Clustering of mineral prospectivity area as an unsupervised classification approach to explore copper deposit

This paper describes the usage of clustering methods including self-organizing map (SOM) and fuzzy c-means (FCM) which are applied to prepare mineral prospectivity map. Different evidential layers, including geological, geophysical, and geochemical, to evaluate Now Chun copper deposit located in the Kerman province of Iran are used. Clustering approaches are used to reduce the dimension of 13 feature vectors derived from different layers. At first, Geospatial Information Systems (GIS) is employed to analyze and integrate different layers, and the area under study is prioritized to five classes. Then, the SOM as an unsupervised classification method is carried out to classify this area into five clusters. Produced clusters are compared with GIS prospect map, while the SOM results are matched with the GIS output. The main reason to use the FCM is that a vector belongs simultaneously to more than one cluster so that membership values of each cluster can be mapped. As a consequence, clusters generated by the SOM and FCM are considerably matched with five-class-map of the GIS approach. The chosen cluster as a high potential location to additional drilling is matched to the main alteration and faults zone. To validate generated clusters for mineral potential mapping, geological matching of study area and selected proper cluster can be a satisfactory way. Finally, clustering methods can be a very fast approach to interpret the area under study.     

基于GIS和单元簇的模糊逻辑推理及其在区域矿产预测中的应用

论述了 GIS支持下的一种基于“单元簇”概念和模糊逻辑推理的多元地学信息综合分析方法及其在区域矿产预测中的应用。针对以往矿产定量预测中的单元划分方法对空间信息利用不足的问题 ,用单元的空间组合 (“单元簇”)代替单元作为定量类比的基本单位 ,从而能较充分地利用地质变量的局部空间结构信息 ;将单元作为 GIS区图元 ,利用 GIS空间分析功能实现对单元及单元簇的管理和操作 ;建立两个层次即变量对单元和组成单元对单元簇的模糊推理规则 ,经两次模糊推理计算出所有未知单元的找矿有利度 ,为进一步圈定找矿远景区提供了基础 ,并以新疆康古尔塔格地区金矿预测实例说明了其应用效果     

Methods for geographic profiling of biological invasions with multiple origin sites

Geographic profiling is a method that proved to be useful also in order to investigate the point of origin of a biological invasion. K-means clustering and Voronoi diagrams can partition a data set of geographic positions of populations invading a defined area and are, therefore, useful in cases in which an invasion had more introduction events as points of origin. One critical point of the method is to identify the right number of clusters in which to divide the starting data set formed by groups of points on a map. The Silhouette method proved to be capable of identifying the best number of subsets (clusters) of the general set of observations by providing different values for different subdivisions of the set of observations in clusters. For each cluster, the corresponding Voronoi tessellation was built on the starting map. To test the method, we did a simulation of clusters of data (points) on a map and we verified whether the proposed methods worked efficiently with the simulated data set with hundred repeats and using a varying number of clusters on the same map. The used techniques revealed to be efficient in finding the highest probability area of the map that would include the starting points for each cluster. A case study consisted in a known data set, that is, the spreading pattern of Caulerpa racemosa var. cylindracea (sea grapes), that was compatible (highest probability) with an original point of introduction in southern Italy and long distance (thousands of kilometers) secondary spreads via anthropic dispersal. The proposed techniques may also be applied to other kinds of data sets of biological data distributed on a map or in general on a geometrical surface.     

Cluster analysis applied to regional geochemical data: Problems and possibilities

Cluster analysis can be used to group samples and to develop ideas about the multivariate geochemistry of the data set at hand. Due to the complex nature of regional geochemical data (neither normal nor log-normal, strongly skewed, often multi-modal data distributions, data closure), cluster analysis results often strongly depend on the preparation of the data (e.g. choice of the transformation) and on the clustering algorithm selected. Different variants of cluster analysis can lead to surprisingly different cluster centroids, cluster sizes and classifications even when using exactly the same input data. Cluster analysis should not be misused as a statistical “proof” of certain relationships in the data. The use of cluster analysis as an exploratory data analysis tool requires a powerful program system to test different data preparation, processing and clustering methods, including the ability to present the results in a number of easy to grasp graphics. Such a tool has been developed as a package for the R statistical software. Two example data sets from geochemistry are used to demonstrate how the results change with different data preparation and clustering methods. A data set from S-Norway with a known number of clusters and cluster membership is used to test the performance of different clustering and data preparation techniques. For a complex data set from the Kola Peninsula, cluster analysis is applied to explore regional data structures.     

