Decomposing of mixed pattern of arsenic using fractal model in Gangdese belt,Tibet, China

Decomposing mixed geochemical patterns is a challenge in geochemical exploration and environmental assessment. In this paper, the spectrum–area technique (S–A) is used to decompose a mixed pattern of arsenic in Gangdese belt based on stream sediment data. S–A is a multifractal model based on power–law relationships between area of the set consisting of wave numbers with spectral energy density above S[A(>S)] on the 2D frequency domain. The original spatial distribution map of arsenic obtained by inverse distance weighted (IDW) shows a mixed pattern due to superposition of different geological processes or events and is converted into the frequency domain by means of Fourier transformation. Two components, including power spectrum density and phases, are obtained. The spectrum energy density (S) and the area (A) enclosed by the above-threshold spectrum energy density is plotted on a log–log scale. Two cutoff values determined by three straight lines define three filters which decompose the original map of arsenic into background, anomalous, and high frequency (noise) components. The areas with high anomaly of arsenic mainly are located surrounding known Cu deposits, indicating that arsenic anomalies may be related to Cu mineralization.     

新疆阿尔泰地区断裂控矿的多重分形机理

新疆阿尔泰地区断裂构造非常发育并对热液成矿有重要控制作用。分形分析表明该区断裂和矿床的空间分布均为多重分形分布,断裂的奇异指数为1.597～2.403,多重分维谱值为0.551～1.706;矿床的奇异指数为0.925～2.287,分维谱值为0.138～1.363。断裂的高的奇异指数和分维谱值表明该区断裂构造具有较高的成熟度和连通性,有利于提高岩石渗透性、促进流体流动和热液矿床的形成。断裂构造的多重分形分布导致该区热液成矿作用的多重分形分布。断裂体系演化过程中不同断裂部位变形和渗透性存在明显差异,数值模拟表明断裂与岩性和流体之间存在强烈的耦合作用并导致不同岩性的断裂具有明显不同的断裂渗透率。断裂-脉体系演化是一个自组织过程,元胞自动机模拟表明只有在分形渗透临界以上连通性较好的脊骨断裂部位是最有利于流体流动和成矿作用的。因此只有在部分有利的断裂部位才能形成矿床,并导致了断裂构造的奇异指数和多重分维谱值明显高于矿床。     

地球化学图纹理的多重分形模拟

利用一个简单的基于De Wijs模型的多重分形模型, 可以模拟元素富集值的各种地球化学纹理.每种纹理在平均值上是自相似的, 因为将乘积阶次模型(multiplicative cascade model) 应用到任何子区均能得出类似的纹理样式.在其他的试验中, 通过叠加一个二维趋势纹理(2-dimensional trend pattern) 以及把它与一个常值富集模型混合, 原始的自相似纹理就产生畸变.本文将要研究这些畸变是如何改变用三步矩(3-step method of moments) 所估测的多重分形谱(multifractal spectrum).推导出了满足De Wijs模型纹理的离散和连续频率分布模型.这些模拟纹理满足离散频率分布模型, 当乘积阶次模型(multipicative cascade model) 无限细分时, 假设离散频率分布模型的上界是一连续频率分布, 这个离散分布就在形式上逼近该连续频率分布的上边界.这一极限分布在中心是对数正态的, 但有两个巴利多(Pareto) 分布的尾.这种方法在矿产和油气评价中有重要的潜在意义.      

Multifractal Simulation of GeochemicalMap Patterns

INTRODUCTIONThe mathematical modeling of geochemical data continuesto present an important challenge to earth scientists. Basically,the available data are 2-dimensional realizations of 3dimensional patterns, which are the results of one or more genetic processes that usually are poorly understood. It may bedifficult to project from the observations into the rock mass. Inthis paper, multifractal modeling is advocated as a methodologyto characterize geochemical patterns. If a geochemical pa…     

Application of local singularity model to delineate geochemical anomalies in Xiong'ershan gold and molybdenum ore district,Western Henan province,China

The local singularity model involved in the context of multifractal theory calculates an index which indicates the local elemental enrichment or depletion and can be used to delineate the weak anomalies. The index, called singularity exponent can be calculated using the total amount model and density model, respectively. The former is based on the power–law relationship between the cumulative concentrations of the neighboring samples in variable cell sizes and cell size, while the latter is between the average concentration and cell size. The influence of the two models on the calculation of the local singularity was estimated in this paper. The total amount model was thought to be preferable in calculating the singularity exponent, which was applied to stream sediment data from the Xiong'ershan gold and molybdenum ore district, Western Henan province, China, and an algorithm based on the window-based method was advanced to map the local singularity distributions of Au and Mo. The thresholds of Au and Mo calculated on the singularity map were used to delineate anomalies which were associated not only with known gold and molybdenum ore deposits in the northern part of EW-trending Machaoying fault, but also with the areas south of Machaoying fault where no gold deposits have yet been discovered. Neither were they clearly identified by the Concentration–Area model and mean + standard deviation of Au concentrations. The results show that weak anomalies hidden within the strong variance of background can be well identified by the local singularity model, and the delineated anomalies should be considered as favorable target areas.     

