No-association of proportions

This note has three purposes: to briefly review the role of neutrality as a criterion of no-association of proportions; to compare neutrality with a criterion proposed by Snow in this journal; to describe a simple test of neutrality in the median.     

Effects of search parameters on kriged reserve estimates

Summary Reliable ore reserve estimates for deposits with highly skewed grade distributions are difficult tasks to perform. Although some recent geostatistical techniques are available to handle problems with these estimations, ordinary kriging or conventional interpolation methods are still widely used to estimate the ore reserves for such deposits. The estimation results can be very sensitive to the search parameters used during the interpolation of grades with these methods.This paper compares the ore reserve estimates from ordinary kriging using several cases in which certain search parameters are varied. The comparisons are extended to different mineralizations to show the changing effects of these parameters.     

副坝工程的安全监测

工程安全监测是采用外部和内部相结合对坝体进行长期稳定性监测。介绍了两种情况下,官家冲副坝的监测成果及分析,认为该坝应该与主体工程同步进行监测。     

各向异性矿化特征的分析与模拟 及其在储量估算中的应用

矿化作用往往是地质事件及局部过程共同作用的结果,导致矿体空间形态复杂多变、矿石品位呈各向异性、尺度不一的非线性空间变异模式.传统方法无论是在矿石量的计算方面还是在矿块内平均品位的确定上都存在多种误差,并且无法实现信息的动态管理及直观表达.文章以安庆铜矿中心矿区为例,采用对数块kriging与三维地学模拟技术相结合的方法...     

A new approach to null correlations of proportions

Much work on the statistical analysis of compositional data has concentrated on the difficulty of interpreting correlations between proportions with an assortment of tests for nullcorrelations, for independence except for the constraint, F-independence of bounded variables, neutrality in the mean and in the median. This paper questions the appropriateness of characterizing the dependence structure of proportions in terms of such concepts, suggests an alternative method of modeling, develops necessary distribution theory and tests, and illustrates the methodology in applications.     

Definition of geochemical patterns on the soil of Paul de Arzila using correspondence analysis

The aim of this study is to define geochemical and geological patterns, not only inside of Paul de Arzila natural reserve but in the surrounding area. The Correspondence Analysis was used as a discriminate technique to separate previously identified groups, in this case three types of soils (cambisols + luvisols + fluvisols). The purpose was to identify the main chemical association representative for the local types of soils. The results allow us to separate the chemical elements that are related to natural sources from the anthropogenic sources.     

Estimation of potential failure risks in a mine slope using indicator kriging

Indicator kriging has been applied to the study of failure mechanisms in a mine slope in Minas Gerais, Brazil, to estimate potential failure risks in limited areas along this slope. Timbopeba Mine, Vale Company, is an open pit iron mine situated in the Quadrilátero Ferrífero, a very important mining district in Minas Gerais. A slope excavated in quartzite with a maximum height of 200 m at the time of this study, has presented many failure problems involving the sliding of blocks formed by discontinuities. These blocks are of limited size in comparison to the dimensions of the overall slope. They appear along the entire slope, wherever discontinuity orientations have led to the kinematic feasibility of these blocks. Geostatistics permits the estimation of local failure probability distributions associated to these local failures, which would not be possible with traditional statistical models. The geostatistical method employed in this study, indicator kriging, is quite suitable because it is unnecessary to assume a particular global distribution of the phenomena being modeled. The model was used for locating areas with a great tendency for sliding failure, as it considers the local spatial variability of discontinuity orientations. Copyright © 2010 John Wiley & Sons, Ltd.     

西昆仑塔什库尔干沉积变质型铁矿基于GIS的多元信息成矿预测

本文在全面总结以往地质和勘探报告等资料的基础上,重点对赋存于下元古界布伦阔勒群地层中的沉积变质型铁矿进行研究,从成矿地质背景分析入手,以区域成矿学理论和典型矿床剖析为指导,总结成矿规律,在GIS软件平台上对多元化信息进行成矿有利分析,运用证据权重法结合网格单元法的矿产预测方法,对西昆仑塔什库尔干地区沉积变质型铁矿资源进行成矿预测研究。对沉积变质型铁床圈定了A类远景区3处,B类靶区5处,C类远景区2处。     

Reducing the Impact of Outliers in Ore Reserves Estimation

Mining applications commonly faces surprising high values designated as outliers. These values impact dramatically statistical analysis and interpretation. A comprehensive analysis on the causes for the presence of unexpected high values was recommended. However, if an erroneous value was accepted as a part of the solution, some form of correction is recommended. A methodology based on the robust kriging (RoK) algorithm is proposed to be used in exploratory data analysis and also to deal with problems associated with the presence of outliers in the sample data set. The efficiency of RoK method as an interpolator is tested in different types of mineralizations. Importantly, the parent population from which the data was sampled is available, thus allowing direct quantitative assessment of the effectiveness of the estimation technique. The performance of the method is tested in the context of ore reserves estimation. RoK model is compared to models generated by ordinary kriging, median indicator kriging, and lognormal kriging. RoK proved to be more accurate and more precise than those methods reducing substantially the number of misclassified blocks.     

Hybrid Estimation of Semivariogram Parameters

Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation. The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical) spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram by weighted least squares methods be amended to include hybrid estimation as an option.     

