The multivariate (co)variogram as a spatial weighting function in classification methods

The multivariate variogram and the multivariate covariogram are used as spatial weighting functions for forming spatially homogeneous groups automatically. The groups are created after either deflating similarities between distant samples with the multivariate covariogram or by inflating dissimilarities between distant samples with the multivariate variogram. These approaches can be seen as generalization of the Oliver and Webster proposal. Two data sets show the efficiency of the two weighting functions when compared to the classical approach which does not take spatial information into account. In one case study, the weighting of similarities by the multivariate covariogram showed more interpretable results than the weighting of dissimilarities by the multivariate variogram.     

Numeric examination of multivariate soil samples

Numerical methods for the examination of multivariate soil samples are presented in geometric terms. Techniques of coordinate representation by principal components, by nonmetric scaling, and by a new method are discussed, as are techniques for agglomerative hierarchic cluster analysis. These are illustrated by two sets of previously published data.     

Spatial analysis of two-dimensional orientation data

A frequently encountered problem in structural geology is the analysis and interpretation of directional data with a geographical distribution. Such data may arise, for example, as samples of fracture strikes collected at a number of locations (rocky outcrops, road cuttings, etc.), trends of geological structures mapped in underground mines where they are exposed in the tunnel roof, or as lineaments annotated on aerial or satellite photographs. From such data, it is of interest to determine the structural domains in the area, that is, to partition the area into subareas of homogeneous structural pattern. This paper presents a method for performing such an analysis, and applies it to a data set collected from an underground coal mine.     

面向国土空间规划的地表基质分层分类调查监测研究

新时代生态文明建设为自然资源科学管理和国土空间现代化治理提出了更高的要求。基于此,自然资源部印发《自然资源调查监测体系构建总体方案》,首次提出“地表基质”概念,并已组织开展典型地区地表基质试点调查工作。然而目前地表基质三级分类、调查对象、调查内容、技术体系等仍未形成统一认识和标准,严重制约着地表基质调查研究工作。笔者等通过深入辨析地表基质科学内涵,综合考虑国土农业空间、国土生态空间、国土城镇空间规划的数据支撑需求,依据地表基质空间属性特征,建立了地表基质分层分类模型。基于科学性、统一性、操作性和应用性的分类原则,提出了地表基质三级分类方案,进一步探讨明确了地表基质分层分类调查对象和调查内容,建立了一套地表基质调查监测技术体系。本研究可为进一步开展地表基质调查研究提供理论依据和借鉴参考。     

An empirical assessment and illustration of some multivariate morphometric techniques

An artificial data set is used to illustrate the morphologic properties of some common multivariate techniques and consideration of three common situations. The first concerns a sample showing no obvious groupings. In this situation principal components (or coordinates) and factor analyses give a logical ordination of form variation; cluster analysis produces sizedominated groups. The second situation considers an homogeneous sample where size and shape have important implications. Principal components are tested for association with size and shape, both of which can be isolated if isometry exists; if allometry is present, isolation of shape is possible only by size elimination, e.g., conversion to ratios. The third situation examines a sample of unknown groupings in which shape variation is the only interest. Aside from ratios, two other methods which produce shape-dominant clusters are assessed. Some of the options available in cluster analysis are also examined.     

Use of indicator variograms for an enhanced spatial analysis

Flat variograms often are interpreted as representing a lack of spatial autocorrelation. Recent research in earthquake engineering shows that nearby field noise can substantially mask a prominent spatial autocorrelation and result in what appears to be a purely random spatial process. A careful selection of threshold in assigning an indicator function can yield an indicator variogram which reveals underlying spatial autocorrelation. Although this application involves use of seismic data, the results are relevant to geostatistical applications in general.     

基于地质统计学反演方法的洛带气田储层预测

研究区域为洛带气田遂宁组,该储层具有厚度薄、低孔隙度、低渗透层等特征,单一的约束稀疏脉冲反演难以达到精确刻画有利相带。地质统计学反演适用于复杂储层的地震预测和描述,与常规波阻抗反演相比,具有较高的垂向分辨率,能更有效地反映厚度薄的储层,反演结果更接近实际地质特征,能够很好地弥补约束稀疏脉冲反演缺陷,实现对储层特征的精细描述。针对研究区地质特点,根据储层发育特征和地质规律,基于地质统计学理论,采用岩性划分及统计学参数分析等技术方法进行储层预测,有效地预测了洛带气田的砂体厚度、平均孔隙度平面以及储层厚度。     

A method for seafloor classification using directional variograms, demonstrated for data from the western flank of the Mid-Atlantic Ridge