多标度分形与地球化学场分解

在地球化学叠加场内，不同时期、不同规模的地质作用形成的地球化学景观具有不同的分形标度区间和分维。利用多标度分形方法把黑龙江省团结沟金矿外围的叠加地球化学场分解成了分别与北东向和北面向构造相对应的地球化学正常场和异常场，并在此基础上，讨论了地球化学场的演化。     

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

勘查地球化学和地球物理场的局部空间结构变化性应包括空间自相关性以及奇异性 .前者可通过地质统计学中常用的变异函数来实现 ;后者可用多重分形模型进行刻划 .具有自相似性或统计自相似性的多重分形分布 (multifractaldistributions)的奇异性 (α)可以反映地球化学元素在岩石等介质中的局部富集和贫化规律 .而多重分形插值和估计方法可以同时度量以上两种局部结构性质 (空间自相关性以及奇异性 ) ,因而 ,它不仅能够进行空间数据插值 ,同时还能保持和增强数据的局部结构信息 ,这对于地球化学和地球物理异常分析和识别是有益的 .应用该方法处理加拿大NovaScotia省西南部湖泊沉积物地球化学砷等元素数据表明 ,地球化学数据的局部奇异性在该区能够反映局部金和钨 -锡 -铀矿化蚀变带或岩相变化以及构造交汇等局部成矿有利部位 .     

Fractal and Multifractal Properties of Geochemical Fields

A fractal model, introduced by De Wijs to study the distribution, redistribution, or enrichment/depletion of element concentrations in a region, has become widely accepted. This paper uses it to simulate various geochemical fields for element concentration values. The frequency distribution and spatial pattern of the simulated values or concentrations are analyzed by the method of moments and the concentration–area (C–A) model. The spatial pattern of the original De Wijs model is shown to be intrinsically characterized by -shaped and symmetrical multifractal spectrum curves, whose center and width change systematically with the enrichment factors set in the simulation. The corresponding frequency distribution pattern on the log–log plot of frequency versus concentrations is called simple continuous multifractal (SCM) by the authors. In other experiments, when a De Wijs model is locally superimposed by another De Wijs model of different enrichment factors, the symmetry of the multifractal spectrum graph is broken and a different pattern of frequency distribution is found. It is referred to as highly accumulated continuous multifractals (HACM). Concentrations of 12 elements in 1448 rock samples from Shaoguan district, North Guangdong Province, South China, and 12 oil/gas indexes in surface soils from Sangtamu region, Tarim Basin, Northwest China, have been applied. The real geochemical fields, both metallic and oil/gas, are found to be remarkably compatible to those simulated patterns of De Wijs models with backgrounds of various enrichment and different degrees of superimposition, indicating that the frequency and spatial distribution patterns revealed by the authors are most possibly universal features of geochemical fields. It is particularly interesting to note that the major geochemical indicators of oil/gas geochemical fields are closer to the results of De Wijs models with a small enrichment factor, either with or without local superimposition, whereas those of the metallic geochemical field correspond more closely to De Wijs models with a background field of larger enrichment factors. The results obtained herein potentially have important implications in mineral and oil/gas resource assessment.     

A comparison study of the C–A and S–A models with singularity analysis to identify geochemical anomalies in covered areas

Fractal/multifractal modeling of geochemical data is an interesting topic in the field of applied geochemistry. Identification of weak anomalies for mineral exploration in covered areas is one of the most challenging tasks for utilization of geochemical data. In this study, three fractal models, consisting of the concentration–area (C–A), spectrum–area (S–A) and singularity index models were applied to identify geochemical anomalies in the covered area located in the Chaobuleng Fe polymetallic district, Inner Mongolia (China). The results show that (1) the grassland cover weakens the concentrations of geochemical elements; (2) the C–A model has a limitation to identify weak anomalies in covered areas; (3) the S–A model is a powerful tool to decompose mixed geochemical patterns into a geochemical anomaly map and a varied geochemical background map but suffers edge effects in an irregular shaped study area; and (4) the singularity index is a useful tool to identify weak geochemical anomalies.     

