Extensions to Spatial Factor Methods with an Illustration in Geochemistry

Many applications involving spatial data require several layers of information to be simultaneously analyzed in relation to underlying geography and topographic detail. This in turn generates a need for forms of multivariate analysis particularly oriented to spatial problems and designed to handle spatial structure and dependency both within and between spatially indexed multivariate responses. In this paper we focus on one group of such methods sometimes referred to as spatial factor analysis. Use of these techniques has so far been mostly restricted to applications in the geosciences and in some forms of image processing, but the methods have potential for wider use outside these fields. They are concerned with identifying components of a multivariate data set with a spatial covariance structure that predominantly acts over a particular spatial range or zone of influence. We review the various forms of spatial factor analysis that have been proposed and emphasize links between them and with the linear model of coregionalization employed in geostatistics. We then introduce extensions to such methods that may prove useful in exploratory spatial analysis, both generally and more specifically in the context of multivariate spatial prediction. Application of our proposed exploratory techniques is demonstrated on a small but illustrative geochemical data set involving multielement measurements from stream sediments.     

非负矩阵分解方法在水系沉积物地球化学数据处理中应用

鉴于水系沉积物地球化学数据可以表示为非负矩阵,这使得利用非负矩阵分解(NMF)方法处理该类数据成为可能.介绍了非负矩阵分解方法的基本原理和方法,讨论了基于非负矩阵分解方法处理水系沉积物地球化学数据的可能和效果.以个旧水系沉积物地球化学数据为例,运用NMF方法和主成分分析(PCA)方法对其进行异常分析,并对这两种方法的处理结果进行了比较,发现NMF方法对于处理水系沉积物地球化学数据是一种有效的方法.尽管这两种方法各自有其优越性,但就本实例数据而言,NMF方法优于PCA方法.     

Compositional Data Analysis of Some Alkaline Glasses

The approach to the analysis of compositional data involving log-ratio transformation of the data has not been generally adopted by researchers wishing to analyse such data. In the context of exploratory methods of multivariate analysis, such as principal components analysis, where the hope is to identify (cluster) structure in the data, this may be because traditional methods can produce more interpretable results than the log-ratio approach. After illustrating this with an example, circumstances under which the log-ratio approach performs poorly when traditional approaches work well are identified. Log-ratio analysis can be dominated by variables having low absolute presence and high relative variation that do not contribute to, and can obscure, structure in the data. Traditional methods can detect certain kinds of structure in the data that correspond to structure on a ratio scale, after a suitable redefinition of the composition. Since traditional methods often detect such structure more directly than log-ratio analysis it can be concluded that claims that the traditional analysis is inappropriate or meaningless are exaggerated. This conclusion is based on empirical experience rather than theoretical concerns. The arguments are illustrated using compositional data for alkaline glasses, but have more general application.     

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.     

融合化探信息的遥感异常提取

遥感信息与化探信息为地表地质体或地质现象物理特性和化学特性的表现,矿物特征光谱是对矿物化学组分的响应,二者存在密切的关联。2种信息融合既要达到空间位置的精确对应,又要根据物质成因的相关性,实现2种数据间数据层、决策(符号)层等不同层次的数据耦合,提高异常信息提取的准确度。通过对遥感与化探信息形成机理及特点的分析可知,二者在空间和成因上具有一定的相关性。采用反距离加权插值法,将化探散点数据转化为栅格数据结构并进行空间尺度的转换和配准,选择和研究区异常相关的4种元素(Au、As、Sb、Bi)与原始遥感数据进行融合,对融合后数据采用主成分分析的方法对内蒙古苏尼特左旗地区进行蚀变信息提取,较单独利用遥感数据提取结果剔除了无意义的异常信息点,异常区域更为具体。经野外检查,验证多处地表岩石蚀变的存在,证实了该方法的有效性。     

Deciphering Groundwater Flow Systems in Oasis Valley, Nevada, Using Trace Element Chemistry, Multivariate Statistics, and Geographical Information System