Seafloor classification is aimed at quantitatively characterizing seafloor properties such as roughness and anisotropy, and at using such spatial characteristics to distinguish geological provinces automatically. From geostatistical principals, a variogram method is developed for seafloor classification and it is demonstrated for data from the western flank of the Mid-Atlantic Ridge at 25°45N to 26°40N. This study uses HYDROSWEEP bathymetric data which have been ping-edited to flag erroneous data records, and navigation corrected. The classification method can handle the resultant data gaps inside the survey swaths as well as interpret data from several swaths. For a suite of test areas representative of different geological provinces, directional variograms are calculated, and characteristic parameters are extracted for the classification. Examples include a sediment pond, abyssal hill terrain in several segments and of variable spacing, inside and outside corners of ridge discontinuities, and mixed morphological forms. The dependency of the results on random or regular subsampling and on the size of the test area is investigated.     

基于PCA法和Fisher判别分析法的岩体质量等级分类

岩体质量等级分类在实际的工程中有着很重要的作用。基于主成分分析（PCA）法和与Fisher判别分析法相结合建立岩体质量等级判别模型,选取单轴抗压强度、岩体体积节理数、声波纵波速度、节理面风化变异系数、节理面粗糙度系数和透水性系数6种指标作为岩体质量分级判别的判别因子。以永平铜矿露天矿区工程岩体特征资料中的20个样本为训练样本,10个为待判样本,对该模型进行检验和应用,并与传统的RMR法、Fisher判别分析模型的结果进行比较,相应正确率分别为87%、70%、77%,判断结果表明利用主成分分析法和Fisher判别分析法建立的模型判别能力更高。     

一种新的岩浆岩分类定量方法

目前,岩浆岩的超基性、基性、中性、酸性的分类均根据SiO2的含量,但这种单一含量判别标准并不严谨,含量经常与分类不完全对应。使用TraceElem 1.0软件对各种岩浆岩进行逐步判别分析、聚类分析和对应分析研究,据此认为超基性岩由MgO和FeO组成的因子确定,基性岩则由P2O5、Fe2O3、TiO2、CaO、MnO组成的因子确定,中性岩由Na2O和Al2O3组成的因子确定,酸性岩由K2O和SiO2组成的因子确定。岩浆岩的分类宜以SiO2为主、以MgO和CaO为辅,尤其要引入MgO。在SiO2含量相同的情况下,MgO、CaO含量越高,基性程度越强。基于这一分析结果,提出一种新的酸度指数（ADI)计算方法,即ADI=w(SiO2)-0.75w(MgO)-0.23w(CaO),ADI<38.0%为超基性岩,在38.0%～52.0%之间为基性岩,在52.0%～62.5%之间为中性岩,>62.5%为酸性岩。     

Numerical classification by association analysis of multivariate mineralogic, petrographic, presence-absence data from some Sub-Himalayan carbonates; Northwest India

Fourteen mineralogical and petrographic variables for 82 samples of Sirban Limestone of Riasi, Jammu, and Kashmir State, and 18 mineralogical and petrographic variables for 36 samples of Bilaspur Limestone, Himachal Pradesh, India, were numerically classified based on presence-absence data using association analysis. The samples were collected along vertical profiles. The variables for the Sirban Limestone of Riasi were classified into three groups: (a) dolomite (b) micrites, and (c) terrigenous material represented by clay minerals. These three groups correspond to (a) near-shore sabkha dolomites, (b) deep water micrites, and (c) terrigenous contribution of clay minerals (except corrensite) to the carbonate depositional basin. Bilaspur Limestone samples were classified also into the same three groups. The results of the present study corroborate the earlier conclusions of the writer that the Sub-Himalayan carbonates of Northwest India generally represent rocks of shallow carbonate depositional basins, showing transition from near shore sabkha dolomites to basinal limestones and shales.     

Choosing the level of detail for depicting two-variable spatial relationships

A method for determining the most appropriate scale for presentation of spatial relationships between two variables combines the principle of entropy decomposition with Phipps' entropy-based method for determining mutual information of landscape patterns. The method enables determination of the optimal level of detail for maps, data matrices, or other depictions of two spatially associated phenomena. An example from wetland mapping is given.     

