分形求和法及其在地球化学数据分组中的应用

分形建模广泛地应用于具有自相似性不同尺度测量的地质现象空间分布特征。分形分布的特点要求大于等于某一尺度的数目,与物体大小之间存在幂函数关系,这种关系具有尺度不变性。这里提出的分形求和法可以确定地球化学数据分组界限。应用澳大利亚新南威尔士东北地区汇水沉积物地球化学数据,采用分形求和法确定其分组界限,并与传统的概率图模型结果进行比较。铜(Cu)元素数据划分二个部分,一部分是元素含量少于20 ppm的正态分布数据,另一部分是元素含量大于20 ppm的多个对数正态分布数据,能识别第三纪玄武岩区域和铜的主要矿化区。这一结论与使用传统的概率图模型方法得到的结论一致。该方法不仅适用于地球化学铜元素数据,而且还适用于其它元素和地质数据,具有普遍的意义。     

分形不变分布及其在山东地区金矿床中的应用

自相似性(标度不变性)是地学中的一个普遍现象。研究表明,地球化学元素含量、矿床储量规模及其空间分布具有分形结构。分形不变分布的特点要求大于某一尺度物体的数目与物体大小之间存在幂指数关系。论证了幂函数分布、帕累托分布、对数正态分布和齐波夫定律在一定条件下具有分形不变性质,它们是分形模型的数学基础。基于分形模型,用求和方法确定中国山东省金地球化学元素异常值范围。等值线大于或等于金地球化学元素临界值(200×10-9)围成的异常面积包含了已知的大型、超大型金矿床。     

http://www.sciencedirect.com/science/article/pii/S1674987110000320

The self-similar is a common phenomena arising in the field of geology.It has been shown that geochemical element data,mineral deposits,and spacial distribution conform to a fractal structure.A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size.This paper shows that a number of distributions,including power-function,Pareto, lognormal,and Zipf,display fractal properties under certain conditions and that this may be used as the mathemat...     

Selection of threshold values in geochemical data using probability graphs

A method of choosing threshold values between anomalous and background geochemical data, based on partitioning a cumulative probability plot of the data is described. The procedure is somewhat arbitrary but provides a fundamental grouping of data values. Several practical examples of real data sets that range in complexity from a single population to four populations are discussed in detail to illustrate the procedure.The method is not restricted to the choice of thresholds between anomalous and background populations but is much more general in nature. It can be applied to any polymodal distribution containing adequate values and populations with appropriate density distribution. As a rule such distributions for geochemical data closely approach a lognormal model. Two examples of the more general application of the method are described.     

The chi-square plot: a tool for multivariate outlier recognition

In large multi-element regional surveys statistically derived threshold levels of the form that define, for example, the top 2% of the data for each element as worthy of further investigation have led to the generation of inordinately large lists of geochemical samples for detailed study. This problem is compounded when a number of geological and secondary environments exists of sufficiently different character that separate thresholds should be estimated for each. Additionally, single-element thresholds for multi-element surveys can, in certain circumstances, lead to obviously out-of-character individuals not being recognized.Numerical approaches to the problem of anomaly recognition have commonly used a principal-component or regression analysis procedure as their basis. These, as indeed do all such approaches, have a common drawback in that the outliers being sought can distort the analysis being used to detect them. In addition, regression models have the further problem that there may be outliers in both the response and explanatory variables.A relatively simple approach would be to prepare a multivariate cumulative probability plot where each multi-element geochemical sample is represented as a single value. The resulting diagram would be interpreted much as a univariate probability plot where the presence of more than one straight-line segment is taken as evidence of multiple populations, and outliers as individuals or small groups are separated from the remaining data by gaps on the plot.Such a diagram may be prepared by plotting the rank-ordered values of the generalized or Mahalanobis distance, a multivariate distance measure, versus values of the chi-square statistic. This procedure is based on the covariance matrix of the data, a measure that underlies both principal-component and regression model approaches. In order to work effectively a statistically robust starting covariance matrix is essential.The procedure is described in detail with two examples, one a synthetic bivariate data set containing known outliers, and the other a small, well studied stream sediment data set from Norway extensively used in methodological comparison studies. The result of the procedure is to identify statistical outliers, which are candidates for interpretation as true geochemical anomalies, and to isolate a multi-element subset that is representative of the geochemical background.     