Statistical analysis for the hydrogeological evaluation of the fracture networks in hard rocks

The hydrogeological effectiveness of fracture sets is determined and evaluated by the fuzzy c-mean and hierarchical clustering. These cluster analyses combine the geological spatial attributes and the hydraulic relevant attributes of fractures. Based on the results of the clustering the fracture set volumes are estimated.     

Geometallurgical Modeling at Olympic Dam Mine, South Australia

Modeling of geometallurgical variables is becoming increasingly important for improved management of mineral resources. Mineral processing circuits are complex and depend on the interaction of a large number of properties of the ore feed. At the Olympic Dam mine in South Australia, plant performance variables of interest include the recovery of Cu and U₃O₈, acid consumption, net recovery, drop weight index, and bond mill work index. There are an insufficient number of pilot plant trials (841) to consider direct three-dimensional spatial modeling for the entire deposit. The more extensively sampled head grades, mineral associations, grain sizes, and mineralogy variables are modeled and used to predict plant performance. A two-stage linear regression model of the available data is developed and provides a predictive model with correlations to the plant performance variables ranging from 0.65–0.90. There are a total of 204 variables that have sufficient sampling to be considered in this regression model. After developing the relationships between the 204 input variables and the six performance variables, the input variables are simulated with sequential Gaussian simulation and used to generate models of recovery of Cu and U₃O₈, acid consumption, net recovery, drop weight index, and bond mill work index. These final models are suitable for mine and plant optimization.     

A general family of counting distributions suitable for modeling cluster phenomena

The two-dimensional spatial distribution of precious stones, such as diamonds in alluvial and coastal deposits, shows a high degree of clustering. Usually, stones tend to gather in relatively small clusters or traps, made by potholes, gullies, or small depressions in the rough bedcock. Therefore, when taking samples of such deposits, discrete distributions of the number of stones counted in each sample yield an extreme skewness. Most samples have no stones, whereas samples containing a few hundred stones are not unusual. This paper constructs a model and a method for fitting a new and general family of counting distributions based on the Neyman-Scott cluster model and the mixed Poisson process, which can be used to model a differing degree of clustering. General recursion equations for the discrete probabilities of these distributions are derived. Application of this model to simulated data shows that information such as cluster size, number of point events per cluster, and number of clusters per measurement unit can be extracted easily from this model. Fitting the model to data of two real diamond deposits of a totally different nature—small rich clusters of Namibia versus larger but less rich clusters of Guinea—demonstrates its flexibility.     

The dynamism of clustering: Interweaving material and discursive processes

The aim of this paper is to contribute to an understanding of clusters, including both the material and discursive dynamism of cluster construction, and shed light on how clusters—once established—affect the actors, institutions and processes that constitute them. It does this by viewing clusters as an actant, i.e. something that acts or to which activity is granted by others. The empirical analysis examines two clusters in the public cluster programme Norwegian Centre of Expertise (NCE): the Møre maritime cluster and the Hordaland subsea cluster. It focuses on the type of development paths they are following and how the material and discursive processes are interweaved in these paths. The clusters are related to the concept of cluster construction, which is triggered by ideas, representations, policy and industry practice. The Møre maritime cluster is characterized by bottom-up clustering processes and illustrates how the material practices of firms can trigger clustering processes such as the establishment of a cluster and the identification of a prototype of best cluster practice. On the other hand, the Hordaland subsea cluster expresses a top-down process and how the ideal world of academics and policy-making can encourage processes of clustering among co-located firms. Based on these observations of material and discursive interweaved clustering processes and how they affect both those who are practicing and those who are promoting them, we find it reasonable to argue for a stronger awareness of such feedback loops in cluster studies.     

Hyperspectral image betweenness centrality clustering based adaptive spatial and spectral neighborhood approach for anomaly detection

Segmentation-based anomaly detectors proceeds to the clustering of the hyperspectral image as a first step. However, most of the well-known clustering methods cluster anomalous pixels as a part of the background. This paper presents a new hyperspectral image clustering approach based on the betweenness centrality measure. The proposed approach starts by the construction of an adaptive spatial and spectral neighborhood for each pixel. This neighborhood is based on the selection of the nearest spectral and spatial neighbors in multiple windows around each pixel to allow well-suited representation of the image features. In the next step, this neighborhood is clustered based on the edge betweenness measure algorithm that splits the image into regions sharing similar features. This approach (1) allows the reduction of intercluster relationship, (2) favors intracluster relations, and (3) preserves small clusters that can hold anomalous pixels. Experimental results show that the proposed approach is efficient for clustering and overcomes the state of the art approaches.     

Bolshetagninskoe Deposit Microcline-Pyrochlore Ore Process Mineralogy

Bolshetagninskoe deposit is one of the most important Russia niobium potential sources. It is confined to carbonatite complex of the same name that is situated in the Sayan Mountains, Eastern Siberia. In the result of VIMS exploration niobium ores reserves have been applied by Russian State Reserve Committee in 2012 year. Ores contain about 1% Nb2O5 and are unique in that the economic pyrochlore mineralization is concentrated in alkaline metasomatic rocks but not in carbonatites[1]. During exploration 47 borehole samples and 6 bulk samples were collected and studied by process mineralogy techniques (optic mineralogical analyze, optic image analyzer system, XRD, EPMA). 26 borehole samples and 2 bulk samples were tested by rougher floatation to define geometallurgical items and to understand the ore’s behavior. Four volumetric samples have been tested by commissioned flowsheet (radiometric separation → impact milling → selective floatation → pyrochlore leaching → ferroniobium). There are three ore types in the Bolshetagninskoe deposit: microcline-pyrochlore (MP), biotite-columbite-pyrochlore (BCP) and carbonate-pyrochlore (CP). MP type is the most important one. MP ore consists of microcline (59wt%–70wt%) with minor carbonates, apatite, sulfides, goethite. Pyrochlore, the essential Nb mineral (94% of ore Nb content), occurs as fine grains (weighted average grain size is 57 μn). Since pyrochlore grains are fine and friable, the ore preparation size and method is a main problem of its treatment. While primary ore processing is effective to remove about 30% waste material it is important to evaluate its influence on floatation feed grade.     

Research and application of cluster and association analysis in geochemical data processing

For applications of data mining techniques in geosciences, through mining spatial databases which are constructed with geophysical and geochemical data measured in fields, critical knowledge, such as the spatial distribution of geological targets, the geophysical and geochemical characteristics of geological targets, the differentiation among the geological targets, and the relationship among geophysical and geochemical data, can be discovered. Due to the complexity of geophysical and geochemical data, traditional mining methods of cluster analysis and association analysis have limitations in processing complex data. In this paper, a clustering algorithm based on density and adaptive density-reachable is presented which has the ability to handle clusters of arbitrary shapes, sizes, and densities. For association analysis, mining the continuous attributes may reveal useful and interesting insights about the data objects in geoscientific applications. An approach for distance-based quantitative association analysis is presented in this paper. Experiments and applications indicate that the algorithm and approach are effective in real-world applications.     

The application of geochemical pattern recognition to regional prospecting: A case study of the Sanandaj–Sirjan metallogenic zone,Iran

In regional exploration programs, the distribution of elements in known mineral deposits can be used as a guide for the classification of deposits, search for new prospects and modeling ore deposit patterns. The Sanandaj–Sirjan Zone (SSZ) is a major metallogenic zone in Iran, containing lead and zinc, iron, gold, copper deposits. In the central part of the SSZ, lead and zinc mineralization is widespread and hitherto exploration has been based on geological criteria. In this study, we used clustering techniques applied to element distribution for classification lead and zinc deposits in the central part of the SSZ. The hierarchical clustering technique was used to characterize the elemental pattern. Elements associated with lead and zinc deposits were separated into four clusters, encompassing both ore elements and their host rock-forming elements. It is shown that lead and zinc deposits in the central SSZ belong to two genetic groups: a MVT type hosted by limestone and dolomites and a SEDEX type hosted by shale, volcanic rocks and sandstone. The results of elemental clustering were used for pattern recognition by the K-means method and the respective deposits were classified into four distinct categories. K-means clustering also reveals that the elemental associations and spatial distribution of the lead and zinc deposits exhibit zoning in the central part of the SSZ. The ratios of ore-forming elements (Sb, Cd, and Zn) vs. (Pb and Ag) show zoning along an E–W trend, while host rock-forming elements (Mn, Ca, and Mg) vs. (Ba and Sr) show a zoning along a SE–NW trend. Large and medium deposits occur mainly in the center of the studied area, which justify further exploration around occurrences and abandoned mines in this area. The application of a pattern recognition method based on geochemical data from known mineralization in the central SSZ, and the classification derived from it, uncover elemental zoning, identify key elemental associations for further geochemical exploration and the potential to discover possible target areas for large to medium size ore deposits. This methodology can be applied in a similar way to search for new ore deposits in a wide range of known metallogenic zones.     

Automatic Identification of Rock Fracture Sets Using Finite Mixture Models

The clustering and classification of fracture orientation data are crucial tasks in geotechnical engineering and rock engineering design. The explicit simulation of fracture orientations is always applied to compensate for the lack of direct measurements over the entire rock mass. In this study, a single step approach based on the theory of finite mixture models, where the component distributions are Fisher distributions, is proposed for automatic clustering and simulation of fracture orientation data. In the proposed workflow, the spherical K-means algorithm is applied to select the initial cluster centers, and the component-wise expectation–maximization algorithm using the minimum message length criterion is used to automatically determine the optimal number of fracture sets. An additional advantage of the proposed method is the representation of orientation data using a full sphere, instead of the conventional hemispherical characterization. The use of a full spherical representation effectively solves the issue of clustering for fractures with high dip angles. In addition, the calculation process of the mean direction is also simplified. The effectiveness of the model-based clustering method is tested with a complicated artificial data set and two real world data sets. Cluster validity is introduced to evaluate the clustering results. In addition, two other clustering algorithms are also presented for comparison. The results demonstrate that the proposed method can successfully detect the optimal number of clusters, and the parameters of the distributions are well estimated. In addition, the proposed method also exhibits good computational performance.     

地质冶金学及其在金和关键金属赋存状态研究中的新应用

地质冶金学(Geometallurgy)是一门交叉学科,将矿体的地质学、地球化学和矿物学特征与冶金性能联系起来,目标是描述和了解矿体的冶金性质的多样性,并建立三维地质冶金学模型,用于协助矿山开采计划和优化工艺设计流程等。金矿石依据选冶难度可以分为易选矿石和难选矿石,其中难选矿石的原因主要可以归结为金的包裹和脉石矿物影响两种因素。金的地质冶金学需要查清金的赋存状态,包括金矿物的种类与矿石难选冶的原因,从而为选矿提供指导。金的赋存形态包括显微金、亚显微金和表面金,研究金的赋存状态需要使用自动矿物分析系统等分析显微金矿物,并结合多种选矿试验来交叉验证,加上对载金矿物中亚显微金的分析,得到金的全部分布特征。不同成因类型的金矿床往往具有不同的地质冶金学特征,同时金的地质冶金学研究还可以对矿床的成因和演化过程提供依据。本文简要介绍了近年来典型的热液金矿床包括斑岩型、浅成低温热液型、铁氧化物-铜-金(IOCG)型、卡林型和矽卡岩型的地质冶金学的研究进展,以及应用于地质冶金学上的新方法如VNIR-SWIR高光谱技术、地球化学数据机器学习。关键金属具有含量低、矿物细小的研究难点,与金的地质冶金学研究具有诸多相似之处,因此本文提出将金的赋存状态研究的流程和新技术方法应用于关键金属矿床,并设计了关键金属赋存状态的研究流程和规范化表达,进一步延伸了地质冶金学的内涵和外延。     

Risk assessment of cultural heritage sites clusters using satellite imagery and GIS: the case study of Paphos District,Cyprus

This paper aims to assess the risk of natural and anthropogenic hazards for cultural heritage in Cyprus by integrating multi-temporal GIS and earth observation analysis, in the area of Paphos District. The work presented here attends to re-evaluate previous results from earth observations and GIS analysis and go a step forward targeting more reliable outcomes for cultural heritage management. The scope of the paper was to develop a more accurate methodology for risk assessment against natural and anthropogenic hazards (e.g., soil erosion; urban expansion), based on homogeneous clustering of the monuments under consideration. The accomplished assessment approach, being lopsided and generic, cannot be applied across the board and undistractedly for cultural heritage management of all types of monuments of the district. Instead, the proposed clustering of monuments based on a variety of parameters is taking into consideration characteristics of their immediate environment, resulting rational local-based outcomes more useful for monuments and sites safeguarding and for prevention measurements. For each one of the five clusters of monuments located in the Paphos District, an analytical hierarchy process (AHP) method was followed in order to address the individual and unique characteristics of the monuments and sites within the same cluster area. Subsequently, the weight factors from these clusters were interpolated to the whole district, prior to the application of the overall AHP risk assessment. Ultimately, the results were compared with the overall AHP method applied for the entire Paphos District, indicating that the proposed methodology can be more accurate and realistic for the different groups of the monuments.     