A PDF-based analysis of the spatial structure of retailing

The present paper proposes a new method for analyzing the spatial structure of retailing, using microscale locational data of individual retail stores. The method is based on the probability density function (PDF) of stores estimated from their locational data, and consequently it is applicable to both micro- and macro-scale retail analyses. The PDF approach provides a set of quantitative methods that permit us (1) to measure the degree of agglomeration, (2) to classify spatial patterns of store location, (3) to analyze the relationship between the size and function of retail agglomerations, and (4) to analyze the spatial structure of retail agglomeration. An empirical study is performed to test the validity of the method, and some empirical findings are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Bayesian framework for updating model parameters while considering spatial variability

The study presents a recent slope failure in India which resulted in the burial of a village and claimed large number of lives. Current methods of probabilistic back analysis incorporate uncertainty in the analysis but do not consider spatial variability. In this study, back analysis is performed using Bayesian analysis in conjunction with random field theory. The probabilistic method is shown to be efficient in back-analysing a slope failure. It also provides confidence in parameter values to be used for post-failure slope design. The back analysis method which does not consider spatial variability overestimates the uncertainty in analysis, which can lead to uneconomical slope remediation design and measures.     

A spatial analysis method for geochemical anomaly separation

One purpose of using statistical methods in exploration geochemistry is to assist exploration geologists in separating anomalies from background. This always involves two types of negatively associated errors of misclassification: type I errors occur when samples with background levels are rejected as background; and type II errors occur when samples with anomalous values are accepted as background. A new spatial statistical approach is proposed to minimize errors of total misclassification using a moving average technique with variable window radius. This method has been applied for geochemical anomaly enhancement and recognition as demonstrated by a case study of Au and Au-associated data for 698 stream sediment samples in the Iskut River area, northwestern British Columbia. Similar results were obtained using the fractal concentration-area method on the same data. By employing spatial information in the analysis, the process of selecting anomalies becomes less subjective than in more traditional approaches.     

基于多元统计方法的河流水质空间分析

基于聚类分析和判别分析探讨了河流水质空间分析方法,旨在识别采样点的空间相似性与差异性,从而为水质监测网络优化提供支持。该方法首先利用kurtosis和Skewness检验数据分布特征和进行数据对数转化与标准化处理;然后利用聚类分析进行空间相似性分析,确定空间尺度分类情况;最后利用判别分析识别显著性污染指标,以此反映上述空间尺度分类的差异性。以香港后海湾水质管制区为例,结果表明:①通过对数转化显著改善数据分布特征,使绝大部分污染指标呈正态或接近正态分布;②该区域采样点在个案链锁距离与最大链锁距离之比(D_link/D_max)×100<35处明显分为3类,它们分别代表轻度、中度、重度污染3种类型,且后两者属于采样点主要属于营养盐和重金属污染类型,需要控制其生活污水、畜牧污染、工业污染和地表径流污染;③后退式判别分析具有良好的指标降维能力,仅需7个显著性污染指标(pH,NH₃-N,NO₃-N,F.coil,Fe,Ni和Zn)可以反映整体水质的空间差异性,且具有90.65%的正确判别能力;④归纳起来,从3类采样点中选择一个或多个、监测7个显著性污染指标即可全面反映后海湾水质管制区的水质空间特征,实现水质监测网络优化。     

Soil erosion susceptibility assessment and validation using a geostatistical multivariate approach: a test in Southern Sicily

A certain number of studies have been carried out in recent years that aim at developing and applying a model capable of assessing water erosion of soil. Some of these have tried to quantitatively evaluate the volumes of soil loss, while others have focused their efforts on the recognition of the areas most prone to water erosion processes. This article presents the results of a research whose objective was that of evaluating water erosion susceptibility in a Sicilian watershed: the Naro river basin. A geomorphological study was carried out to recognize the water erosion landforms and define a set of parameters expressing both the intensity of hydraulic forces and the resistance of rocks/soils. The landforms were mapped and classified according to the dominant process in landsurfaces affected by diffuse or linear water erosion. A GIS layer was obtained by combining six determining factors (bedrock lithology, land use, soil texture, plan curvature, stream power index and slope-length factor) in unique conditions units. A geostatistical multivariate approach was applied by analysing the relationships between the spatial distributions of the erosion landforms and the unique condition units. Particularly, the density of eroded area for each combination of determining factors has been calculated: such function corresponds, in fact, to the conditional probability of erosion landforms to develop, under the same geoenvironmental conditions. In light of the obtained results, a general geomorphologic model for water erosion in the Naro river basin can be depicted: cultivated areas in clayey slopes, having fine-medium soil texture, are the most prone to be eroded; linear or diffuse water erosion processes dominate where the topography is favourable to a convergent or divergent runoff, respectively. For each of the two erosion process types, a susceptibility map was produced and submitted to a validation procedure based on a spatial random partition strategy. Both the success of the validation procedure of the susceptibility models and the geomorphological coherence of the relationships between factors and process that such models suggest, confirm the reliability of the method and the goodness of the predictions.