crustal evolution and gold metallogeny in the Northwestem Jiaodong Penisula, China, from SHRIMP, U-Pb zircon studies of granitoids [J].Ore Geology Reviews, 1998,13:275-291.
[61] Wang X, Wen z, Huang Z.A. Capital Asset Pricing Model Under Stable Paretian Distributions in a Pure Exchange Economy[J]. Acta Mathematicae Applicatae Sinica, English Series, 2004, 20(04):675—684.
[62] Weron R. Levy-Stable Distributions Revisited: Tail Index >2 Does Not Exclude The Levy-Stable Regime[J]. Intemational Journal of Modem Physics C, 2001, 12(2): 209-223.
[63] Zhou T. H, Lu G. X. Tectonics, granitoids and mesozoic gold deposits in East Shandong, China[J]. Ore Geology Reviews, 2000, 16:71-90.
[64] 埃德加·E·彼得斯.分形市场分析:将混沌理论应用于投资与经济理论上[M](中译本).北京:经济科学出版社,2002.
[65] 敖力布,林鸿溢.分形学导论[M].呼和浩特:内蒙古人民出版社,1996.
[66] 岑况,於崇文.成矿流体的流动-反应-输运耦合与金属成矿[J].地学前缘,2001,(03):9-28.
[67] 陈建平,唐菊兴,李志军.混沌理论在三江北段成矿地质条件研究上的应用——以玉龙成矿带北段元素地球化学异常分析为例[J].地质与勘探,2003,39(3):1-4.
[68] 陈时军,David Harte,马丽等.新西兰地区地震活动时空分布的多重分形特征研究[J].地震学报,2003,(03):71-80.
[69] 陈时军,David Harte,王丽凤等.广义地震应变能释放的多重分形特征[J].地震学报,2003,(02):68-76.
[70] 陈彦光,刘继生.城市等级体系分形模型中的最大熵原理[J].自然科学进展,2001,11(11):1770-1774.
[71] 陈颙,陈凌.分形几何学[M].北京:地震出版社,1998.
[72] 陈永清,赵鹏大,刘红光.鲁西金矿成矿组分的聚集与演化[J].地球科学.中国地质大学学报,2001,(01):96-100.
[73] 成秋明.多维分形理论和地球化学元素分布规律[J].地球科学——中国地质大学学报,2000,3:311-318.
[74] 成秋明.多重分形与地质统计学方法用于勘查地球化学异常空间结构和奇异性分析[J].地球科学-中国地质大学学报,2001a,(02):36-45.
[75] 成秋明.空间自相似性与地球物理和地球化学场的分解方法[J].地球物理学进展,2001b,(02):9-18.
[76] 成秋明.从美国地球物理学会2001秋季年会谈非线性地球物理进展[J].地球物理学进展,2002,(02):173-176.
[77] 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-中国地质大学学报,2003,(04):85-94.
[78] 成秋明.空间模式的广义自相似性分析与矿产资源评价[J].地球科学-中国地质大学学报,2004,(06):106-116.
[79] 池顺都,赵鹏大.地质建造组合熵异常与找矿有利地段圈定[J].现代地质,2000:14(04):423-428.
[80] 邓军,陈学明,方云,等.粤北盆地流体系统及其矿化特征[J].地学前缘,2000,(03):95-102.
[81] 邓军,方云,杨立强,等.剪切蚀变与物质迁移及金的富集——以胶东矿集区为例[J].地球科学-中国地质大学学报,2000,(04):97-101.
[82] 邓军,方云,周显强,等.胶东半岛西北部金矿带成矿构造应力场及成矿微量元素分布特征研究[J].地球学报-中国地质科学院院报,1995,(01):10-21.
[83] 邓军,黄定华,王庆飞,等.铜陵矿集区印支-燕山期盖层形变场三维结构的实验重塑[J].中国科学D辑,2004a,(11):3-11.
[84] 邓军,王庆飞,杨立强,等.胶西北金矿集区成矿作用发生的地质背景[J].地学前缘,2004b,11(4):527-533.
[85] 邓军,孙忠实,王建平,等.动力系统转换与金成矿作用[J].矿床地质,2001,(01):71-77.
[86] 邓军,孙忠实,杨立强,等.吉林夹皮沟金矿带构造地球化学特征分析[J].高校地质学报,2000,(03):38-44.
[87] 邓军,王庆飞,杨立强,等.胶东西北部金热液成矿系统内部结构解析[J].地球科学-中国地质大学学报,2005,(03):49-54.
[88] 邓军,徐守札,孙希贤.模糊数学在胶东西北部金矿带成矿预测研究中的应用[J].现代地质,1994,(02):229-235.
[89] 邓军,杨立强,方云,等.成矿系统嵌套分形结构和自有序效应[J].地学前缘,2000,(01):134-147.
[90] 邓军,杨立强,刘伟,等.胶东招掖矿集区巨量金质来源和流体成矿效应[J].地质科学,2001,(03):4-15.
[91] 邓军,杨立强,孙忠实,等.胶东花岗-绿岩带金矿构造成矿动力学模型[J].地质学报,2003,(04):161.
[92] 邓军,翟裕生,杨立强,等.构造演化与成矿系统动力学——以胶东金矿集中区为例[J].地学前缘,1999,(02):122-130.
[93] 邓军,翟裕生,杨立强,等.论剪切带构造成矿系统[J].现代地质,1998,(04):38-45.
[94] 邓军,刘伟,孙忠实,等.幔源流体判别标志及多层循环成矿作用动力学—以山东夏甸金矿床为例[J].中国科学(D辑),2003a,46(增刊):96-104
[95] 邓军,吕古贤,杨立强,等.构造应力场转换与界面成矿[J].地球学报,1998,19(03):244-250.
[96] 邓军,杨立强,方云,等.成矿系统嵌套分形结构和自有序效应[J].地学前缘,2000,7(1):133-146.
[97] 邓军,杨立强,方云,等.胶东壳—幔相互作用与金成矿效应[J].地质科学,2000a,35(01):60-70.
[98] 董连科.分形动力学[M].沈阳:辽宁科学技术出版社,1994.
[99] 董连科.分形理论及其应用[M].沈阳:辽宁科学技术出版社,1991.
[100] 范增节,牛志仁,施行觉.岩石剖面线的自仿射分形研究[J].内陆地震,1992,6(02):188-190.
[101] 冯少彤,韩典荣,丁鹤平.用光学分数Fourier变换的方法测定自仿射分形的Hurst指数[J].中国科学G辑,2004,(02):28-33.
[102] 傅菁华,吴元芳,刘连寿.高能多粒子末态的多重分形维数与动力学起伏强度[J].高能物理与核物理,1999,(10):992-997.
[103] 顾娟,茆诗松.稳定分布的参数估计[J].应用概率统计,2002,(04):8-12.
[104] 郭科,施泽进,唐菊兴,等.用多重分形研究元素的共生组合性[J].电子科技大学学报,2004,(02):110-113.
[105] 韩茂安,顾圣士.非线性系统的理论和方法[M].北京:科学出版社,2001.
[106] 何玉梅,吴小平.地震序列自仿射分形及自相似分形的计算与比较[J].地震研究,1996,(04):363-370.
[107] 侯景儒,郭光裕.矿床统计预测及地质统计学的理论与应用[M].北京:冶金工业出版社,1993.
[108] 胡金艳,张太镒,张春梅.基于分数布朗运动和概率神经网络的自然纹理分类[J].电子与信息学报,2004,(03):55-59.
[109] 胡尊国,孟宪国.第一届全国分形理论与地质科学学术讨论会论文集[M].武汉:中国地质大学出版社,1993.
[110] 黄大富.关于可以表示成自仿射分形的生物体两种维数的计算[J].生物数学学报,1999,(04):435-439.