The origin of groundwater discharging via evapotranspiration and from springs within Oasis Valley, Nevada, is of concern owing to the close proximity of the Nevada Test Site (NTS) and the possible contamination of groundwater as a result of underground nuclear testing. Principal components analysis, cluster analysis, and population partitioning, along with a Geographical Information System, were used to decipher groundwater flow patterns in Oasis Valley, Nevada. These multivariate statistical techniques were applied to the trace element chemistry of groundwater samples collected from 26 springs and wells within Oasis Valley, the NTS, and the Nellis Air Force Range. The results of all statistical analyses showed similar geographical trends in the trace element chemistry of the groundwaters included in this study. Differences are observed between the groundwaters from the NTS and those of Oasis Valley based on the concentrations of the elements Li, Ge, Mo, Rb, Ba, U, and Ru. A concentration gradient is observed from lower concentrations in the NTS to increasing concentrations toward Oasis Valley suggesting groundwater flow in an overall southwestward direction from the NTS. Also, a different trace element signature is observed for the waters collected in the northern and western region of Oasis Valley, suggesting another source of groundwater to this area.     

基于主成分和半参数的大坝变形监测回归模型

主成分分析在一定程度上可以解决大坝变形监测回归模型因子间的复共线性,然而当提取的主成分信息不充分时,主成分回归用于大坝安全预测可能失效。提出以主成分分析提取的主成分作为半参数回归的参数分量,剩余成分和模型误差作为未知的非参数分量对主成分回归进行补偿,建立一种基于主成分和半参数的大坝变形监测混合回归模型。利用某大坝实测资料进行建模分析,结果表明该混合模型能克服回归因子间的复共线性,避免半参数回归补偿最小二乘估计中法矩阵的病态性,比传统的主成分回归和逐步回归模型具有更好的拟合和预报精度。     

Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry

A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used.     

Fourier packing ordinate: A univariate size-independent measurement of the polygonal packing variation in Paleozoic bryozoans

The Fourier packing ordinate provides a highly sensitive, univariate, and size-independent measurement of the polygonal packing variation in Paleozoic bryozoan colonies. It is potentially useful in quantifying a wide variety of natural packing arrays or polygonal networks, and is preferable to counting the sides of polygons, the frequency of triple or quadruple junctions, the nearest-neighbor statistic, measurements of surface area per unit cell, or individual harmonic amplitudes. Fourier shape analysis provides exact measurements of the levels of two- to six-fold rotational symmetry in all natural packing gradients. In bryozoans these symmetries are intercorrelated because as each order of symmetry is increasing, the previous order is decreasing. Shapes in these packing arrays are normally hybrids of two or more orders of rotational symmetry. The levels of rotational symmetry involved in these packing gradients are significantly correlated with a single principal component, the Fourier packing ordinate, which is independent of both size and cell boundary phenomena. Spatial analysis of the Fourier packing ordinate within an Ordovician bryozoan colony reveals both variation in packing caused by subcolony budding, as well as large scale trends which vary from the colony center to the free-growing margin.     

相干算法提取嫦娥数据月表地质特征

经典的边缘提取算法可从月球影像数据中提取出月表的构造特征, 但难以提取出与月貌有关的特征信息.本文提出的相干法月球影像地质特征提取技术, 其基本思想是基于相干运算来考察图像上像素或像素组之间的相似性, 以获取月表的构造特征和月貌特征.该方法已经应用在嫦娥一号月球探测器获取的部分影像数据上, 相比于几种常规的边缘提取方法, 本方法优势明显, 不仅能有效地提取环形构造和线性构造等地质特征, 还可以很好地提取月貌特征, 对具有一定规模的小直径撞击坑的识别也有不错的效果.该方法可以用于计算机自动识别或辅助手工解译月表构造, 划分月貌单元等研究.      