Separation of a geochemical anomaly from background by fractal and U-statistic methods,a case study: Khooni district,Central Iran

Separation of geochemical anomalies from background are one of the important steps in mineral exploration. The Khooni mineral district (Central Iran) has complex geochemical surface expression due to a complex geological background. This region was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods, spatial statistical methods and fractal and multi-fractal methods. In this article, two efficient methods, i.e. U-statistics and the fractal concentration-area for separation and detection of anomalous areas of the background were used. The U spatial statistic method is a weighted mean, which considers sampling point positions and their spatial relation in the estimation of anomaly location. Also, fractal and multi-fractal models have also been applied to separate anomalies from background values. In this paper, the concentration–area model (C–A) was suggested to separate the anomaly of background. For this purpose, about 256 stream sediment samples were collected and analyzed. Then anomaly maps of elements were generated based on U spatial statistics and the C-A fractal methods for Au, As and Sb elements. According to obtained results, the U-statistics method performed better than C-A method. Because the comparisons of the known deposits and occurrences against the anomalous area created using thresholds from U-statistics and C-A method show that the spatial U-statistics method hits all of 3 known deposits and occurrences, the C-A fractal method hits 1 and fails 2. In addition, the results showed that these methods with regard to spatial distribution and variability within neighboring samples, in addition to concentration value frequency distributions and correlation coefficients, have more accurate results than the traditional approaches.     

Geochemical anomaly definition using multifractal modeling,validated by geological field observations: Siah Jangal area,SE Iran

Recognition of geochemical anomalies is a pivotal assignment in exploration projects. This study aims to delineate different AuCu geochemical anomalies using number-size (N-S) and concentration-area (C-A) multifractal models in the Siah Jangal area, SE Iran. In this research, lithogeochemical datasets were applied for the exploration of Au and Cu. A comparison between geochemical anomaly maps based on the N-S and C-A fractal models shows the N-S fractal modeling is a powerful tool for separation of weak elemental geochemical anomalies in all of sampling zones. Based on a comparison between the results of these two methods and field studies, the geochemical anomaly zones, defined by the N-S fractal model, are more accurate than those recognized by the C-A fractal model. The obtained results of the N-S and C-A fractal models have been interpreted with the extensive set of information including structural interpretation, geological and alteration data. Au and Cu mineralization in the Siah Jangal area are hosted mainly by Oligocene-Miocene sub-volcanic rocks, especially strongly altered porphyric quartz diorite, hornblende diorite and diorite. Moreover, the positive dependence between various alteration zones and high concentrations of Au and Cu proves that strongly anomalous areas are correlated with these alteration zones. High grade Au (> 1000 ppb) and Cu (>150 ppm) are associated with the altered sub-volcanic rocks in the northern, eastern, and SW parts of the study area. Therewith, the strong anomaly populations are mostly occurred within the fault and fracture systems in the study area. This is a promising signal because quartz-sulfide veins and veinlets are associated with such structures.     

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.      

Recognition of mineralized belts and lithologic patterns in the Silver City-South Mountain region, Idaho, in terms of geochemical reconnaissance data

It seems unreasonable to use one population to fit the distribution of an element, and then to determine a threshold to separate anomalous data from background data in an analysis of geochemical data. Statistically, anomaly, background, and other geological categories may be represented by different component populations overlapping one another. Therefore, anomaly, background, and other geological categories should be distinguished from one another by distributions rather than by thresholds. This paper uses a method of decomposition of mixtures to identify observed distributions of five elements, obtained in a geochemical reconnaissance of the Silver City-South Mountain region, Idaho, into component populations. Observations have been assigned to populations and mapped; finally, these populations have been interpreted leading to recognition of both mineralized belts and lithologic patterns.during the period in which this study was carried out.     

A Study of the Method for the Recognition of Anomalies in Geochemical Hydrocarbon Exploration

ＩＮＴＲＯＤＵＣＴＩＯＮＡｎｏｍａｌｙｔｈｒｅｓｈｏｌｄｉｓｃｏｍｍｏｎｌｙｄｅｔｅｒｍｉｎｅｄｂｙｃａｌｃｕｌａｔ－ｉｎｇｔｈｅｍｅａｎｐｌｕｓｎｓｔａｎｄａｒｄｄｅｖｉａｔｉｏｎｓｏｒｂｙｕｓｉｎｇｔｒｅｎｄｓｕｒ－ｆａｃｅａｎａｌｙｓｉｓ．Ｕｎ...     