[111] 黄诒蓉.中国股市分形结构的理论研究与实证分析[博士学位论文]厦门:厦门大学,2004
[112] 江田汉,邓莲堂.Hurst指数估计中存在的若干问题[J].地理科学,2004,24(02):177-182.
[113] 蒋海昆,王忠民,刁守中,等.中强地震前后能量分布的自仿射特性[J].地震,1996,(02):33-41.
[114] 蒋仁言.威布尔模型族特性、参数估计和应用[M].北京:科学出版社,1998.
[115] 金友渔,赵鹏大.分形—判别非线性数学模型及勘探线剖面致矿地质异常分析[J].地质科技情报,2000,(02):100-103.
[116] 肯尼斯·法尔科内[英].分形几何—数学基础及其应用[M].沈阳:东北大学出版社,2003.
[117] 李长江,麻土华,徐有浪.地球化学景观吸引子的发现及其意义[J].浙江地质,1995,11(01):86-90.
[118] 李长江,麻土华,朱兴盛等.分形布朗运动与地球化学测量[J].地质评论,1999,45(01):76-84.
[119] 李长江,麻土华.矿产勘查中的分形、混沌与ANN[M].北京:地质出版社,1999.
[120] 汪富泉,李后强.分形几何与动力系统[M].哈尔滨:黑龙江教育出版社,1993年
[121] 李锰,朱令人,龙海英.天山地区地貌系统的自仿射分形与多重分形特征研究[J].中国地震,2002,(04):85-92.
[122] 李锰,朱令人,龙海英.新疆天山地区地貌分形与多重分形特征研究[J].内陆地震,2003,(01):21-27.
[123] 李平,胡可乐,汪秉宏.多重分形谱在材料分析中的应用研究[J].南京航空航天大学学报,2004,(01):79-83.
[124] 李强.大震过程中地壳形变的混沌和多重分形特征及其预报意义[J].地球物理学进展,1999,(01): 84-92.
[125] 李庆谋,成秋明.分形奇异(特征)值分解方法与地球物理和地球化学异常重建[J].地球科学-中国地质大学学报,2004,(01):109-118.
[126] 李曙光,E.Jagoutz,肖益林,等.大别山-苏鲁地体超高压变质年代学——I.Sm-Nd同位素体系[J].中国科学(D辑),1996,26(03):249-257.
[127] 李曙光,李惠民,陈移之,等.大别山-苏鲁地体超高压变质年代学——Ⅱ.锆石U-Pb同位素体系[J].中国科学(D辑),1997,27(03):200-206.
[128] 李新中,赵鹏大,肖克炎,等.矿床统计预测单元划分的方法与程序[J].矿床地质,1998,(04):82-88.
[129] 李旭涛,曹汉强,赵鸿燕.分形布朗运动模型及其在地形分析中的应用[J].华中科技大学学报(自然科学版),2003,(05):54-56.
[130] 林海燕,王恩元,刘贞堂.煤岩粒度分形分布规律探讨及应用[J].江苏煤炭,1995,(04):7-10,6.
[131] 林文蔚,赵一鸣,赵国红等.胶东金矿铅同位素地质特征及成矿年代讨论[J].长春科技大学学报,1999,29(02):117-121.
[132] 刘伯土,周维奎,夏遵义.岩性序列定量地层划分对比方法[J].石油实验地质,2000,(05):371-374.
[133] 刘长海,刘义高,张军.中强地震前后地震时间序列的自仿射分形特征[J].地震学报,1994,(03):352-360.
[134] 刘建明,张宏福,孙景贵等.山东幔源岩浆岩的碳—氧和锶釹同位素地球化学研究[J].中国科学,2003,33(10):921-930.
[135] 刘庆生,燕守勋,赵善仁.齐波夫金矿资源量预测[J].地质与勘探,1999,35(4):33-35.
[136] 刘式达.自然科学中的分形与混沌[M].北京:北京大学出版社,2003.
[137] 龙期威.金属中的分形与复杂性[M].上海:上海科学技术出版社,1999.
[138] 卢方元.中国股市收益率波动性研究[博士学位论文].四川:西南交通大学,2005
[139] 卢焕章,袁万春,张国平,等.玲珑-焦家地区主要金矿床稳定同位素及同位素年代学[J].桂林工学院学报.1999.19(01):1-8.
[140] 路东尚,林吉照,郭纯毓,等.招远金矿集中区地质与找矿[M],地震出版社,2002,174-177.
[141] 罗镇宽,关康,苗来成,等.招远—莱州地区花岗岩类继承锆石年龄及其意义[J].山东地质,1999,15(03):24-57.
[142] 曼德尔布洛特(法).分形对象——形、机遇和维数[M](中译本).北京:世界图书出版公司,1999.
[143] 毛景文,郝英,丁悌平.胶东金矿形成期间地幔流体参与成矿过程的碳氧氢同位素证据[J].矿床地质,2002,21(02):122-128
[144] 孟宪国,赵鹏大.论地质现象中的分形统计学[J].地球科学,1996 22(01):601-603
[145] 孟宪伟,张晓华.多标度分形与地球化学场分解[J].地球科学,1996 22(01):601-603
[146] 苗来成,罗镇宽,关康,等.玲珑花岗岩中锆石的离子质谱U-Pb年龄及其岩石学意义[J].岩石学报,1998,14(02):199-206.
[147] 邱天爽,李小兵,孙永梅,等.分数代阶α稳定分布及其应用中的若干问题[J].探测与控制学报,2004,(02):7-11.
[148] 曲晓明,王鹤年,饶冰.胶东群部分熔化实验及其对花岗岩成因的指示作用[J].地球化学,2000,19(02):154-161.
[149] 屈世显,张建华.复杂系统的分形理论与应用[M].西安:陕西人民出版社,1996.
[150] 申维,赵鹏大.分形统计模型的理论研究及其在地质学中的应用[J].地质科学,1998,33(02):234-242.
[151] 申维.n维自仿射分形及其在地球化学中的应用[J].地质论评,2005,51(2):208-211
[152] 申维.多维自仿射分布及其在地球化学中的应用[J].高校地质学报,1999,(1):60-66.
[153] 申维.分形混沌与矿产预测[M].北京:地质出版社,2002.
[154] 申维.矿化富集动力学模型及其在矿产预测中的应用[J].地学前缘,2000,7(1):189-194.
[155] 施行觉,许和明.岩石断面的自仿射分形及其分维的计算[J].中国地震,1992,8(3):1-6.
[156] 石博强,申焱华.机械故障诊断的分形方法[M].北京:冶金工业出版社,2001.
[157] 苏菲,谢维信,董进.时间序列中的多重分形分析[J].数据采集与处理,1997,(03):178-181.
[158] 孙华山,赵鹏大,张寿庭,等.基于5p成矿预测与定量评价的系统勘查理论与实践[J].地球科学-中国地质大学学报,2005,(03):16-20.
[159] 孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科学技术大学出版社,2003.10.
[160] 孙英君,王劲峰,柏延臣.地统计学方法进展研究[J].地球科学进展,2004,19(02):268-274.
[161] 谭凯旋,谢焱石,王清良,等.新疆阿尔泰地区断裂构造的多重分形特征及其对热液成矿的控制[J].地学前缘,2004,(04):115-116.
[162] 王国富,王志忠.应用统计[M].湖南长沙:中南大学出版社,2003,7.
[163] 王建华,王玉玲,柯开明.中国股票收益率的稳定分布拟合与检验[J].武汉理工大学学报,2003,(10):101-104.
[164] 王金安,谢和平.岩石断裂面的各向异性分形和多重分形研究[J].岩土工程学报,1998,(06):19-24.
[165] 王祖伟,周永章,姚东良,等.两广庞西垌—金山成矿带银金矿床分形性研究[J].矿床地质,1999,18(02):183-188.
[166] 魏民,赵鹏大,刘红光,等.中国岩金矿床品位-吨位模型研究[J].地球科学-中国地质大学学报,2001,(01):43-50.
[167] 魏民,赵鹏大.试论矿化空间分布的有序性规律及矿体定位预测[J].地球科学-中国地质大学学报,1995,(02):144-148.
[168] 文志英.分形几何的数学基础[M].上海:上海科技教育出版社,2000.
[169] 吴根耀,马力,陈焕疆,等.苏皖地块构造演化、苏鲁造山带形成及其耦合的盆地发育[J].大地构造与成矿学,2003,27(04):337-353.
[170] 吴敏金.分形信息导论[M].上海:上海科学技术文献出版社,1994.
[171] 夏庆霖,张寿庭,赵鹏大,等.幂律度与成矿预测[J].成都理工大学学报(自然科学版),2003,(03):65-69.
[172] 肖斌,赵鹏大,陈玉玲,等.时空多元协同克立格的理论研究[J].物探化探计算技术,1998,(01):2-9.
[173] 肖斌,赵鹏大,侯景儒.纯时间域多元信息地质统计学[J].物探化探计算技术,1998,(03):14-21.
[174] 肖斌,赵鹏大,侯景儒.现代地质统计学的新进展[J].世界地质,1999a(03):82-88+92.
[175] 肖斌,赵鹏大,侯景儒.时空域中的指示克立格理论研究[J].地质与勘探,1999b,(04):27-30.
[176] 肖斌,赵鹏大,周龙茂.归来庄金矿床w(Au)/w(Ag)异常的地质统计学研究[J].地球科学-中国地质大学学报,2000a,(01):81-84.
[177] 肖斌,赵鹏大,侯景儒.地质统计学新进展[J].地球科学进展,2000b,(03):54-57.
[178] 肖斌,赵鹏大,侯景儒.归来庄金矿床综合化探金异常的地质统计学研究[J].北京大学学报(自然科学版),2000c,(04):95-102.
[179] 肖克炎,李景朝,陈郑辉等.中国铜矿床品位吨位模型[J].地质论评,2004,50(01):50-55.
[180] 谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京:科学出版社,1997.
[181] 谢和平.分形几何:数学基础与应用[M].重庆:重庆大学出版社,1991.
[182] 谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.
[183] 谢淑云,鲍征宇,苏江玉,等.新疆塔里木盆地艾协克-桑塔木南地区油气地球化学指标的多重分形性分析[J].地质论评,2005,(01):107-112.
[184] 谢淑云,鲍征宇.多重分形与地球化学元素的分布规律[J].地质地球化学,2003,(03):98-103.
[185] 谢文录,谢维信.几种分形参数估计方法的性能分析和比较[J].西安电子科技大学学报,1997b,(02):17-24.
[186] 谢文录,谢维信.时间序列中的分形分析和参数提取[J].信号处理,1997a,(02):97-104.
[187] 辛厚文.分形理论及其应用[M].合肥:中国科学技术大学出版社,1993.
[188] 邢君,孙洪泉,李维涛.岩土性质的空间信息统计分析[J].岩土工程技术,2004,(01):7-9.
[189] 熊刚,赵惠昌,梁彦.基于分形自仿射特性的混沌预测方法研究[J].现代雷达,2004,(04):40-44.
[190] 徐贵忠,周瑞,闫臻,等.论胶东地区中生代岩石圈减薄的证据及其动力学机制[J].大地构造与成矿学,2001,25(04):368-380.
[191] 徐绪松,马莉莉,陈彦斌.R/S分析的理论基础:分数布朗运动[J].武汉大学学报(理学版),2004,(05):20-23.
[192] 杨进辉,周新华,陈立辉.胶东地区破碎带蚀变岩型金矿时代的测定及其地质意义[J].岩石学报,2000,16(03):454-458.
[193] 杨文采,余长青.根据地球物理资料分析大别—苏鲁超高压变质带演化的运动学与动力学[J].地球物理学报,2001,44(03):347-359.
[194] 杨展如.分形物理学[M].上海:上海科技教育出版社;1996.
[195] 叶中行,曹奕剑.Hurst指数在股票市场有效性分析中的应用[J].系统工程,2001,19(03):21-24.
[196] 仪垂样.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.
[197] 殷勇.稳定分布假设及投资组合模型研究[J].数量经济技术经济研究,1996,(11):61-65.
[198] 於崇文.成矿动力系统在混沌边缘分形生长——一种新的成矿理论与方法论(上)[J].地学前缘,2001a,(03):9-28.
[199] 於崇文.成矿动力系统在混沌边缘分形生长——一种新的成矿理论与方法论(下)[J].地学前缘,2001b,(04):471-489.
[200] 於崇文.大型矿床和成矿区(带)在混沌边缘[J].地学前缘,1999,6(01):85-101.
[201] 於崇文.地球化学系统的复杂性探索[J].地球科学-中国地质大学学报,1994,(03):7-10.
[202] 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-中国地质大学学报,2002,27(05):509-519.
[203] 於崇文.地质系统的复杂性——地质科学的基本问题(Ⅱ)[J].地球科学-中国地质大学学报,2003,(07):36-41.
[204] 於崇文.多重水力断裂的分形扩张[J].地学前缘,2004,(03):16-40.
[205] 於崇文.揭示地质现象的本质与核心——地质作用与时-空结构[J].地学前缘,2000,(02):2-37.
[206] 於崇文.数学地质的方法与应用[M].北京:冶金工业出版社,1980.
[207] 曾秋华,李后强.多标度分形上的输运方程[J].高压物理学报,1999,(03):48-54.
[208] 张东晖,杨浩,施明恒.多孔介质分形模型的难点与探索[J].东南大学学报(自然科学版),2002,(05):10-15.
[209] 张连昌,沈远超,李厚民,等.胶东地区金矿床流体包裹体的He、Ar同位素组成及成矿流体来源示踪[J].岩石学报,2002,18(04):559-565
[210] 张均,周乔伟.川西北地区控矿断裂的分形特征及其预测意义[J].长春科技大学学报,2000,30(04):26-27+30.
[211] 张强,马润年,许进.1/f过程与稳定分布过程的关系[J].系统工程与电子技术,2001,(12):342-27+30.
[212] 张寿庭,赵鹏大,陈建平,等.多目标矿产预测评价及其研究意义[J].成都理工大学学报(自然科学版),2003,(06):42-44+103.
[213] 张卫东,葛洪魁,唐治平,等.疏松砂岩储层粒度分形分布研究及应用[J].石油钻探技术,2003,(06):22-24.
[214] 张哲儒,毛华海.分形理论与成矿作用[J].地学前缘,2000,7(01):195-204.
[215] 赵鹏大,陈建平,陈建国.成矿多样性与矿床谱系[J].地球科学-中国地质大学学报,2001,(05):72-77.
[216] 赵鹏大,陈建平,张寿庭.“三联式”成矿预测新进展[J].地学前缘,2003,(05):4-5+14.
[217] 赵鹏大,陈建平.21世纪矿产资源经济展望[J].自然资源学报,2000,(03):1-4
[218] 赵鹏大,陈建平.地质异常理论与遥感地质研究[J].大自然探索,1996,(02):29-34.
[219] 赵鹏大,陈建平.非传统矿产资源体系及其关键科学问题[J].地球科学进展,2000,(03):12-16.
[220] 赵鹏大,陈永清,刘吉平.地质异常成矿预测理论与实践[M].北京:中国地质大学出版社1999.
[221] 赵鹏大,陈永清.地质异常矿体定位的基本途径[J].地球科学-中国地质大学学报,1998,(02):5-8.
[222] 赵鹏大,陈永清.基于地质异常单元金矿找矿有利地段圈定与评价[J].地球科学-中国地质大学学报,1999,(05):443-448.
[223] 赵鹏大,池顺都,陈永清.查明地质异常:成矿预测的基础[J].高校地质学报,1996,(04):2-14.