应用近红外光谱法研究泻湖湿地沉积物重金属活动态特征及生态风险评价

沉积物中的重金属元素经自然作用下可以活动态进行迁移,具有潜在生物可利用性及潜在的区域生态风险。利用近红外光谱(NIRS)技术开展不同基体类型样品响应机理研究,可为评估重金属活动态提供无损、快速的分析方法,为生态风险研究提供依据。天津七里海泻湖湿地沉积物具有低有机质-高黏土含量的特征,本文基于近红外光谱分析技术,建立了沉积物中Co、Ni、Cu、Zn、Cd、Pb重金属活动态组分含量近红外光谱-偏最小二乘回归预测模型。实验结果表明:样品在7290～6390cm~(-1)和4683～4000cm~(-1)波段存在的双羟基O—H伸缩振动、AlAl—OH及Al(Mg)—OH弯曲振动特征吸收,间接指示了重金属元素活动态含量。光谱预测结果显示,近百年来七里海沉积物中Co、Ni、Cu、Zn、Cd、Pb活动态组分的变化特征对应了当地1934—1948年、1956—1963年、1976年至今三次较明显的升温过程,也对应了1980年七里海水库建设等大型人为扰动。本研究样品中Co、Ni、Cu、Zn、Cd、Pb总量及活动态均低于国家标准中规定的生态风险阈值,七里海内村镇及周边农田来自湿地释放的重金属生态风险极低。     

Identification of Anthropogenic Features Through Application of Principal Component Analysis to Hydrochemical Data from the Sines Coastal Aquifer, SW Portugal

The Sines coastal sedimentary basin, a tectonic trough with a NE-SW orientation filled with Mesozoic and Cenozoic deposits, has two hydrogeological systems: the Mio-Pliocene and the Jurassic. Both systems are supplying water to the entire region with highly populated and industrialized areas. The aquifers are recharged in the outcrop areas, although the Jurassic aquifer also receives some contribution from the overlying Miocene rocks. The main groundwater flow direction in the Jurassic aquifer is E to W towards the Atlantic Ocean. In order to understand the influence of anthropogenic activities on the water quality, a statistical principal components analysis (PCA) was performed on the physical–chemical data from groundwater samples in both aquifers. Four components were obtained in the Jurassic and three in the Miocene. The principal components analyses indicate water–rock interactions as the major mechanism responsible for the groundwater solutes (mainly calcium-bicarbonate type), from the calcareous and dolomitic units. Anthropogenic contamination was identified in the influence of the water compositions, corresponding to local polluting inputs. These were magnesium, sulfate, nitrate, iron and copper for PC 3 in the Jurassic and sodium, chloride, nitrate and manganese for PC 2 in the Miocene. These account for about 13% of the system total variance in the Jurassic aquifer and near 23% in the Miocene one.     

Thoughts on use of principal component analysis in petrogenetic problems

The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.     

空心包体应变计地应力分量计算方法及应用

为进一步改进和完善空心包体应变计地应力计算方法,基于地应力现场实测过程中空心包体应变计的安装方式,采用线性参数的最小二乘拟合方法对地应力分量计算公式进行了推导,得出了6个地应力分量的改进算法及其标准误差的计算公式。采用实现完全温度补偿并考虑岩体非线性的地应力测量技术,对弓长岭井下矿-160、-220、-280 m 3个水平3个测点进行了地应力现场实测,得到了3组孔壁应变数据。分别使用常规算法和改进算法对3个测点的地应力分量进行计算并分析其标准误差。结果表明：采用改进算法计算得到的地应力分量其标准误差普遍小于常规算法计算地应力分量产生的标准误差,说明改进算法比常规算法具有更高的可靠度。在此基础上,对弓长岭井下矿地应力赋存规律进行了研究。结果显示：矿区地应力场以水平构造应力为主导,最大水平主应力的走向总体上为南东东-北西西方向,最大水平主应力、最小水平主应力和垂直主应力均随深度呈增长关系。     

利用测井资料计算机自动识别沉积微相方法研究

以关键井沉积微相分析为基础,将测井学同地质、现代数学相结合,从测井资料中提取反映各种微相的测井特征参数,并应用一套多元统计分析方法,建立各种沉积微相的判别模式,研究开发一套软件系统,实现计算机根据测井资料自动分析判别陆相地层沉积微相.应用该软件对某油田西区的十几口井的测井资料进行处理,并绘制出沉积微相平面图.     

