【作者】 谢淑云；

【导师】 Zhengyu Bao；

【作者基本信息】 中国地质大学 ， Geochemistry， 2003， 博士

【摘要】 地球化学场(geochemical fields)时-空结构研究是区域成矿作用动力学的重要内容，对区域和矿区矿产预测和新一轮国土资源调查发挥着十分重要的作用。分形(fractal)与多重分形(multifractal)理论作为非线性科学的一个分支，是研究复杂系统时-空结构特征的基本理论和有效方法，已广泛应用于地球科学的各个领域 ，也是地球化学家关注的焦点，许多地球化学过程，如成矿作用、火山活动等都被认为具有自相似（self-similarity）或自仿射(self-affinity)的性质，即具有分形或多重分形的特征。因此，用分形与多重分形的方法研究地球化学场的时空结构具有重要的意义。本文主要运用两种典型的分形与多重分形方法，即矩分析方法(the method of moments)和经过改进的浓度面积法（ACAF model），辅助以频率分析法QQ 图（QQ plot）和直方图(histogram)，分析了地球化学场可能的分形与多重分形特征。论文主要包括三大部分，即不同的De Wijs模型模拟、实例分析和Monte Carlo模拟。实例分析主要选择了粤北4292km2内1448个基岩样品的25项元素、安徽省江南江北各约22000 km2 和 18100 km2内5489个和4524个水系沉积物样品的14项元素、塔里木盆地４个含油气区的6418个土壤样品的酸解烃(C1～C5)、紫外、荧光、蚀变碳酸盐和汞等共计330,000余个地球化学数据。所涉及地球化学指标之多、地域之广、样品数量之大，在国内外众多研究中都是空前的。第一部分De Wijs模型及其改进模型的模拟结果均加深了我们对地球化学场分形与多重分形特征的认识。通过二维De Wijs模型模拟具有不同浓集系数(enrichment factor)、有局部削减(local suppression)和局部叠加(local superimposition)的地球化学场，本文首先分析了其多重分形谱(multifractal spectrum)的形态特征、ACAF分布模式及频率检验（probability test）结果。结果显示：①基本的二维De Wijs模型能产生完美的连续多重分形(continuous multifractal)， De Wijs模拟结果在空间上具有标度不变性(scale-invariant)。②传统的De Wijs模拟结果其多重分形谱完全对称(symmetric)，参数???（多重分形谱最高点的奇异指数（singularity exponent）值）和 ???（奇异指数的宽度）随着浓集系数的增加单调增加。任意高值或低值部分的削减都会打破这种对称性，从而造成多重分形谱函数f(?)曲线右偏或左偏，即右偏多重分形(right-deviated multifractal，RM)和左偏多重分形(left-deviated multifractal，LM)。以??为界，??可以分成左右两部分Δ?L和Δ?R，其比率R（非对称系数，asymmetry index）对于刻画潜在的局部富集与贫化十分有效。如果将较高浓集系数d2的De Wijs模拟结果局部叠加于另一具有较小浓集系数d1的De Wijs模拟结果上，最后结果其多重分形谱函数左偏。当d1不变时，随着d2的增大， f(?) 曲线左偏越来越明显，相应地Δ?,Δ?L 以及R 的值随之增加，但多重分形谱函数右侧改变甚少。③在双对数坐标图（log-log diagram）上，上述多重分形的ACAF分析结果具有两种分布模式，即简单的两直线段拟合模式(bi-segment pattern，BS pattern)和多直线段拟合模式(multi-segment pattern，MS pattern)。任何有局部叠加的De Wijs模拟结果均服从MS分布模式，而基本的De Wijs模拟结果却服从BS分布模式。④基本的De Wijs模拟结果主要服从对数正态(lognormal distribution)分布。金属地球化学场（metallic geochemical fields）与油气地球化学场(oil/gas geochemical<WP=6>fields)实例分析结果表明：①地球化学场具有连续多重分形特征，这一规律具有普适性。同时，金属地球化学场与油气地球化学场在场的空间结构上具有很大的差异。②对主要的成油指标（major oil/gas forming indexes）,其质量指数（mass exponent）与矩级次(order, moment)之间呈一定程度的线性相关，其多重分形谱函数较窄，部分指标呈单钩状(single spike)。所有这些证实，主要的成油气指标具有较弱的多重分形特征，部分显示为明显的单一分形。而主要的成矿元素（major ore-forming elements）的质量指数与矩级次之间呈一曲线，多重分形谱宽而连续，因此主要的成矿指标在金属地球化学场中具有连续多重分形特征。主要成矿指标非对称的多重分形谱函数正预示着在长期的形成过程中，地球化学场曾经历过不同的局部叠加或贫化。非对称指数R可望用于成矿潜力(potential)评价中。③网格化数据分析结果表明，过密或者过稀的网格密度均不能较好地刻划地球化学场的本质特征，这是因为，较小的网格密度可能会产生一系列“假”数据，而网格密度太大又可能导致部分原始数据被“平滑”甚至忽略，这样得出的结果极有可能偏离实际。本论文通过不同网格密度的网格化与数据实际数据结果的对比研究，发现，平均每个网格内取1.5个数据比较合适，这样使得采样较密区域的网格内有2个或2个以上样品，采样较稀区域的网格内有1个样品，部分网格内没有样品，即为采样空白区。④在双对数坐标图上，主要的成矿元素和主要油气化探指标均不同程度地显示服从MS分布模式，而其他多表现为BS 分布模式。不同的分布模式可望用于区域含矿含油性和区域环境评价，更多还原