[224] 赵鹏大,池顺都.当今矿产勘探问题的思考[J].地球科学-中国地质大学学报,1998,(01):72-76.
[225] 赵鹏大,胡旺亮,李紫金.矿床统计预测[M].北京:地质出版社,1994.
[226] 赵鹏大,王京贵,饶明辉,等.中国地质异常[J].地球科学-中国地质大学学报,1995,(02):117-127.
[227] 赵鹏大,张寿庭,陈建平.危机矿山可接替资源预测评价若干问题探讨[J].成都理工大学学报(自然科学版),2004,(Z1):16-18.
[228] 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-中国地质大学学报,2002,(03):64-68+89.
[229] 赵鹏大.当今地学高新技术应用及发展态势[J].国土资源科技管理,1995,(05):48-59+35.
[230] 赵鹏大.地球科学的新使命——认知和发现非传统矿产资源[J].地球物理学进展,2001,(05):1-10.
[231] 赵鹏大.地质勘探中的统计分析[M].武汉:中国地质大学出版社,1990.
[232] 赵鹏大.定量地学方法及应用[M].北京:高等教育出版社,2004.
[233] 赵鹏大.非传统矿产资源研究:可持续发展的重要课题[J].中国地质,2001,(03):89-95.
[234] 赵阳升,马宇,段康廉.岩层裂缝分形分布相关规律研究[J].岩石力学与工程学报,2002,(02):219-222.
[235] 周宏昆,丁宗强,雷祖志等.金属矿床大比例尺定量预测[M].北京:地质出版社,1993.
[236] 周洪涛,费奇.基于分形分布的投资组合选择理论研究[J].科技进步与对策,2003,(03):115-116.
[237] 周炜星,王延杰,于遵宏.多重分形奇异谱的几何特性I.经典Renyi定义法[J].华东理工大学学报,2000,(04):57-61.
[238] 周炜星,吴韬,于遵宏.多重分形奇异谱的几何特性Ii.配分函数法[J].华东理工大学学报,2000,(04):62-67.
[239] 周越,杨杰.基于多重分形模型的非高斯信号建模[J].上海交通大学学报,2002,(08):63-67.
[240] 邹新月,许涤龙.H指数估计方法的有效性检验[J].统计研究,2004,(08):37-39.
[241] 朱光,宋传中,牛漫兰,等.郯庐断裂带的岩石圈结构及其成因分析[J].高校地质学报,2002,8(03):249-256.
[242] 朱光,王道轩,刘国生,等.郯庐断裂带的伸展活动及其动力学背景[J].地质科学,2001,36(3):269-278.
[243] 朱炬波,梁甸农.组合分形Brown运动模型[J].中国科学(E辑),2002,30(04):312-319.
[244] 朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算[J].地震,2000,(03):2-9.
[2] Balankin A.S, Susarrey O.H. A new statistical distribution function for self-affine crack roughness parameters[J]. Philosopcal Magazine Letters, 1999, 79(8): 629-637.
[3] Bening V.E, Korolev V Y, Kolokol'tsov V N. Estimation of Parameters of Fractional Stable Distributions[J].Journal of Mathematical Sciences, 2004, 123(1): 3722-3732.
[4] Caniego F.J, Espejo R, Mart in M A et al. Multifractal scaling of soil spatial variability[J].Ecological Modelling 2005, 182 291-303.
[5] Cargill S.M, Root D. H., Bailey E.H et al. Resource estimation from historical data: Mercury, a test case[J]. Math.Geol., 1980, 12: 489-522.
[6] Castroa J.J, Carsteanu A.A, Flores C G. Intensity-duration-area-frequency functions for precipitation in a multifractal framework [J]. Physiea A 2004, 338: 206-210.
[7] Chaudhari A, Yan C.S, Lee S.L. Multifraetal scaling analysis of autopoisoning reactions over a rough surfaee[J].Journal of Physics A: Mathematical and General, 2003, 36: 3757-3772.
[8] Cheng Q.M, Agterberg F.P, Ballantyne S.B. The Separation of Geochemical Anomalies from Background by Fractal Methods[J].J.Geoehem.Explor., 1994, 51(2): 109-130.
[9] Cheng Q.M.Agterberg F P. Multifraetal modeling and spatial point processes[J]. Math.Geol., 1995, 27: 831-845.
[10] Cheng Q.M. Discrete multifraetals[J]. Math Geol, 1997a, 9(2): 245-266.
[11] Cheng Q.M. Multifractal modeling and lacunarity analysis [J]. Math Geol, 1997b, 29: 919-932.
[12] Cheng Q.M. Multifractality and spatial statistics[J]. Computer & Geoseiences, 1999a, 25(9): 949-962.
[13] Cheng Q .M. Spatial and scaling modeling for geochemical anomaly separation [J]. Geochem Explor,1999b, 65: 175-194.
[14] Cheng Q .M. Markov processes and discrete multifraetals [J]. Math. Geol., 1999c, 31(4): 455-469.
[15] Cheng Q.M. Multifractal theory and geochemical element distribution pattern[J].Earth Science, 2000, 25(3): 311-318~
[16] Cheng Q.M. Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum: Application Gold Deposits in Abitibi Area,Ontario,Canada [J].Joumal of China University of GeoscienceS, 2003, 14(3): 199-206.
[17] Cummings A, O'sullivan G, Hanan W G et al. Multifractal analysis of selected rare-earth elements[J] Physical Jouranal B: At.Mol.Opt.Phys., 2001, 34: 2547-2573.
[18] Deng J, Fang Y, Yang L. Numerical modelling of ore-forming dynamics of fractal dispersive fluid systems[J]. Acta geologica sinica, 2001, 75(2): 220-232.
[19] Deng J, Yang L.Q, Sun Z.S, et al. Metallogenie Model of Gold Deposits of the Jiaodong Granite-Greenstone Belt[J]. Acta Geologica Siniea, 2003,77(4).
[20] Deng J, Huang D, Wang Q. The Formation Mechanism of the Drag Depressions and the Irregular Boundaries in Intraplate Deformation[J]. Acta Geologica Sinica, 2004, 78(1): 267-272.
[21] Fedl M. Global and Local Multiscale Analysis of Magnetic Susceptibility Data[J].Pure and Applied Geophysics, 2003, 160: 2399-2417.
[22] Gao X, Dodds R.H. Loading rate effects on parameters of the Weibull stress model for ferritic steels[J].Engineering Fracture Mechanics 2005, 72: 2416-2425.
[23] Hippolyte F, Johnp N. Tail Behavior, Modes and other Characteristics of Stable Distributions[J].Extremes, 1999,2(1): 39-58.
[24] Huillet T, Raynaud H.F. Rare events in a log-Weibull scenario Application to earthquake magnitude data[J]. The Eurpean Physical Journal B, 1999, 12: 457-469.
[25] Jun D, Yun F, Li W. Fuzzy comprehensive appraisal of concealed ore deposit [J]. Journal of China University of Geosciences, 2000, 11(2): 134-139.
[26] Kanji G.K, Arif O.H. Median rankit control chart for Weibull distribution [J].Total Quality Management 2001, 12(5): 629- 642.
[27] Katsev S, L'heureux I. Are Hurst exponents estimated from short or irregular time series meaningful[J].Computers & Geosciences 2003,29: 1085-1089.
[28] Katsuragi H. Evidence of multi-affinity in the Japanese stock market[J].Physica A: Statistical Mechanics and its Applications, 2000,278(1-2): 275.
[29] Kentwell D. J, Bloom L .M, Comber G. A. Improvements in Grade Tonnage Curve Prediction via Sequential Gaussian Fractal Simulation [J]. Mathematical Geology, 1999,31(3): 311-325.
[30] Khue P.N, Huseby O, Saucier A et al. Application of generalized multifractal analysis for characterization of geological formations [J]. J. Phys.: Condens.Matter 2002, 14 2347-2352.