Multifractality in seismic sequences of NW Himalaya

Multifractal behaviour of interevent time sequences is investigated for the earthquake events in the NW Himalaya, which is one of the most seismically active zones of India and experienced moderate to large damaging earthquakes in the past. In the present study, the multifractal detrended fluctuation analysis (MF-DFA) is used to understand the multifractal behaviour of the earthquake data. For this purpose, a complete and homogeneous earthquake catalogue of the period 1965–2013 with a magnitude of completeness M _w 4.3 is used. The analysis revealed the presence of multifractal behaviour and sharp changes near the occurrence of three earthquakes of magnitude (M _w ) greater than 6.6 including the October 2005, Muzaffarabad–Kashmir earthquake. The multifractal spectrum and related parameters are explored to understand the time dynamics and clustering of the events.

     

个旧锡多金属矿集区高松矿田矿化元素局部富集的奇异性特征

多重分形理论能够有效地分析地球化元素局部富集和贫化规律。对取自个旧高松矿田的1 783件断裂构造地球化学样品的13种元素进行了多重分形统计以及局部奇异性方法分析。结果表明:多重分形维谱函数α-f(α)曲线呈连续上凸的特征,曲线的不对称反映了元素局部富集程度差异,并据此将13种元素划分为包含Sn、Cu、Pb、Ag、As、Mn在内的主要成矿元素组合以及包含Zn、Sb、Cd、W、Mo、Bi、Hg的次要成矿元素或伴生元素组合。多重分形的特征值τ″(1)以及Dq的变化规律表明:在主要成矿元素中,Sn在断裂空间上局部富集程度最高,其次为Ag,而Cu相对最低,各元素的τ″(1)值与对应的变异系数的大小具有较为显著的相关性;各元素在空间上的奇异性指数α增强了地球化学富集地段的指示信息,可以作为判别局部富集的重要参数。运用多重分形方法可揭示矿化元素局部富集的奇异性特征以及空间局部富集规律。     

Climate extremes: an observation and projection of its impacts on food production in ASEAN

Multifractal behaviour of interevent time sequences is investigated for the earthquake events in the NW Himalaya, which is one of the most seismically active zones of India and experienced moderate to large damaging earthquakes in the past. In the present study, the multifractal detrended fluctuation analysis (MF-DFA) is used to understand the multifractal behaviour of the earthquake data. For this purpose, a complete and homogeneous earthquake catalogue of the period 1965–2013 with a magnitude of completeness M _w 4.3 is used. The analysis revealed the presence of multifractal behaviour and sharp changes near the occurrence of three earthquakes of magnitude (M _w ) greater than 6.6 including the October 2005, Muzaffarabad–Kashmir earthquake. The multifractal spectrum and related parameters are explored to understand the time dynamics and clustering of the events.     

Investigating the spatial distribution of antimony geochemical anomalies located in the Yunnan-Guizhou-Guangxi region,China

The Yunnan-Guizhou-Guangxi region is well known for its abundant mineral resources, and low-temperature hydrothermal mineralization represented by the elemental association of gold, arsenic, antimony and mercury is widely developed there. Many studies on the geological-geochemical characteristics of gold have been conducted, but a comprehensive understanding of the antimony geochemical pattern is still lacking. This paper studied the Sb distribution characteristics and the cause of geochemical anomalies based on the geochemical data of stream sediments and rocks in the study area. In addition, the geochemical data of Au, As, Sb and Hg were centered and log-ratio transformed to eliminate the closure effect, and then random forest regression (RFR) with Au, As and Hg as the characteristic variables was used to investigate the ore-related geochemical anomalies of Sb. Seven geochemical provinces were delineated from the original geochemical data, and they are not entirely consistent with the known deposits. Sb moves from the rocks to the stream sediments during weathering. The variation trend in the Sb background values in stream sediments in each tectonic unit is consistent with that in the rocks themselves, implying that Sb in the stream sediments is inherited from the background rocks. The distributions of Sb predicted by RFR are similar to the distribution pattern of Sb in stream sediments. Of the three elements considered, the influence of As on the variations in the Sb geochemical background is the greatest, followed by Au and then Hg. The geochemical anomalies extracted by the residuals produced in this algorithm are consistent with where the known Sb metallogenic district is located, indicating that this method of recognizing geochemical anomalies is feasible and effective and has theoretical and practical significance.     