崇明东滩表层沉积物的粒度空间分布特征

经对崇明东滩45个现代表层沉积物样品粒度分析表明：潮滩沉积物绝大部分以淤泥质粉砂为主，平均粒径16．1—46．5μm。沉积物粒度组成具有明显的空间分布特点：高—中—低潮滩依次出现细粉砂、中粉砂和粗粉砂；从潮滩北部至南部，沉积物粒度由细变粗。上述特征与水动力条件基本对应，同时也受到植被分布状况的制约。     

基于ASTER 和ETM+数据的蚀变信息提取 比较研究———以西藏泽当矿田为例

利用ASTER和ETM+数据分别对西藏泽当矿田试验区进行了遥感数据矿物蚀变信息提取。根据研究区岩石矿物光谱特征,采用主成分分析法,提取了含三价Fe离子和粘土矿化蚀变信息,通过对两者提取的结果进行比较之后认为,ASTER数据比ETM+数据在矿化蚀变信息提取中能进一步识别不同类型的含羟基蚀变矿物,并且也能很好的提取含三价Fe离子蚀变信息,未来具有较大的优势。     

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。     

沉积物粒度分析方法的比较

近年来激光粒度分析法在沉积物粒度分析方面的应用得到了进一步扩展。本文利用美国麦克奇公司生产的S3500型激光粒度分析仪开展沉积物粒度分析方法实验,研究表明:S3500型仪器较优的样品用量约为0.2 g;稀释过程会影响样品的粒度分布;样品分取方式会带来不同的随机误差。与薄片图像法和筛析法两种传统粒度分析方法获得的粒度分布参数比较表明:激光法测得的平均粒径较薄片图像法和筛析法偏细;激光法和筛析法的峰度相关性较好。采用Malvern 2000和Micro S3500两种激光粒度分析仪测量结果的比较表明:Malvern 2000测得的平均粒径较Micro S3500测得的平均粒径偏细,但二者的相关性很好(r=0.9574),研究认为这两种粒度仪的测试结果会给岩石粒度定名带来差异。由于各种粒度分析方法存在差异和局限性,在实际工作中粒度分析应尽可能建立在同一测量体系上,以便资料对比。     

天津滨海平原区深孔沉积物环境敏感粒度提取及其意义

沉积物环境敏感粒度是进行古环境研究的重要方法之一, 然而华北平原地区很少进行完整的第四纪全取心深孔沉积物环境敏感粒度组分的提取及分析.对天津渤海湾G1和G2孔第四纪沉积物样品进行粒度分析, 采用粒级-标准偏差和主成分分析两种方法进行了沉积物环境敏感粒度组分提取.对比提取结果发现, 两种方法存在差异性的同时还存在一定的兼容性, 沉积层理厚度越薄, 兼容性越明显; 主成分分析方法对沉积物环境敏感粒度组分刻画得更为细致, 粒级-标准偏差方法不适合深孔沉积物整体敏感粒度组分的提取.G1孔环境敏感粒度组分的粒度峰值为6.700μm、15.650μm、36.240μm、176.900μm、282.100μm、716.800μm; G2孔环境敏感粒度组分的粒度峰值为0.578μm、176.000μm, 分别对应6个和3个粒度分布区间, 指示两孔整体上的沉积物来源及沉积环境空间存在差别.G2孔相对于G1孔整体上的沉积强度大且沉积环境较为稳定, 适合于开展高分辨率的古环境重建工作.