Joint High-Order Simulation of Spatially Correlated Variables Using High-Order Spatial Statistics

Joint geostatistical simulation techniques are used to quantify uncertainty for spatially correlated attributes, including mineral deposits, petroleum reservoirs, hydrogeological horizons, environmental contaminants. Existing joint simulation methods consider only second-order spatial statistics and Gaussian processes. Motivated by the presence of relatively large datasets for multiple correlated variables that typically are available from mineral deposits and the effects of complex spatial connectivity between grades on the subsequent use of simulated realizations, this paper presents a new approach for the joint high-order simulation of spatially correlated random fields. First, a vector random function is orthogonalized with a new decorrelation algorithm into independent factors using the so-termed diagonal domination condition of high-order cumulants. Each of the factors is then simulated independently using a high-order univariate simulation method on the basis of high-order spatial cumulants and Legendre polynomials. Finally, attributes of interest are reconstructed through the back-transformation of the simulated factors. In contrast to state-of-the-art methods, the decorrelation step of the proposed approach not only considers the covariance matrix, but also high-order statistics to obtain independent non-Gaussian factors. The intricacies of the application of the proposed method are shown with a dataset from a multi-element iron ore deposit. The application shows the reproduction of high-order spatial statistics of available data by the jointly simulated attributes.     

Maximum likelihood classification for facies inference from reservoir attributes

A cluster analysis methodology is developed to recover facies realizations from observed reservoir attributes. A maximum likelihood estimator allows us for identifying the most probable underlying facies using a spatial clustering algorithm. In seismic characterization, this algorithm can yield relevant geological models for subsequent history-matching studies. In history-matching procedures, it provides informative facies maps as well as starting points for further studies.     

A Methodology for the Definition of Geotechnical Mine Sectors Based on Multivariate Cluster Analysis

This paper offers a new method for the definition of geotechnical sectors in open pit mines based on multivariate cluster analysis. A geological-geotechnical data set of a manganese open pit mine was used to demonstrate the methodology. The data set consists of a survey of geological and geotechnical parameters of the rock mass, measured directly in several points of the mine, structured initially in twenty-eight variables. After the preprocessing of the data set, the clustering technique was applied using the k-Prototype algorithm. The squared Euclidean distance was used to quantify the proximity between numerical variables, and the Jaccard's coefficient of similarity was used to quantify the proximity between the nominal variables. The different cluster results obtained were validated by the multivariate analysis of variance. The identification of cluster structures was achieved by plotting them on the mine map for spatial visualization and definition of geotechnical sectors. These sectors are spatially contiguous and relatively homogeneous regarding their geological–geotechnical properties, indicated by a high density of points of the same group. It was possible to observe a great adherence of the proposed sectors to the mine geology, demonstrating the practical representativeness of the clustering results and the proposed sectors.

     

Fuzzy Modeling for Reserve Estimation Based on Spatial Variability

This article addresses a new reserve estimation method which uses fuzzy modeling algorithms and estimates the reserve parameters based on spatial variability. The proposed fuzzy modeling approach has three stages: (1) Structure identification and preliminary clustering, (2) Variogram analysis, and (3) Clustering based rule system. A new clustering index approach and a new spatial measure function (point semimadogram) are proposed in the paper. The developed methodology uses spatial variability in each step and takes the fuzzy rules from input-output data. The model has been tested using both simulated and real data sets. The performance evaluation indicates that the new methodology can be applied in reserve estimation and similar modeling problems     

基于深层土壤数据的多维分形成矿异常识别研究 ——以铜陵矿集区Cu元素为例

以铜陵矿集区Cu元素为例,开展基于深层土壤数据的多维分形成矿异常识别研究。结果表明,在土壤采样密度相对较低、元素含量空间分布差异不大的情况下,多维分形克里格插值法较普通克里格插值法对于成矿异常的识别具有极大的优势。对于铜陵矿集区这类矿床开采、开发程度已较高,表层土壤元素分布主要受控于外源污染的老矿集区,基于深层土壤样品数据的多维分形克里格方法可以有效地进行成矿异常识别,服务于老矿集区的深部、外围隐伏矿床找矿。而对于空白研究区,无论是基于深层土壤数据还是表层土壤数据,多维分形克里格方法应同样有效。多维分形方法下土壤元素成矿预测的异常下限值确定尚无标准,文中采用元素含量 矿床数目累积频率的计算方法,基于该方法提取的成矿异常区域较好地识别出了绝大多数已知矿床,同时识别出了值得作进一步异常查证的空白异常区域。