空间模式的广义自相似性分析与矿产资源评价

尺度不变性(scale invariance)包括自相似性(各向同性)、自仿射性(成层结构)、广义自相似性(各向异性标度不变性),是由各种地质过程和地质事件所产生的地质特征和模式的本质属性．尺度不变性可用分形和多重分形模型来表征．这些尺度特征的定量化可为刻画地质空问模式和模式识别提供有力的工具．例如。热液矿床的群聚现象可以用局部分形特征(局部奇异性)来刻画．通过在特征空问中(如频率空问)识别空问模式的广义自相似性．可以将空间混合模式进行分解或异常的识别．介绍了几种相关的分形模型和方法。包括度量空问模式广义尺度独立性(GSI)的线性模型;基于广义尺度独立性的异常分解S—A方法;度量空问模式的局部奇异性方法;以及如何利用分形特征预测未发现矿床的2种方法．有些方法已应用于许多矿产资源评价实例中．给出了对加拿大Nova Scotia省西南部湖泊沉积物样品中的4种元素As、Pb、Zn和Cu的地球化学数据处理分析结果。证明了局部奇异性分析和S—A异常分解方法对地球化学异常的增强和分离的有效性．研究表明：由S—A方法分解的异常往往具有多重分形的特点,而且普遍具有局部奇异性．研究区内具有明显奇异性的地区(元素含量富集区)是金矿异常区域。它们与金矿成矿作用和已知矿床的赋存密切相关．     

基于S-A多重分形滤波方法的深层土壤Au元素异常识别—以皖东张八岭—管店地区为例

张八岭—管店地区位于皖东张八岭构造带北部,区内已发现多处金多金属矿点,但尚未取得显著突破。近年来,多维分形理论与地球化学勘查相结合的方法已被广泛应用于Au、Cu矿床的找矿勘查工作,其中S-A(能谱密度-累计面积)方法是一种建立在能谱空间上的分形滤波技术,能够利用傅里叶变换对物化探数据进行异常和背景分解。以张八岭—管店地区深部土壤Au元素为例,利用S-A方法对研究区深部土壤中Au元素地球化学场进行异常识别。结果显示,该方法能够有效分离地球化学背景,识别已知金铜矿点的矿致异常信息,在区内已知矿点以外识别出多个Au元素异常区域。研究成果可为进一步找矿勘探提供新的目标和方向。     

Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum： Application to Gold Deposits in Abitibi Area, Ontario, Canada

A number of fractal/multifractal methods are introduced for quantifying the mineral de-lmsit spectrum which include a number-size, grade-tonnage model, power spectrmn model,multi-fractal model and an eigeavalue spectrmn model The first two models characterize mineral deposits spec-tra based on relationships among the measures of mineral deposits.These include the number of deposits,size of deposits,concentration and volume of mineral deposits.The last three methods that deal with the spatial-temporal spectra of mineral deposit studies are all expected to be popularized in near future.A case study of hydrothermal gold deposits from the Abitibi area,a world-class mineral district is used to demonstrate the principle as well as the applications of methods proposed in this paper,It has been shown that fractal and multifractal models are generally applicable to modeling of mineral deposits and occurrences.Clusters of mineral deposits were identified by several methods including the power spectral eral deposits in the Timmins and Kirkland Lake camps.     

多维分形理论和地球化学元素分布规律

多维分形模型不仅采用常规的低阶矩统计, 而且采用高阶矩统计对多维分形分布进行度量, 从而能较细致地刻划正常值以及异常值.地球化学元素的正常值往往服从统计学中的大数定量, 即满足正态分布或对数正态分布, 然而异常值会服从分形分布(Preato).介绍了多维分形领域中的最新发展以及在地球化学研究中特别是研究超常元素空间分布和富集规律中的应用.结果表明, 通常的统计方法只对应于多维分形围绕均值周围的局部特征.为了有效地研究异常值的分布和富集规律, 建议采用高阶矩统计方法和多维分形方法, 并给出了两种分析地球化学元素, 并突出异常值贡献的方法.这些方法不仅可应用于研究微量元素的空间分布和富集规律, 而且可以区分地球化学背景与矿化有关的异常值.还介绍了该方法在对加拿大B.C.省西北部Mitchell-Sulphurets地区金铜矿化蚀变带研究中的应用.      

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

用分形与多重分形的方法研究地球化学场中地球化学指标的分布规律具有重要的意义。本文运用多重分形矩方法研究了新疆塔里木盆地艾协克一桑塔木南地区2000km^2内采集的2085个土壤样中20项油气化探指标的多重分形谱函数形态特征。结果表明，主要成油气指示指标的多重分形谱基本上呈单一“钩状”，显示较弱的多重分形或单一分形；而其他指标多显示较强的多重分形特征。这些性质在研究区广泛存在，将对区域含油性研究有重要的指示意义。     

Multifractal modeling and spatial statistics

In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis.