Mapping by simple indicator kriging

The problem of predicting the type of an unsampled point in a two-type map is addressed using a procedure called simple indicator kriging. This procedure estimates the conditional probability that the point is of one type or the other given the types of sample points. Simple indicator kriging is applied to examples of certain map models. It is shown to perform well, and in some cases to be exact in a specified sense. Use of simple indicator kriging to estimate multivariate normal quandrant probabilities is explored.     

“三江”地区北段区域地球化学元素组合异常提取及其找矿意义

由于地球化学元素携带了某种矿化信息,因此元素地球化学异常往往是指示矿床存在的一种直接标志。随着勘查地球化学的深入发展,有关矿致地球化学异常圈定方法已成为人们关注的焦点。利用“三江”北段1∶20万地球化学数据, 运用R型因子分析,查明该区不同矿化类型的指示元素组合,以因子得分为综合指标,采用泛克里格剩余值圈定地球化学异常。结果得到2种元素组合：Ag-Zn-Pb-Sb-Bi组合(与热液型铅锌银矿床有关)和Mo-Cu组合(与斑岩型钼矿床有关)。圈定的组合异常与已知的矿床点在空间上具有很好的对应关系,说明利用R型因子分析与泛克里格法相结合圈定元素组合异常的方法能够较好地确认地球化学元素组合异常,并提示异常与矿化类型之间密切相关的规律性,为“三江”北段地区找矿提供信息。     

Restricted kriging: A link between sample value and sample configuration

Restricted kriging provides a simple and quick remedy for the problem known as the weight independence of data in ordinary kriging. A major consequence of this problem is the effect of over-smearing in estimates, which, in turn, adds one uncertain factor to subsequent mine decisions. A detailed count is reported here on a restricted kriging system that incorporates two restrictions—one for high-grade samples and the other for low-grade samples. The restriction of high grade samples is because of their low priori likelihoods, whereas the main reason to restrict low grade samples is their nature as being waste and low analysis precisions. The two constraints reinforce each other in terms of enhancing the variables of estimates. A detailed case study on an epithermal gold deposit is carried out in terms of both cross validation and block modeling, showing that restricted kriging is superior over OK in mimicking the variables of original data.     

Using landscape characteristics to define an adjusted distance metric for improving kriging interpolations

Interpolation of point measurements using geostatistical techniques such as kriging can be used to estimate values at non-sampled locations in space. Traditional geostatistics are based on the spatial autocorrelation concept that nearby things are more related than distant things. In this study, additional information was used to modify the traditional Euclidean concept of distance into an adjusted distance metric that incorporates similarity in terms of quantifiable landscape characteristics such as topography or land use. This new approach was tested by interpolating soil moisture content, pH and carbon-to-nitrogen (C:N) ratio measured in both the mineral and the organic soil layers at a field site in central Sweden. Semivariograms were created using both the traditional distance metrics and the proposed adjusted distance metrics to carry out ordinary kriging (OK) interpolations between sampling points. In addition, kriging with external drift (KED) was used to interpolate soil properties to evaluate the ability of the adjusted distance metric to incorporate secondary data into interpolations. The new adjusted distance metric typically lowered the nugget associated with the semivariogram, thereby better representing small-scale variability in the measured data compared to semivariograms based on the traditional distance metric. The pattern of the resulting kriging interpolations using KED and OK based on the adjusted distance metric were similar because they represented secondary data and, thus, enhanced small-scale variability compared to traditional distance OK. This created interpolations that agreed better with what is expected for the real-world spatial variation of the measured properties. Based on cross-validation error, OK interpolations using the adjusted distance metric better fit observed data than either OK interpolations using traditional distance or KED.     

Additive models in mining and exploration

In this paper we present the use of additive models (AMs) for geostatistical applications. AMs are generalizations of linear regression models which hold the central place in the toolbox of applied statisticians. Generally speaking, the linear relationship between response and predictors is replaced with a general functional form. Recently such models were introduced in geostatistics. Especially, we give an approach for binary data. In this case we get generalized additive models (GAMs). Logistic regression is quite popular in medical and biological research. Using logit links also in GAMs we get so called additive logistic models. An application for geostatistical data is introduced. In a second approach we use AMs for spatial prediction and surface modelling. In both cases an advantage of multivariate data can be taken. The proposed applications can be used in the development of exploration strategies, especially in the early stage of exploration     

Solving the kriging problem by using the Gram-Schmidt orthogonalization

This paper presents an approach to solve the kriging problem, defined in terms of projections, by using Gram-Schmidt orthogonalization. The Gram-Schmidt orthogonalization allows us to find an optimal approximationY* in then-dimensional subspaceH _n of any vectorY element of a Hilbert spaceH. This approach requiresO(n ³) multiplication operations to obtain an orthogonal basis, andO(n ²) multiplications needed to calculate kriging solution for a given point.     