东昆仑拉浪麦地区地球化学勘查异常下限确定方法对比研究

东昆仑地区是我国重要成矿带,地球化学勘查作为该区基础性的勘查手段在区域找矿、矿区及其外围找矿发挥了重要作用。地球化学勘查工作中,异常下限的确定是圈定地球化学异常的基础和关键。拉浪麦钨多金属矿区地球化学勘查工作中利用传统统计法、EDA法、含量—面积分形法分别对土壤地球化学分析元素计算确定异常下限,并结合成矿地质条件对三种方法计算出的异常下限进行综合对比研究,发现EDA法得出钨等元素异常不漏掉隐伏矿床形成的矿致异常,从而达到快速精准高效的找矿效果,具有很好代表性。因此,在东昆仑地区寻找钨多金属矿地球化学勘查中,采用EDA法确定异常下限是可行的。     

Delineation of Integrated Anomaly with Generative Adversarial Networks and Deep Neural Networks in the Zhaojikou Pb-Zn Ore District,Southeast China

Geochemical maps are of great value in mineral exploration. Integrated geochemical anomaly maps provide comprehensive information about mapping assemblages of element concentrations to possible types of mineralization/ore, but vary depending on expert’s knowledge and experience. This paper aims to test the capability of deep neural networks to delineate integrated anomaly based on a case study of the Zhaojikou Pb-Zn deposit, Southeast China. Three hundred fifty two samples were collected, and ea...     

Characterization of Geochemical Distributions Using Multifractal Models

The use of multifractals in the applied sciences has proven useful in the characterization and modeling of complex phenomena. Multifractal theory has also been recently applied to the study and characterization of geochemical distributions, and its relation to spatial statistics clearly stated. The present paper proposes a two-dimensional multifractal model based on a trinomial multiplicative cascade as a proxy to some geochemical distribution. The equations for the generalized dimensions, mass exponent, coarse Lipschitz–Hölder exponent, and multifractal spectrum are derived. This model was tested with an example data set used for geochemical exploration of gold deposits in Northwest Portugal. The element used was arsenic because a large number of sample assays were below detection limit for gold. Arsenic, however, has a positive correlation with gold, and the two generations of arsenopyrite identified in the gold quartz veins are consistent with different mineralizing events, which gave rise to different gold grades. Performing the multifractal analysis has shown problems arising in the subdivision of the area with boxes of constant side length and in the uncertainty the edge effects produce in the experimental estimation of the mass exponent. However, it was possible to closely fit a multifractal spectrum to the data with enrichment factors in the range 2.4–2.6 and constant K₁ = 1.3. Such parameters may give some information on the magnitude of the concentration efficiency and heterogeneity of the distribution of arsenic in the mineralized structures. In a simple test with estimated points using ordinary lognormal kriging, the fitted multifractal model showed the magnitude of smoothing in estimated data. Therefore, it is concluded that multifractal models may be useful in the stochastic simulation of geochemical distributions.     

南极松散沉积物粒度分形研究

利用分形理论, 研究了南极纳尔逊冰盖前缘发育的沉积物、风成沉积物及湖泊沉积物的粒度分布分形结构特征. 结果表明: 不同沉积环境下的沉积物粒度分形结构具有明显的差异, 冰盖前缘沉积物具有显著的分形结构特征, 而湖泊沉积物和风成沉积物不具有分形结构特征, 这为识别南极地区松散沉积物沉积环境提供了一种新的判别依据. 对纳尔逊冰盖前缘沉积物粒度分维特征的研究结果表明, 其粒度分布主要与冰川搬运的动力学过程有关, 分维值的大小与当时形成沉积物的动力学过程、沉积环境、冰盖进退及古气候环境的演化密切相关.     

区域地球化学异常空间分形结构及其意义——以浙江省诸暨地区区域地球化学数据为例

区域地球化学数据既具有确定性的特征 ,又具有随机性的特征 ,从而地球化学异常的空间分布具有标度不变性的特征 ,即空间分形结构。本文运用元素含量 等值线面积模型、元素含量的周长与面积模型 ,查明区域地球化学异常分形结构 ,初步探讨了其形成机制 ,并讨论了元素含量与等值线面积的空间分形模型用于划分地球化学异常与背景的意义。     

多重地球化学背景下地球化学弱异常增强识别与信息提取

为对钦州湾-杭州湾成矿带(南段)庞西垌地区地球化学数据进行异常识别研究与信息提取,利用含量-面积法(C-A)得出庞西垌地区成矿主元素的异常下限,得到各元素异常分布图,并与已知矿(床)点进行叠加分析,发现已知矿(床)点与C-A法分析得到的异常区基本吻合,可根据该异常区预测未知矿床,从而为该研究区矿产资源潜力评价提供依据。为进一步从研究区复杂的地球化学背景中分离出与成矿有关的地球化学异常,采用分形滤波技术(S-A)提取致矿异常。研究表明,S-A法可在C-A法揭示的区域异常的基础上更深层次地提取出与矿化有关的局部异常用以反映研究区的多重地球化学背景,S-A法可有效地使弱异常增强进而提取出致矿异常,为庞西垌地区探寻隐伏矿体提供依据。     

基于分形几何理论的DFN模型构建方法研究

以重庆梁-忠（梁平县-忠县）高速公路礼让隧道为工程研究背景,通过测线法调查现场节理,获得了节理产状分布概率密度函数,并从分形几何学的角度分析了节理间距及迹长的分形分布规律,推导出能反映节理间距及迹长分布状态的分形维数D及分形分布概率密度函数。在该基础上采用Matlab软件以及Monte-Carlo随机分析方法,产生节理参数随机数,结合3DEC中最新模块离散裂隙网络(DFN)技术,建立了能反映节理裂隙分布特征的离散裂隙网络模型并验证了模型的有效性,结果表明,分形分布比负指数分布包含更多的间距、迹长分布信息,更接近于实际分布;分形维数D反映了节理间距、迹长在其变化范围内的分布特征,分形维数的大小取决于小间距、小迹长部分数量在总节理数量中的比例,为节理裂隙岩体网络模型构建提供了一种新方法。     

Comparison of U-spatial statistics and C–A fractal models for delineating anomaly patterns of porphyry-type Cu geochemical signatures in the Varzaghan district,NW Iran

The delineation of populations of stream sediment geochemical data is a crucial task in regional exploration surveys. In this contribution, uni-element stream sediment geochemical data of Cu, Au, Mo, and Bi have been subjected to two reliable anomaly-background separation methods, namely, the concentration-area (C–A) fractal and the U-spatial statistics methods to separate geochemical anomalies related to porphyry-type Cu mineralization in northwest Iran. The quantitative comparison of the delineated geochemical populations using the modified success-rate curves revealed the superiority of the U-spatial statistics method over the fractal model. Moreover, geochemical maps of investigated elements revealed strongly positive correlations between strong anomalies and Oligocene–Miocene intrusions in the study area. Therefore, follow-up exploration programs should focus on these areas.     

Predictive geochemical mapping using environmental correlation

The distribution of chemical elements at and near the Earth's surface, the so-called critical zone, is complex and reflects the geochemistry and mineralogy of the original substrate modified by environmental factors that include physical, chemical and biological processes over time.Geochemical data typically is illustrated in the form of plan view maps or vertical cross-sections, where the composition of regolith, soil, bedrock or any other material is represented. These are primarily point observations that frequently are interpolated to produce rasters of element distributions. Here we propose the application of environmental or covariate regression modelling to predict and better understand the controls on major and trace element geochemistry within the regolith. Available environmental covariate datasets (raster or vector) representing factors influencing regolith or soil composition are intersected with the geochemical point data in a spatial statistical correlation model to develop a system of multiple linear correlations. The spatial resolution of the environmental covariates, which typically is much finer (e.g. ∼90 m pixel) than that of geochemical surveys (e.g. 1 sample per 10-10,000 km²), carries over to the predictions. Therefore the derived predictive models of element concentrations take the form of continuous geochemical landscape representations that are potentially much more informative than geostatistical interpolations.Environmental correlation is applied to the Sir Samuel 1:250,000 scale map sheet in Western Australia to produce distribution models of individual elements describing the geochemical composition of the regolith and exposed bedrock. As an example we model the distribution of two elements – chromium and sodium. We show that the environmental correlation approach generates high resolution predictive maps that are statistically more accurate and effective than ordinary kriging and inverse distance weighting interpolation methods. Furthermore, insights can be gained into the landscape processes controlling element concentration, distribution and mobility from analysis of the covariates used in the model. This modelling approach can be extended to groups of elements (indices), element ratios, isotopes or mineralogy over a range of scales and in a variety of environments.