[31] Kim T. S, Kim S. Singularity spectra of fractional Brownian motions as a multi-fractal[J] .Chaos, Solitons and Fractals, 2004, 19:613-619.
[32] Kolokoltsov V, Korolev V, Uchaikin V. Fractional Stable distribution[J] Journal of Mathematical Sciences, 2001,105(6): 2569-2576.
[33] Krvavich Y.V, Mishura Y.S. Differentiability Of Fractional Integrals Whose Kernels Contain Fractional Brownian Motions[J].Ukrainian Mathematical Journal, 2001, 53(1): 35-47.
[34] Lee J. Constrained maximum-entropy sampling[J].Operations Research, 1998,46(5): 655-664.
[35] Li C, Ma T, Shi J. Application of a fractal method relating concentrations and distances for separation of geochemical anomalies from background[J].Journal of Geochemical Exploration 2003, 77: 167-175.
[36] Liu H, Bodvarsson GS, Lu S. A Corrected and Generalized Successive Random Additions Algorithm for Simulating Fractional Levy Motions [J]. Mathematical Geology, 2004, 36(3): 361-378.
[37] Makeev M.A, Barabasi A.L. Effect of surface morphology on the sputtering yields. I. Ion sputtering from self-affine surfaces[J].Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2004,222(3-4): 316.
[38] Mandelbort B.B. Self-affine and fractal dimension [J]. Physica Scripta, 1985,32(4): 425-436.
[39] Mandelbort B.B. The fractals geometry of nature [M].New York: freeman, 1982.
[40] Marinelli C, Rachev S.T, Roll R. Subordinated Exchange Rate Models: Evidence for Heavy Tailed Distributions and Long-Range Dependence [J].Mathematical and Computer Modelling 2001, 34: 955-1001.
[41] Mcculloch J.H, Panton D.B. Precise tabulation of the maximally-skewed stable distributions and densities[J]. Computational Statistics & Data Analysis 1997,23:307-320.
[42] Mourzenko V. V, Thovert J. F, Adler P. M. Permeability of Self-Affine Fractures [J]. Transport in Porous Media 2001,45: 89-103.
[43] Nadarajah S. On the moments of the modified Weibull distribution [J]. Reliability Engineering and System Safety 2005,90: 114-117.
[44] Panahi A, Cheng Q.M, Bonham-Carter G F. Modelling lake sediment geochemical distribution using principal component, indicator kriging and multifractal power-spectrum analysis:a case study from Gowganda, Ontario [J]. Geochemistry: Exploration, Environment, Analysis, 2004,4: 59-70.
[45] Panas E. Estimating fractal dimension using stable distributions and exploring long memory through ARFIMA models in Athens Stock Exchange [J]. Applied Financial Economics, 2001, 11: 395-402.
[46] Park H, Kima S, Chang H. Brownian dynamic simulation for the aggregation of charged particles [J].Aerosol Science 2001, 32:1369-1388.
[47] Pipiras V, Taqqu M. S. Decomposition of self-similar stable mixed moving averages[J]. Probab.Theory Relat. Fields 2002, 123: 412-452.
[48] Pocili S, Mendes R.S, Malacarne L C. q-exponential, Weibull, and q-Weibull distributions: an empirical analysis[J]. Physica A, 2003, 324:678-688.
[49] Rachev S, Han S. Portfolio management with stable distribution[J]. Math meth oper Res, 2000, 51: 341-352.
[50] Rao A .S. On joint Weibull probability density functions [J]. Applied Mathematics Letters 2005, 18: 1224-1227.
[51] Murad S. Taqqu. Stable non-Gaussian Random Processes [M].New York Chapman & Hall, 2000.
[52] Schmitt F.G. A causal multifractal stochastic equation and its statistical properties [J].The Eurpean Physical Jouranal B, 2003, 34: 85-98.
[53] Sengupta A, Roy S. Classification Rules for Stable Distfibutions[J].Mathematical and Computer Modelling.2001, 34:1073-1093.
[54] Shen W, Zhao P.D. The theoretical study of statistical fractal model and its application in mineral resource prediction [J]. computers & Geoscienees, 2002, 28(3): 369～376.
[55] Singh V.P. On Application of the Weibull Distribution in Hydrology[J]. Water Resources Managemenf 1987, 1: 33-43.
[56] Taleb A.A, Rao M.B, Zhang H. Periodic inspection plans: The case of Weibull distribution [J]. Metrika, 2003, 58: 15-30.
[57] Telesea L, Cuomo V, Lapenna V et al. Analysis of the time-scaling behaviour in the sequence of the aftershocks of the Bovec(?) Slovenia/April 12, 1998 earthquake[J].Physics of the Earth and Planetary Interiors 2000, 120:315-326.
[58] Tieling Z, Muqiao Z. Quantitative Study on Characteristics of the Weibull Distribution[J].Joumal of Beijing Institute of Technology[J].Journal of Beijing Institute of Technology, 1999, 8(4): 357-362.
[59] Voituriez R, Nechaev S. Multifraetality of entangled random walks and non-uniform hyperbolic spaces[J]. Joumal of Physics A: Mathematical and General, 2000, 33:5631-5652.
[60] Wang L.G., Qiu Y. M., McNaughton N.J.,et al. Constraints on crustal evolution and gold metallogeny in the Northwestem Jiaodong Penisula, China, from SHRIMP, U-Pb zircon studies of granitoids [J].Ore Geology Reviews, 1998,13:275-291.
[61] Wang X, Wen z, Huang Z.A. Capital Asset Pricing Model Under Stable Paretian Distributions in a Pure Exchange Economy[J]. Acta Mathematicae Applicatae Sinica, English Series, 2004, 20(04):675—684.
[62] Weron R. Levy-Stable Distributions Revisited: Tail Index >2 Does Not Exclude The Levy-Stable Regime[J]. Intemational Journal of Modem Physics C, 2001, 12(2): 209-223.
[63] Zhou T. H, Lu G. X. Tectonics, granitoids and mesozoic gold deposits in East Shandong, China[J]. Ore Geology Reviews, 2000, 16:71-90.
[64] 埃德加·E·彼得斯.分形市场分析:将混沌理论应用于投资与经济理论上[M](中译本).北京:经济科学出版社,2002.
[65] 敖力布,林鸿溢.分形学导论[M].呼和浩特:内蒙古人民出版社,1996.
[66] 岑况,於崇文.成矿流体的流动-反应-输运耦合与金属成矿[J].地学前缘,2001,(03):9-28.
[67] 陈建平,唐菊兴,李志军.混沌理论在三江北段成矿地质条件研究上的应用——以玉龙成矿带北段元素地球化学异常分析为例[J].地质与勘探,2003,39(3):1-4.
[68] 陈时军,David Harte,马丽等.新西兰地区地震活动时空分布的多重分形特征研究[J].地震学报,2003,(03):71-80.
[69] 陈时军,David Harte,王丽凤等.广义地震应变能释放的多重分形特征[J].地震学报,2003,(02):68-76.
[70] 陈彦光,刘继生.城市等级体系分形模型中的最大熵原理[J].自然科学进展,2001,11(11):1770-1774.
[71] 陈颙,陈凌.分形几何学[M].北京:地震出版社,1998.
[72] 陈永清,赵鹏大,刘红光.鲁西金矿成矿组分的聚集与演化[J].地球科学.中国地质大学学报,2001,(01):96-100.
[73] 成秋明.多维分形理论和地球化学元素分布规律[J].地球科学——中国地质大学学报,2000,3:311-318.
[74] 成秋明.多重分形与地质统计学方法用于勘查地球化学异常空间结构和奇异性分析[J].地球科学-中国地质大学学报,2001a,(02):36-45.
[75] 成秋明.空间自相似性与地球物理和地球化学场的分解方法[J].地球物理学进展,2001b,(02):9-18.
[76] 成秋明.从美国地球物理学会2001秋季年会谈非线性地球物理进展[J].地球物理学进展,2002,(02):173-176.
