Estimation of a multidimensional covariance function in case of anisotropy

A model of a multivariate covariance function with an ellipsoidal directional correlation scale has been developed. The axes of the ellipsoidal scale are related to the eigenvalues and eigenvectors of a matrix B which characterizes the ellipsoid of the range of influence. The matrix B is found to be related to a matrix T which can be estimated directly from sparse sampling data and can be used to determine estimates of the matrix B. The method has been applied to both two-dimensional and three-dimensional cases. The numerical results show that the satisfactory accuracy is obtained with sparse sampling data from an anisotropic random function.     

矿化富集中心地质因素多元统计分析及应用

本文导出了通过控矿地质因素逻辑信息法的研究来建立矿化富集中心数学模型的公式,使矿化富集中心数学模型与控矿地质因素定量地联系起来。还给出了单个矿化富集中心趋势面分析的数学模型和矿床空间分布模型。在这基础上,以某锡-多金属成矿带中某远景区的研究为例说明怎样应用矿化富集中心地质因素多元统计分析（逻辑信息法、趋势面分析、逐步回归分析和聚类分析）进行矿床统计预测。     

小块体重的多元线性回归方程在锡铁山铅锌矿床储量计算中的应用

从锡铁山铅锌矿床小块体重样品原始测定数据入手，运用数学地质中的回归分析，建立了本矿床的小块体重多元线性回归方程，为矿床储量计算提供了科学参数。利用回归方程法计算小块体重进而可以推广到所有贱金属矿床的储量计算中。     

A partial least-squares regression approach to land use studies in the Suzhou-Wuxi-Changzhou region

In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares (PLS) regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and in-fluencing factors demonstrate the land use character of rural industrialization and urbaniza-tion in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.     

通过对调查数据的趋势和多变量分析确定宏观场

通过多变(相关分析)和趋势分析等统计方法对宏观调查数据进行了解释.这种方法使我们通过评定不同宏观效应叠加的程度、估计调查数据的不确定性更客观地评定烈度.通过滤波确定烈度场的区域分量,使我们消除观测中的局部变化.给出了选取适当滤波参数的准则.本文应用这一方法对发生在意大利的一次地震的调查数据进行了处理.     

Drought assessment in a south Mediterranean transboundary catchment

ABSTRACT

Predicting the impacts of climate change on water resources remains a challenging task and requires a good understanding of the dynamics of the forcing terms in the past. In this study, the variability of precipitation and drought patterns is studied over the Mediterranean catchment of the Medjerda in Tunisia based on an observed rainfall dataset collected at 41 raingauges during the period 1973–2012. The standardized precipitation index and the aridity index were used to characterize drought variability. Multivariate and geostatistical techniques were further employed to identify the spatial variability of annual rainfall. The results show that the Medjerda is marked by a significant spatio-temporal variability of drought, with varying extreme wet and dry events. Four regions with distinct rainfall regimes are identified by utilizing the K-means cluster analysis. A principal component analysis identifies the variables that are responsible for the relationships between precipitation and drought variability.     

Calibration of diatoms along a nutrient gradient in Florida Everglades Water Conservation Area-2A, USA

The relationship between diatom taxa preserved in surface soils and environmental variables at 31 sites in Water Conservation Area 2A (WCA-2A) of the Florida Everglades was explored using multivariate analyses. Surface soils were collected along a phosphorus (P) gradient and analyzed for diatoms, total P, % nitrogen (N), %carbon (C), calcium (Ca), and biogenic silica (BSi). Phosphorus varied from 315-1781 g g^-1, and was not found to be correlated with the other geochemical variables. Canonical correspondence analysis (CCA) was used to examine which environmental variables correlated most closely with the distributions in diatom taxa. Canonical correspondence analysis with forward selection, constrained and partial CCA, and Monte Carlo permutation tests of significance show the most significant changes in diatom assemblages along the P gradient (p < 0.01), with additional species differences correlated with soil C, N, Ca, and BSi.Weighted-averaging (WA) regression and calibration models of diatom assemblages to P and BSi were developed. The diatom-based inference model for soil [P] had a high apparent r² (0.86) with RMSE_boot = 218 g g^-1. Indicator diatom species identified by assessing species WA optima and WA tolerance to [P], such as Nitzschia amphibia and N. palea for high [P] (~1300-1400 g^-1) and Achnanthes minutissima var. scotica and Mastogloia smithii for low [P] (~400-600 g g^-1), may be useful as monitoring tools for eutrophication in WCA-2A as well as other areas of the Everglades. Diatom assemblages analyzed by cluster analysis were related to location within WCA-2A, and dominant taxa within clusters are discussed in relation to the geochemical variables measured as well as hydrology and pH. Diversity of diatom assemblages and a Disturbance Index based on diatom data are discussed in relation to the historically P-limited Everglades ecosystem. Diatom assemblages should be very useful for reconstructions of [P] through time in the Florida Everglades, provided diatoms are well preserved in soil cores.     

Visual classification of very fine-grained sediments: Evaluation through univariate and multivariate statistics

Classifying very fine-grained rocks through fabric elements provides information about depositional environments, but is subject to the biases of visual taxonomy. To evaluate the statistical significance of an empirical classification of very fine-grained rocks, samples from Devonian shales in four cored wells in West Virginia and Virginia were measured for 15 variables: quartz, illite, pyrite and expandable clays determined by X-ray diffraction; total sulfur, organic content, inorganic carbon, matrix density, bulk density, porosity, silt, as well as density, sonic travel time, resistivity, and -ray response measured from well logs. The four lithologic types comprised: (1) sharply banded shale, (2) thinly laminated shale, (3) lenticularly laminated shale, and (4) nonbanded shale. Univariate and multivariate analyses of variance showed that the lithologic classification reflects significant differences for the variables measured, difference that can be detected independently of stratigraphic effects. Little-known statistical methods found useful in this work included: the multivariate analysis of variance with more than one effect, simultaneous plotting of samples and variables on canonical variates, and the use of parametric ANOVA and MANOVA on ranked data.     

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.     

Patterns of genetic and morphometric diversity in the marbled crab (Pachygrapsus marmoratus, Brachyura, Grapsidae) populations across the Tunisian coast

The present study reports on population structure analysis of the marbled crabPachygrapsus marmoratus (Fabricius, 1787) from the Tunisian coast, an appropriate location to study biogeographical process...