区域化变量的空间聚类分析

传统的聚类分析方法利用数据对平均值的偏差，研究变量之间的相互关系。当它应用于区域化变量的分类时，因缺乏对区域化变量的空间结构的考虑，对合理解释区域化变量之间的相互关系不利。空间聚类分析方法比较好地解决了这个问题。本文介绍了该方法的基本原理及其算法，并说明了它在非条件模拟及在某矿区中的应用情况。     

空间相关阵的一种快速算法

空间因子分析和空间聚类分析是近五年发展起来的新方法，对于区域化变量的数据处理质量的提高有着重要意义。它们的标准算法运算速度极慢，影响了其实际应用。为此本文介绍一种快速计算空间相关阵以提高空间因子分析和空间聚类分析运算速度的算法。     

地质统计学中的区域化变量理论

着重介绍了地质统计学中最基本的问题－区域化变量理论，包括对区域化变量的解释、概率表示、平稳假设，以及协同区域化问题。最后，介绍了研究区域化变量的几个基本工具：变差函数和协方差；估计方差和离散方差。     

协同泛克立格法—数据处理的新方法

协同克立格法是多元地质统计学的一个重要方法，它以协同区域化变量为研究对象，充分考虑了变量的空间相关性和变量间的统计相关性，因而有着单变量克立格法无可比拟的优点。非平稳条件下的协同泛克立格法不仅能对变量进行线性、无偏、最优估计，而且能对漂移和剩余进行估计。协同泛克立格法在数据处理中有着十分乐观的发展前景。     

地质统计学及其在第四纪研究中的应用

地质统计学是数学地质领域最为活跃而实用的分支,它是以区域化变量理论为基础,以变异函数为基本工具,研究那些在空间分布上既具有随机性又具有结构性的自然现象的科学。在第四纪研究中的很多特征(变量)均可看成区域化变量进行地质统计学分析。作者在讨论了经典概率论及数理统计方法简单地应用于第四纪研究可能出现的问题后,着重介绍了用于第四纪研究中的若干地质统计学方法及基本理论,同时,对地质统计学方法应用于第四纪研究中的前景进行了分析。     

岩溶水区域化变量特异值识别与处理方法研究

在岩溶水区域化变量克立格估计中,特异值的存在将对区域化变量局部估计精度产生重要影响。本文针对岩溶发育的极不均匀性,分析了特异值产生的客观物理背景,并结合实际探讨了影响岩溶水区域化变量克立格估计精度的特异值的识别与处理方法。      

对应聚类分析

对应聚类分析是一种多元统计分析方法。它吸取了对庆分析和聚类分析的主要优点，在充分利用多维空间信息的基础上，该方法将变量类别，样品类别和它们间的对应关系清晰显示单一图件，即对应聚类谱系图。近年来的许多实例说明该方法，通过一些验证性实例介绍了方法，并简要讨论了为什么能获得较好效果的原因。     

PC-1500袖珍计算机数学地质应用程序(续)

六、多元线性回归分析 (一)方法概述及其在地质方面应用回归分析是研究变量间相互关系的一种统计方法,多元线性回归分析是研究某一变量与多变量之间的线性关系(非线性也可以转化为线性关系),它是以大量观测收集到数据为基础,找出相关变量之间的内部规律性,以定量形式建立一个变量与另一个变量(或另几个变量之间关系的数学表达式,从而可以根据一个或几个变量的观测值来预测(预报)另一个变量的估计值,并能从多个指标中找出对所研究的问题起重要作用的某些指标及它们之间转换关     

一种协克里格法的矩阵分析

协克里格法所研究的是关于协同区域化变量的估计问题.Myers用矩阵方法研究了一般的估计问题.问题的提法是:设有k维区域化向量,或k维协同区域化变量记为     

岩溶含水介质渗透性参数空间最优估计的原理与方法

本文着重阐述区域化变量理论和克立格法在岩溶含水介质渗透性分析中的应用，并对岩溶含水介质渗透性参数空间最优估计的方法进行了探讨。     

因子分析中变量和样品空间的统一

以空间结构分析为基础，提出了一个统一的变量和样品空间，由此得到因子空间，依据因子空间中变量和样品的相关性，很容易确定样品点群的成因，还讨论了因子分析中变量坐标和样品坐标的概念，指出因子得分不是样品的坐标，因而把因子得分图看作为因子空间坐标图是不合适的。     