[77] 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-中国地质大学学报,2003,(04):85-94.
[78] 成秋明.空间模式的广义自相似性分析与矿产资源评价[J].地球科学-中国地质大学学报,2004,(06):106-116.
[79] 池顺都,赵鹏大.地质建造组合熵异常与找矿有利地段圈定[J].现代地质,2000:14(04):423-428.
[80] 邓军,陈学明,方云,等.粤北盆地流体系统及其矿化特征[J].地学前缘,2000,(03):95-102.
[81] 邓军,方云,杨立强,等.剪切蚀变与物质迁移及金的富集——以胶东矿集区为例[J].地球科学-中国地质大学学报,2000,(04):97-101.
[82] 邓军,方云,周显强,等.胶东半岛西北部金矿带成矿构造应力场及成矿微量元素分布特征研究[J].地球学报-中国地质科学院院报,1995,(01):10-21.
[83] 邓军,黄定华,王庆飞,等.铜陵矿集区印支-燕山期盖层形变场三维结构的实验重塑[J].中国科学D辑,2004a,(11):3-11.
[84] 邓军,王庆飞,杨立强,等.胶西北金矿集区成矿作用发生的地质背景[J].地学前缘,2004b,11(4):527-533.
[85] 邓军,孙忠实,王建平,等.动力系统转换与金成矿作用[J].矿床地质,2001,(01):71-77.
[86] 邓军,孙忠实,杨立强,等.吉林夹皮沟金矿带构造地球化学特征分析[J].高校地质学报,2000,(03):38-44.
[87] 邓军,王庆飞,杨立强,等.胶东西北部金热液成矿系统内部结构解析[J].地球科学-中国地质大学学报,2005,(03):49-54.
[88] 邓军,徐守札,孙希贤.模糊数学在胶东西北部金矿带成矿预测研究中的应用[J].现代地质,1994,(02):229-235.
[89] 邓军,杨立强,方云,等.成矿系统嵌套分形结构和自有序效应[J].地学前缘,2000,(01):134-147.
[90] 邓军,杨立强,刘伟,等.胶东招掖矿集区巨量金质来源和流体成矿效应[J].地质科学,2001,(03):4-15.
[91] 邓军,杨立强,孙忠实,等.胶东花岗-绿岩带金矿构造成矿动力学模型[J].地质学报,2003,(04):161.
[92] 邓军,翟裕生,杨立强,等.构造演化与成矿系统动力学——以胶东金矿集中区为例[J].地学前缘,1999,(02):122-130.
[93] 邓军,翟裕生,杨立强,等.论剪切带构造成矿系统[J].现代地质,1998,(04):38-45.
[94] 邓军,刘伟,孙忠实,等.幔源流体判别标志及多层循环成矿作用动力学—以山东夏甸金矿床为例[J].中国科学(D辑),2003a,46(增刊):96-104
[95] 邓军,吕古贤,杨立强,等.构造应力场转换与界面成矿[J].地球学报,1998,19(03):244-250.
[96] 邓军,杨立强,方云,等.成矿系统嵌套分形结构和自有序效应[J].地学前缘,2000,7(1):133-146.
[97] 邓军,杨立强,方云,等.胶东壳—幔相互作用与金成矿效应[J].地质科学,2000a,35(01):60-70.
[98] 董连科.分形动力学[M].沈阳:辽宁科学技术出版社,1994.
[99] 董连科.分形理论及其应用[M].沈阳:辽宁科学技术出版社,1991.
[100] 范增节,牛志仁,施行觉.岩石剖面线的自仿射分形研究[J].内陆地震,1992,6(02):188-190.
[101] 冯少彤,韩典荣,丁鹤平.用光学分数Fourier变换的方法测定自仿射分形的Hurst指数[J].中国科学G辑,2004,(02):28-33.
[102] 傅菁华,吴元芳,刘连寿.高能多粒子末态的多重分形维数与动力学起伏强度[J].高能物理与核物理,1999,(10):992-997.
[103] 顾娟,茆诗松.稳定分布的参数估计[J].应用概率统计,2002,(04):8-12.
[104] 郭科,施泽进,唐菊兴,等.用多重分形研究元素的共生组合性[J].电子科技大学学报,2004,(02):110-113.
[105] 韩茂安,顾圣士.非线性系统的理论和方法[M].北京:科学出版社,2001.
[106] 何玉梅,吴小平.地震序列自仿射分形及自相似分形的计算与比较[J].地震研究,1996,(04):363-370.
[107] 侯景儒,郭光裕.矿床统计预测及地质统计学的理论与应用[M].北京:冶金工业出版社,1993.
[108] 胡金艳,张太镒,张春梅.基于分数布朗运动和概率神经网络的自然纹理分类[J].电子与信息学报,2004,(03):55-59.
[109] 胡尊国,孟宪国.第一届全国分形理论与地质科学学术讨论会论文集[M].武汉:中国地质大学出版社,1993.
[110] 黄大富.关于可以表示成自仿射分形的生物体两种维数的计算[J].生物数学学报,1999,(04):435-439.
[111] 黄诒蓉.中国股市分形结构的理论研究与实证分析[博士学位论文]厦门:厦门大学,2004
[112] 江田汉,邓莲堂.Hurst指数估计中存在的若干问题[J].地理科学,2004,24(02):177-182.
[113] 蒋海昆,王忠民,刁守中,等.中强地震前后能量分布的自仿射特性[J].地震,1996,(02):33-41.
[114] 蒋仁言.威布尔模型族特性、参数估计和应用[M].北京:科学出版社,1998.
[115] 金友渔,赵鹏大.分形—判别非线性数学模型及勘探线剖面致矿地质异常分析[J].地质科技情报,2000,(02):100-103.
[116] 肯尼斯·法尔科内[英].分形几何—数学基础及其应用[M].沈阳:东北大学出版社,2003.
[117] 李长江,麻土华,徐有浪.地球化学景观吸引子的发现及其意义[J].浙江地质,1995,11(01):86-90.
[118] 李长江,麻土华,朱兴盛等.分形布朗运动与地球化学测量[J].地质评论,1999,45(01):76-84.
[119] 李长江,麻土华.矿产勘查中的分形、混沌与ANN[M].北京:地质出版社,1999.
[120] 汪富泉,李后强.分形几何与动力系统[M].哈尔滨:黑龙江教育出版社,1993年
[121] 李锰,朱令人,龙海英.天山地区地貌系统的自仿射分形与多重分形特征研究[J].中国地震,2002,(04):85-92.
[122] 李锰,朱令人,龙海英.新疆天山地区地貌分形与多重分形特征研究[J].内陆地震,2003,(01):21-27.
[123] 李平,胡可乐,汪秉宏.多重分形谱在材料分析中的应用研究[J].南京航空航天大学学报,2004,(01):79-83.
[124] 李强.大震过程中地壳形变的混沌和多重分形特征及其预报意义[J].地球物理学进展,1999,(01): 84-92.
[125] 李庆谋,成秋明.分形奇异(特征)值分解方法与地球物理和地球化学异常重建[J].地球科学-中国地质大学学报,2004,(01):109-118.
[126] 李曙光,E.Jagoutz,肖益林,等.大别山-苏鲁地体超高压变质年代学——I.Sm-Nd同位素体系[J].中国科学(D辑),1996,26(03):249-257.
[127] 李曙光,李惠民,陈移之,等.大别山-苏鲁地体超高压变质年代学——Ⅱ.锆石U-Pb同位素体系[J].中国科学(D辑),1997,27(03):200-206.
[128] 李新中,赵鹏大,肖克炎,等.矿床统计预测单元划分的方法与程序[J].矿床地质,1998,(04):82-88.
[129] 李旭涛,曹汉强,赵鸿燕.分形布朗运动模型及其在地形分析中的应用[J].华中科技大学学报(自然科学版),2003,(05):54-56.
[130] 林海燕,王恩元,刘贞堂.煤岩粒度分形分布规律探讨及应用[J].江苏煤炭,1995,(04):7-10,6.
[131] 林文蔚,赵一鸣,赵国红等.胶东金矿铅同位素地质特征及成矿年代讨论[J].长春科技大学学报,1999,29(02):117-121.
[132] 刘伯土,周维奎,夏遵义.岩性序列定量地层划分对比方法[J].石油实验地质,2000,(05):371-374.
[133] 刘长海,刘义高,张军.中强地震前后地震时间序列的自仿射分形特征[J].地震学报,1994,(03):352-360.
[134] 刘建明,张宏福,孙景贵等.山东幔源岩浆岩的碳—氧和锶釹同位素地球化学研究[J].中国科学,2003,33(10):921-930.
[135] 刘庆生,燕守勋,赵善仁.齐波夫金矿资源量预测[J].地质与勘探,1999,35(4):33-35.
[136] 刘式达.自然科学中的分形与混沌[M].北京:北京大学出版社,2003.
[137] 龙期威.金属中的分形与复杂性[M].上海:上海科学技术出版社,1999.
[138] 卢方元.中国股市收益率波动性研究[博士学位论文].四川:西南交通大学,2005
[139] 卢焕章,袁万春,张国平,等.玲珑-焦家地区主要金矿床稳定同位素及同位素年代学[J].桂林工学院学报.1999.19(01):1-8.
[140] 路东尚,林吉照,郭纯毓,等.招远金矿集中区地质与找矿[M],地震出版社,2002,174-177.
[141] 罗镇宽,关康,苗来成,等.招远—莱州地区花岗岩类继承锆石年龄及其意义[J].山东地质,1999,15(03):24-57.
[142] 曼德尔布洛特(法).分形对象——形、机遇和维数[M](中译本).北京:世界图书出版公司,1999.
[143] 毛景文,郝英,丁悌平.胶东金矿形成期间地幔流体参与成矿过程的碳氧氢同位素证据[J].矿床地质,2002,21(02):122-128
[144] 孟宪国,赵鹏大.论地质现象中的分形统计学[J].地球科学,1996 22(01):601-603
[145] 孟宪伟,张晓华.多标度分形与地球化学场分解[J].地球科学,1996 22(01):601-603
[146] 苗来成,罗镇宽,关康,等.玲珑花岗岩中锆石的离子质谱U-Pb年龄及其岩石学意义[J].岩石学报,1998,14(02):199-206.
[147] 邱天爽,李小兵,孙永梅,等.分数代阶α稳定分布及其应用中的若干问题[J].探测与控制学报,2004,(02):7-11.
[148] 曲晓明,王鹤年,饶冰.胶东群部分熔化实验及其对花岗岩成因的指示作用[J].地球化学,2000,19(02):154-161.
[149] 屈世显,张建华.复杂系统的分形理论与应用[M].西安:陕西人民出版社,1996.
[150] 申维,赵鹏大.分形统计模型的理论研究及其在地质学中的应用[J].地质科学,1998,33(02):234-242.
[151] 申维.n维自仿射分形及其在地球化学中的应用[J].地质论评,2005,51(2):208-211
[152] 申维.多维自仿射分布及其在地球化学中的应用[J].高校地质学报,1999,(1):60-66.
[153] 申维.分形混沌与矿产预测[M].北京:地质出版社,2002.
[154] 申维.矿化富集动力学模型及其在矿产预测中的应用[J].地学前缘,2000,7(1):189-194.
[155] 施行觉,许和明.岩石断面的自仿射分形及其分维的计算[J].中国地震,1992,8(3):1-6.
[156] 石博强,申焱华.机械故障诊断的分形方法[M].北京:冶金工业出版社,2001.
[157] 苏菲,谢维信,董进.时间序列中的多重分形分析[J].数据采集与处理,1997,(03):178-181.
[158] 孙华山,赵鹏大,张寿庭,等.基于5p成矿预测与定量评价的系统勘查理论与实践[J].地球科学-中国地质大学学报,2005,(03):16-20.
[159] 孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科学技术大学出版社,2003.10.
[160] 孙英君,王劲峰,柏延臣.地统计学方法进展研究[J].地球科学进展,2004,19(02):268-274.
[161] 谭凯旋,谢焱石,王清良,等.新疆阿尔泰地区断裂构造的多重分形特征及其对热液成矿的控制[J].地学前缘,2004,(04):115-116.
[162] 王国富,王志忠.应用统计[M].湖南长沙:中南大学出版社,2003,7.
[163] 王建华,王玉玲,柯开明.中国股票收益率的稳定分布拟合与检验[J].武汉理工大学学报,2003,(10):101-104.
[164] 王金安,谢和平.岩石断裂面的各向异性分形和多重分形研究[J].岩土工程学报,1998,(06):19-24.
[165] 王祖伟,周永章,姚东良,等.两广庞西垌—金山成矿带银金矿床分形性研究[J].矿床地质,1999,18(02):183-188.
[166] 魏民,赵鹏大,刘红光,等.中国岩金矿床品位-吨位模型研究[J].地球科学-中国地质大学学报,2001,(01):43-50.
[167] 魏民,赵鹏大.试论矿化空间分布的有序性规律及矿体定位预测[J].地球科学-中国地质大学学报,1995,(02):144-148.
[168] 文志英.分形几何的数学基础[M].上海:上海科技教育出版社,2000.
[169] 吴根耀,马力,陈焕疆,等.苏皖地块构造演化、苏鲁造山带形成及其耦合的盆地发育[J].大地构造与成矿学,2003,27(04):337-353.
[170] 吴敏金.分形信息导论[M].上海:上海科学技术文献出版社,1994.
[171] 夏庆霖,张寿庭,赵鹏大,等.幂律度与成矿预测[J].成都理工大学学报(自然科学版),2003,(03):65-69.
[172] 肖斌,赵鹏大,陈玉玲,等.时空多元协同克立格的理论研究[J].物探化探计算技术,1998,(01):2-9.
[173] 肖斌,赵鹏大,侯景儒.纯时间域多元信息地质统计学[J].物探化探计算技术,1998,(03):14-21.
[174] 肖斌,赵鹏大,侯景儒.现代地质统计学的新进展[J].世界地质,1999a(03):82-88+92.
[175] 肖斌,赵鹏大,侯景儒.时空域中的指示克立格理论研究[J].地质与勘探,1999b,(04):27-30.
[176] 肖斌,赵鹏大,周龙茂.归来庄金矿床w(Au)/w(Ag)异常的地质统计学研究[J].地球科学-中国地质大学学报,2000a,(01):81-84.
[177] 肖斌,赵鹏大,侯景儒.地质统计学新进展[J].地球科学进展,2000b,(03):54-57.
[178] 肖斌,赵鹏大,侯景儒.归来庄金矿床综合化探金异常的地质统计学研究[J].北京大学学报(自然科学版),2000c,(04):95-102.
[179] 肖克炎,李景朝,陈郑辉等.中国铜矿床品位吨位模型[J].地质论评,2004,50(01):50-55.
[180] 谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京:科学出版社,1997.
[181] 谢和平.分形几何:数学基础与应用[M].重庆:重庆大学出版社,1991.
[182] 谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.
[183] 谢淑云,鲍征宇,苏江玉,等.新疆塔里木盆地艾协克-桑塔木南地区油气地球化学指标的多重分形性分析[J].地质论评,2005,(01):107-112.
[184] 谢淑云,鲍征宇.多重分形与地球化学元素的分布规律[J].地质地球化学,2003,(03):98-103.
[185] 谢文录,谢维信.几种分形参数估计方法的性能分析和比较[J].西安电子科技大学学报,1997b,(02):17-24.
[186] 谢文录,谢维信.时间序列中的分形分析和参数提取[J].信号处理,1997a,(02):97-104.