Book Reviews

Books reviewed in this article: Kurt E. Engelmann and Vjeran Pavlakovic (eds.), Rural Development in Eurasia and the Middle East: Land Reform, Demographic Change, and Environmental Constraints Gregory C. Randall, America's Original GI Town: Park Forest, Illinois John B. Rehder, Delta Sugar: Louisiana's Vanishing Plantation Landscape Cathy D. Knepper, Greenbelt, Maryland: A Living Legacy of the New Deal Char Miller (ed.), Fluid Arguments: Five Centuries of Western Water Conflict Edward F. Bergman, The Spiritual Traveler: New York City: The Guide to Sacred Spaces and Peaceful Places Rachel Pain, Michael Barke, Duncan Fuller, Jamie Gough, Robert MacFarlane, and Graham Mowl, Introducing Social Geographies Tor A. Benjaminsen, and Christian Lund, (eds.), Politics, Property, and Production in the West African Sahel: Understanding Natural Resources Management Al Gedicks, Resource Rebels: Native Challenges to Mining and Oil Corporations Maryann P. Feldman and Nadine Massard (eds.), Institutions and Systems in the Geography of Innovation Richard Foglesong, Married to the Mouse: Walt Disney World and Orlando Annick Germain, and Damaris Rose, Montréal: The Quest for a Metropolis George F. Rengert, Mark T. Mattson, and Kristin D. Henderson, Campus Security: Situational Crime Prevention in High–Density Environments Vaclav Smil, Feeding the World: A Challenge for the Twenty–First Century Pu Miao (ed.), Public Places in Asia Pacific Cities: Current Issues and Strategies Lisa M. Benton and John Rennie Short (eds.), Environmental Discourse and Practice: A Reader Philip Scranton (ed.), The Second Wave: Southern Industrialization from the 1940s to the 1970s Barry Dalal–Clayton and David Dent, Knowledge of the Land: Land Resources Information and Its Use in Rural Development     

Restricted kriging for mixture of grade models

A modified type of kriging, referred to as restricted kriging (RK), is proposed in this study. The method incorporates constraints on different grade classes to restrict the influence of the samples having different likelihoods in estimation. RK is motivated by the estimation of mineral reserves when grades have highly skewed distributions. Ordinary kriging tends to produce an overly smoothed interpolated surface by underestimating high grades and overestimating low grades. The fact that ordinary kriging gives a uniform prior treatment to all samples independent of their values is a major factor associated with this smoothing effect. The new approach differentiates each grade portion by preselected cutoffs. RK is developed for a single cutoff and then extended into a general form for any finite number of cutoffs. Restricted cokriging (RCK) is also formulated to simultaneously estimate a set of random functions with restriction conditions. Methods are suggested for determination of the probabilities of occurrence of different grade portions. Finally, the new approach is demonstrated on a case study of an epithermal gold deposit.     

漓江流域表层土壤水分物理性质空间异质性

为了解漓江流域土壤水分空间变化特征及其影响因素,基于2'经纬网格,采用地统计学方法对该流域表层（0~10 cm）土壤水分物理性质的空间变异进行分析。结果表明:从空间结构比上,漓江流域表层土壤含水量、容重、最大和最小持水量均具有高度的空间自相关性（各指标空间结构比均大于0.87）,且其空间分布趋势基本一致,由流域上游向中下游逐渐变化。土地利用对流域表层土壤水分物理性质及其空间变异具有显著影响。受时间尺度和土地利用类型等因素的影响,漓江流域表层土壤含水量相比其他土壤水分物理性质,其空间异质性由随机引起的空间变异增加,空间自相关减小,为0.87;而土壤容重最大,为0.92。相关结果对于漓江流域土壤水分动态模拟与预测研究具有一定参考价值。     

地球形变对重力测量的影响初探

分析了在太阳和月球的引力作用下地球形变对重力测量的影响,给出了一个简便的计算模型,可以比较准确地改正地球形变对重力测量的影响。并就该方法在海洋重力测量中的应用作了探讨。