【Abstract】 It’s of great significance to study geochemical element distribution patterns by using fractal and multifractal methods. This dissertation will apply two fractal and multifractal methods called the method of moments and ACAF model to investigate whether it is a universal feature that a geochemical field is fractal or multifractal and whether lognormal or normal distribution data will yield a multifractal or single fractal with the additional use of QQ plot and histogram. Three important and interesting parts will be contained in this dissertation, including De Wijs modeling, Case studies and Monte Carlo Simulations.Based on simulations of two-dimensional De Wijs models with different parameters, high- and low-value suppression and local superimposition of other De Wijs models, this dissertation first simulated different geochemical element distribution patterns and then investigated their multifractal spectrum function shapes, ACAF distribution patterns and probability testing results. It can be drawn out that: ①Basic two-dimensional De Wijs modeling can produce a perfect continuous multifractal and such De Wijs construction is scale-invariant in space. If the spatial structure keeps the same, the multifractal spectrum shape will not change as neither relatively less or more iteration times nor the global division do have any effect on the multifractal shape.②Conventional De Wijs models exhibit symmetric multifractal spectra and parameters ???and ???increase monotonously with "enrichment factor" d. Any suppression of high values or low values in a simulating geochemical field will break this symmetry and make the spectrum curves f(?) deviate to right or to left, resulting in right-deviated multifractal(RM) and left-deviated multifractal(LM), respectively. The parameterΔ??can then be split intoΔ?L and Δ?R and their ratio R is called asymmetry index by the author and proves to be a pivotal parameter characterizing the underlying enrichment or pauperization mechanism. Local superimposition of De Wijs model of d1 by another De Wijs model of d2 will make the multifractal spectrum curves deviate left. With the increase of enrichment factor d2 of superimposed component, f(?) curves deviate more violently, and hence the parametersΔ?,Δ?L and asymmetric index R increases systematically with the enrichment factor of superimposed component, leaving its right side almost unchanged.③When the concentration bins and the corresponding frequency are drawn on log-log diagrams, the continuous multifractals of simulated geochemical fields following De Wijs construction can be categorized by two patterns: bi-segment pattern (BS pattern) and multi-segment pattern(MS pattern). Any basic De Wijs model follows BS pattern, whereas the De Wijs model with local superimposition obeys MS pattern, which is in agreement with the results of the method of moments.④The principle part of such kind of basic De Wijs modeling data is authentically of lognormal distribution. Whether the tails of it follow Pareto distribution is still in issue as there are so many repeated concentrations in such construction data that it’s nearly impossible to detect the distribution patterns of any small part, such as the tails. For case studies, two distinct data sets will be employed, including elements in metallic<WP=8>geochemical fields, as well as petroleum data from oil/gas regions. The former data set contains concentrations of 25 elements in 1448 whole rock samples from a region of 4290km2 in the north Guangdong Province, South China; 14 elements of 5489 and 4524 stream sediments in South and North Anhui Province, respectively, South China; and the latter with more than 15 hydrocarbons and other indices in 6418 soil samples from 4 oil/gas fields with total survey area 7000 km2 in Tarim Basin, North China. The results indicated that: ①Fractal and multifractal properties are quite universal in geochemical fields. However, metallic geochemical fields and oil/gas geochemical fields are intrinsically different from each other in spatial structu更多还原