[187] 辛厚文.分形理论及其应用[M].合肥:中国科学技术大学出版社,1993.
[188] 邢君,孙洪泉,李维涛.岩土性质的空间信息统计分析[J].岩土工程技术,2004,(01):7-9.
[189] 熊刚,赵惠昌,梁彦.基于分形自仿射特性的混沌预测方法研究[J].现代雷达,2004,(04):40-44.
[190] 徐贵忠,周瑞,闫臻,等.论胶东地区中生代岩石圈减薄的证据及其动力学机制[J].大地构造与成矿学,2001,25(04):368-380.
[191] 徐绪松,马莉莉,陈彦斌.R/S分析的理论基础:分数布朗运动[J].武汉大学学报(理学版),2004,(05):20-23.
[192] 杨进辉,周新华,陈立辉.胶东地区破碎带蚀变岩型金矿时代的测定及其地质意义[J].岩石学报,2000,16(03):454-458.
[193] 杨文采,余长青.根据地球物理资料分析大别—苏鲁超高压变质带演化的运动学与动力学[J].地球物理学报,2001,44(03):347-359.
[194] 杨展如.分形物理学[M].上海:上海科技教育出版社;1996.
[195] 叶中行,曹奕剑.Hurst指数在股票市场有效性分析中的应用[J].系统工程,2001,19(03):21-24.
[196] 仪垂样.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.
[197] 殷勇.稳定分布假设及投资组合模型研究[J].数量经济技术经济研究,1996,(11):61-65.
[198] 於崇文.成矿动力系统在混沌边缘分形生长——一种新的成矿理论与方法论(上)[J].地学前缘,2001a,(03):9-28.
[199] 於崇文.成矿动力系统在混沌边缘分形生长——一种新的成矿理论与方法论(下)[J].地学前缘,2001b,(04):471-489.
[200] 於崇文.大型矿床和成矿区(带)在混沌边缘[J].地学前缘,1999,6(01):85-101.
[201] 於崇文.地球化学系统的复杂性探索[J].地球科学-中国地质大学学报,1994,(03):7-10.
[202] 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-中国地质大学学报,2002,27(05):509-519.
[203] 於崇文.地质系统的复杂性——地质科学的基本问题(Ⅱ)[J].地球科学-中国地质大学学报,2003,(07):36-41.
[204] 於崇文.多重水力断裂的分形扩张[J].地学前缘,2004,(03):16-40.
[205] 於崇文.揭示地质现象的本质与核心——地质作用与时-空结构[J].地学前缘,2000,(02):2-37.
[206] 於崇文.数学地质的方法与应用[M].北京:冶金工业出版社,1980.
[207] 曾秋华,李后强.多标度分形上的输运方程[J].高压物理学报,1999,(03):48-54.
[208] 张东晖,杨浩,施明恒.多孔介质分形模型的难点与探索[J].东南大学学报(自然科学版),2002,(05):10-15.
[209] 张连昌,沈远超,李厚民,等.胶东地区金矿床流体包裹体的He、Ar同位素组成及成矿流体来源示踪[J].岩石学报,2002,18(04):559-565
[210] 张均,周乔伟.川西北地区控矿断裂的分形特征及其预测意义[J].长春科技大学学报,2000,30(04):26-27+30.
[211] 张强,马润年,许进.1/f过程与稳定分布过程的关系[J].系统工程与电子技术,2001,(12):342-27+30.
[212] 张寿庭,赵鹏大,陈建平,等.多目标矿产预测评价及其研究意义[J].成都理工大学学报(自然科学版),2003,(06):42-44+103.
[213] 张卫东,葛洪魁,唐治平,等.疏松砂岩储层粒度分形分布研究及应用[J].石油钻探技术,2003,(06):22-24.
[214] 张哲儒,毛华海.分形理论与成矿作用[J].地学前缘,2000,7(01):195-204.
[215] 赵鹏大,陈建平,陈建国.成矿多样性与矿床谱系[J].地球科学-中国地质大学学报,2001,(05):72-77.
[216] 赵鹏大,陈建平,张寿庭.“三联式”成矿预测新进展[J].地学前缘,2003,(05):4-5+14.
[217] 赵鹏大,陈建平.21世纪矿产资源经济展望[J].自然资源学报,2000,(03):1-4
[218] 赵鹏大,陈建平.地质异常理论与遥感地质研究[J].大自然探索,1996,(02):29-34.
[219] 赵鹏大,陈建平.非传统矿产资源体系及其关键科学问题[J].地球科学进展,2000,(03):12-16.
[220] 赵鹏大,陈永清,刘吉平.地质异常成矿预测理论与实践[M].北京:中国地质大学出版社1999.
[221] 赵鹏大,陈永清.地质异常矿体定位的基本途径[J].地球科学-中国地质大学学报,1998,(02):5-8.
[222] 赵鹏大,陈永清.基于地质异常单元金矿找矿有利地段圈定与评价[J].地球科学-中国地质大学学报,1999,(05):443-448.
[223] 赵鹏大,池顺都,陈永清.查明地质异常:成矿预测的基础[J].高校地质学报,1996,(04):2-14.
[224] 赵鹏大,池顺都.当今矿产勘探问题的思考[J].地球科学-中国地质大学学报,1998,(01):72-76.
[225] 赵鹏大,胡旺亮,李紫金.矿床统计预测[M].北京:地质出版社,1994.
[226] 赵鹏大,王京贵,饶明辉,等.中国地质异常[J].地球科学-中国地质大学学报,1995,(02):117-127.
[227] 赵鹏大,张寿庭,陈建平.危机矿山可接替资源预测评价若干问题探讨[J].成都理工大学学报(自然科学版),2004,(Z1):16-18.
[228] 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-中国地质大学学报,2002,(03):64-68+89.
[229] 赵鹏大.当今地学高新技术应用及发展态势[J].国土资源科技管理,1995,(05):48-59+35.
[230] 赵鹏大.地球科学的新使命——认知和发现非传统矿产资源[J].地球物理学进展,2001,(05):1-10.
[231] 赵鹏大.地质勘探中的统计分析[M].武汉:中国地质大学出版社,1990.
[232] 赵鹏大.定量地学方法及应用[M].北京:高等教育出版社,2004.
[233] 赵鹏大.非传统矿产资源研究:可持续发展的重要课题[J].中国地质,2001,(03):89-95.
[234] 赵阳升,马宇,段康廉.岩层裂缝分形分布相关规律研究[J].岩石力学与工程学报,2002,(02):219-222.
[235] 周宏昆,丁宗强,雷祖志等.金属矿床大比例尺定量预测[M].北京:地质出版社,1993.
[236] 周洪涛,费奇.基于分形分布的投资组合选择理论研究[J].科技进步与对策,2003,(03):115-116.
[237] 周炜星,王延杰,于遵宏.多重分形奇异谱的几何特性I.经典Renyi定义法[J].华东理工大学学报,2000,(04):57-61.
[238] 周炜星,吴韬,于遵宏.多重分形奇异谱的几何特性Ii.配分函数法[J].华东理工大学学报,2000,(04):62-67.
[239] 周越,杨杰.基于多重分形模型的非高斯信号建模[J].上海交通大学学报,2002,(08):63-67.
[240] 邹新月,许涤龙.H指数估计方法的有效性检验[J].统计研究,2004,(08):37-39.
[241] 朱光,宋传中,牛漫兰,等.郯庐断裂带的岩石圈结构及其成因分析[J].高校地质学报,2002,8(03):249-256.
[242] 朱光,王道轩,刘国生,等.郯庐断裂带的伸展活动及其动力学背景[J].地质科学,2001,36(3):269-278.
[243] 朱炬波,梁甸农.组合分形Brown运动模型[J].中国科学(E辑),2002,30(04):312-319.
[244] 朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算[J].地震,2000,(03):2-9.