Standing different ground: the spatial heterogeneity of territorial disputes

Recent developments in spatial analysis and spatial data have allowed researchers to investigate various geographical factors in the quantitative analysis of conflict and war (Ward in Polit Geogr 21(2):155–158, 2002). Despite the importance of territory in interstate conflict, there has been a limited interest in the application of spatial analysis to the study of territorial conflict. Using geographically weighted regression (GWR) we evaluated the existing explanations of territorial conflict provided by a global scale analysis that assumes a spatial consistency in the explanatory variables. Specifically, we revisited Paul Huth’s foundational work by using GWR to examine the spatial pattern in the sign and significance of the variables. The result of GWR shows that the escalation of territorial conflict cannot be fully explained by one universal model. There is a high level of spatial variation in the regression parameters and the explanatory power of the model varies over space. A k-means cluster analysis was implemented for a further investigation of the regional pattern of the underlying causes of territorial disputes. The result of our GWR suggests the necessity and possibility to pursue a local or regional scale approach to the study of territorial conflict, an approach that challenges an epistemology of seeking a single explanation for the causes of conflict that neglects regional context. The spatial heterogeneity in the causes of territorial conflict escalation we find is framed within a narrative of the intertwined processes of colonialism, Cold War legacies, and competition for resources.     

Spatial variability analysis of precipitation in northwest Iran

The spatial variability of precipitation was investigated in the northwestern corner of Iran using data collected at 24 synoptic stations from 1986 to 2015. Principal component analysis (PCA) and cluster analysis (CA) were used to regionalize precipitation in the study area. Eleven precipitation variables were averaged and arranged as an input matrix for the R-mode PCA to identify the precipitation patterns. Results suggest that the study area can be divided into four spatially homogeneous sub-zones. In addition, the spatial patterns of annual precipitation were identified by applying the T-mode PCA and CA to the annual precipitation data. The delineated spatial patterns revealed three distinct sub-regions. The resultant maps were compared with the spatial distribution of the rotated principal components (PCs). Results pointed out that the delineated clusters are characterized by different precipitation variability; and using different precipitation parameters can lead to different spatial patterns of precipitation over northwest Iran.     

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.

     

Relationship of geological and geothermal field properties: Midcontinent area, USA, an example

Quantitative approaches to data analysis in the last decade have become important in basin modeling and mineral-resource estimation. The interrelation of geological, geophysical, geochemical, and geohydrological variables is important in adjusting a model to a real-world situation. Revealing the interdependences of variables can contribute in understanding the processes interacting in sedimentary basins. It is reasonably simple to compare spatial data of the same type but more difficult if different properties are involved. Statistical techniques, such as cluster analysis or principal components analysis, or some algebraic approaches can be used to ascertain the relations of standardized spatial data. In this example, structural configuration on five different stratigraphic horizons, one total sediment thickness map, and four maps of geothermal data were copared. As expected, the structural maps are highly related because all had undergone about the same deformation with differing degrees of intensity. The temperature gradients derived (1) from shallow borehole logging measurements under equilibrium conditions with the surrounding rock, and (2) from non-equilibrium bottom-hole temperatures (BHT) from deeper depths are mainly independent of each other. This was expected and confirmed also for the two temperature maps at 1000 ft which were constructed using both types of gradient values. Thus, it is evident that the use of a 2-point (BHT and surface temperature) straightline calculation of a mean temperature gradient gives different information about the geothermal regime than using gradients from temperatures logged under equilibrium conditions. Nevertheless, it is useful to determine to what a degree the larger dataset of nonequilibrium temperatures could reflect quantitative relationships to geologic conditions. Comparing all maps of geothermal information vs. the structural and the sediment thickness maps, it was determined that all correlations are moderately negative or slightly positive. These results are clearly shown by the cluster analysis and the principal components. Considering a close relationship between temperature and thermal conductivity of the sediments as observed for most of the Midcontinent area and relatively homogeneous heat-flow density conditions for the study area these results support the following assumptions: (1) undifferentiated geothermal gradients, computed from temperatures of different depth intervals and differing sediment properties, cannot contribute to an improved understanding of the temperature structure and its controls within the sedimentary cover, and (2) the quantitative approach of revealing such relations needs refined datasets of temperature information valid for the different depth levels or stratigraphic units.     

Characterization of underground tunnel water hydrochemical system and uses through multivariate statistical methods: a case study from Maddhapara Granite Mine,Dinajpur, Bangladesh

A quality study of the drained water from Maddhapara Granite Mine underground tunnel was undertaken to study their hydrochemical variations and suitability for various uses employing chemical analysis, basic statistics, correlation matrix (r), cluster analysis, principal component/factor analyses, and ANOVA as the multivariate statistical methods. The results of chemical analysis of water show the modest variation in their ionic assemblage among different sampling points of the tunnel where Ca–HCO₃ type of hydrochemical facies is principally dominated. The correlation matrix shows a very strong to very weak positive, even negative, correlation relationship, suggesting the influence of different processes such as geochemical, biochemical processes, and multiple anthropogenic sources on controlling the hydrochemical evolution and variations of water in the mine area. Cluster analysis confirms that cluster 1 contains 68.75% of total samples, whereas cluster 2 contains 31.25%. On the whole, the dominated chemical ions of first cluster groups are Ca and HCO₃, suggesting a natural process similar to dissolution of carbonate minerals. The second cluster group consisted of Cl^? and SO₄ ^2? ions representing natural and anthropogenic hydrochemical process. The results of PCA/FA analysis illustrate that different processes are involved in controlling the chemical composition of groundwater in the mine area. The factor 1 loadings showed that pH, EC, TDS, Na, Mg, chloride, and sulfate which have high loading in this factor are expected to come from carbonate dissolution to oxidation conditions. One-way ANOVA describes the significance of dependent variables with respect to independent variables. ANOVA gives us the idea that EC, K⁺, Fe^total, SO ₄ ² , As, and Pb are the most important factors in controlling spatial differences in water quality in this tunnel. But different results have been encountered for different independent variables which might be due to dissimilar sources of water. From the qualitative analysis, it is clear that water quality is not very favorable for aquatic creatures as well as for drinking purposes. The water can be used for irrigation purposes without any doubt as SAR and RSC analysis provides good results. Moreover, the results of this research confirmed that the application of multivariate statistical analysis methods is apposite to inferring complex water quality data sets with its possible pollution sources. At the end, this research recommends (1) as water becomes more and more important, water treatment plants should be built before the water being used; (2) a detailed water step utilization plan should be set beforehand to guarantee tunnel water being used effectively; and (3) after the water being used for agriculture, elements in crops should be monitored continuously to ensure that ions and compounds that come from the tunnel water are lower than guideline values for human beings health.     

基于地下水多变量空间聚类分析的变异性评价

在现存地下水监测网站中,观测站点分布的任意性、随意性和层次不清以及观测数据的冗余性等问题普遍存在,应用空间聚类原理,对所选研究区域廊坊地下水的监测点位及监测指标分别进行了空间聚类分析,对原始数据和经聚类处理后的数据分别进行了空间变异性评价,结果显示空间聚类分析是有效合理的。试图将空间变异性和空间聚类方法结合起来,为环境监测点的重新布置提供了理论依据,使提高监测效率与监测点的代表性、优化监测网格成为了可能;了解监测指标及监测点位在空间上的相关程度,为环境监测指标的确定提供理论依据,进而为环境管理、污染物控制以及环境资源的综合利用提供基础依据。     

Cluster analysis of a regional-scale soil geochemical dataset in northern California

A regional-scale soil geochemical study was conducted within a 22,000 km² area in northern California including the Sierra Nevada, Sacramento Valley, and northern Coast Range. Over 1300 soil samples were chemically analyzed for 42 elements. The distribution of distinct groups of elements demonstrates the interplay of geologic, hydrologic, geomorphologic and anthropogenic factors; however, it is difficult to fully appreciate the complexity of geochemical transport and weathering processes on a landscape-scale in an area of very complex geology with such a large dataset containing more than 40 variables. To examine the data from a perspective of multi-element groupings, cluster analyses were applied to the dataset. The analysis identified several groups of elements whose spatial patterns could be related to specific geologic sources.     

Poor housing and stroke mortality in population over 64 years old at the parish level,in mainland Portugal

Housing conditions can impact physical and mental health. In 2013, Portugal was still the fourth European Union country with the highest percentage of population without an adequately heated home in winter. Other adverse conditions are, for instance, overcrowding and living in older buildings. Some studies stress the relationship between stroke and poor living conditions in the elderly population, especially cold homes. Univariate and multivariate spatial cluster analysis were used to explore the relationship between excess stroke death risk, from 1998 to 2004, measured by the standardized mortality ratio (SMR) for several cohorts (including persons over 64 years old), and poor housing variables from the 2001 census, at the parish level in continental Portugal. A multivariate cluster of parishes, with population without any form of heating their homes as dominant condition, was detected in northwest Portugal. Mean and median SMR values across all cohorts were consistently higher within this cluster. This strengthens the hypothesis that cold homes deserve more attention in stroke prevention and mitigation amongst elderly persons, especially in northwestern continental Portugal.