滇西惠民式铁矿找矿模型及预测

惠民铁矿产于双江陆缘弧带中元古代惠民岩组中部多旋回含铜铁火山-沉积建造中。每个小旋回底部由火山岩始,顶部至铁矿层终,构成明显的火山喷发-沉积韵律,铁矿层的大小、分叉、尖灭等,与火山岩的多寡、厚薄直接有关,受控于火山岩活动及其中心。将其厘定为云南省云县-澜沧一带区域性的中元古代海相火山-沉积型铁矿典型矿床-惠民式铁矿,并将与之成矿条件类似的双江-澜沧地区中元古代火山岩盆地作为惠民式铁矿的预测工作区,以MRAS定位定量方法,基于GIS矿产资源评价系统进行矿产预测,优选最小预测靶区13个,估算铁矿石资源量75亿吨,做为今后寻找与勘查该类型矿床的依据。     

Estimation of regionalized compositions: A comparison of three methods

A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable.     

Estimation of semivariogram parameters and evaluation of the effects of data sparsity

Semivariogram parameters are estimated by a weighted least-squares method and a jackknife kriging method. The weighted least-squares method is investigated by differing the lag increment and maximum lag used in the fit. The jackknife kriging method minimizes the variance of the jackknifing error as a function of semivariogram parameters. The effects of data sparsity and the presence of a trend are investigated by using 400-, 200-, and 100-point synthetic data sets. When the two methods yield significantly different results, more data may be needed to determine reliably the semivariogram parameters, or a trend may be present in the data.     

On counting the number of data pairs for semivariogram estimation

In planning spatial sampling studies for the purpose of estimating the semivariogram, the number of data pairs separated by a given distance is sometimes used as a comparative index of the precision which can be expected from a given sampling design. Because spatial data are correlated, this index can be unreliable. An alternative index which partially corrects for this correlation, themaximum equivalent uncorrelated pairs, is proposed for comparing spatial designs. The index is developed under the assumption that the underlying stochastic process is Gaussian and is appropriate when the (population) semivariogram is to be estimated by the sample semivariogram.     

基于土壤属性的VIC模型基流参数估计框架

"异参同效"现象是水文模型参数率定过程中的一个难题。为了减少需要率定的模型参数个数,从而降低模型参数的相互作用,构建了利用土壤属性直接估计VIC(Variable Infiltration Capacity)模型3个基流参数的框架,并在3个位于不同水文气候条件下的典型流域中作了实例研究。传统的VIC模型参数估计方法需要率定6个参数;而在新的参数估计框架下,需要率定的模型参数从6个减少为3个。蒙特卡罗模拟结果表明新的参数估计框架提高了参数的敏感性。同时,新的参数估计方法模拟的径流过程和之前通过率定得到的径流过程差别很小。GLUE(Generalised Likelihood Uncertainty Estimation)方法分析得到径流模拟的不确定性结果表明:新的参数估计框架计算径流的90%置信区间要明显小于传统方法,而且对于低流量的模拟效果更加明显,也就是说采用新的参数估计框架可以显著降低径流模拟的不确定性。这种基流参数估计方法可以被应用于其他相似的水文模型中。     

克里格法在离子吸附型稀土矿勘查储量估算中的应用

我国在离子吸附型稀土矿勘查工作中,一般采用地质块段法估算储量,块段法是将矿体划分为不同厚度的块段投影到水平或垂直方向上,块段的划分、各块段的面积和厚度、品位都会影响储量估算结果。本文以赣南某离子吸附型稀土矿床作为研究对象,基于先期勘探钻孔数据资料,运用三维建模软件创建了该矿床钻孔数据库,建立了矿区内矿体的三维DTM模型;采用克里格法对矿体进行稀土氧化物品位分析,将克里格法的储量计算结果与块段法的储量计算结果作对比分析。结果显示,克里格法计算的矿体体积比块段法增加了11.8%,稀土氧化物储量增加了15%,与实际勘探数据相比较,克里格法的计算结果基本合理,且具有快速、准确、方便的特点。本文利用自主开发的以克里格法为基础的三维数字矿山经济评价系统中价格-边界品位敏感性分析模块,动态设置边界品位,灵活圈定不同价格下经济可采的矿体边界,如当精矿的市场价格从10万元/吨变化为12万元/吨时,通过计算获得了此矿山经济可采矿体的空间扩展范围。基于克里格法的三维估算系统能够帮助矿山选择合理的采矿工程布置,有利于满足矿山动态管理的需要以及保证矿产资源的合理利用。     

Geochemical characterization of heavy metal contaminated area using multivariate factorial kriging

This paper describes a geostatistical method, known as factorial kriging analysis, which is well suited for analyzing multivariate spatial information. The method involves multivariate variogram modeling, principal component analysis, and cokriging. It uses several separate correlation structures, each corresponding to a specific spatial scale, and yields a set of regionalized factors summarizing the main features of the data for each spatial scale. This method is applied to an area of high manganese-ore mining activity in Amapá State, North Brazil. Two scales of spatial variation (0.33 and 2.0 km) are identified and interpreted. The results indicate that, for the short-range structure, manganese, arsenic, iron, and cadmium are associated with human activities due to the mining work, while for the long-range structure, the high aluminum, selenium, copper, and lead concentrations, seem to be related to the natural environment. At each scale, the correlation structure is analyzed, and regionalized factors are estimated by cokriging and then mapped.     

Revisiting the accurate calculation of block-sample covariances using Gauss quadrature

Block-sample covariances may be calculated by discretizing a block into regularly spaced grid points, computing punctual covariance between each grid point and the sample, then averaging. Gauss quadrature is a better, more accurate method for calculating block-sample covariance as has been demonstrated in the past by other authors (the history of which is reviewed herein). This prior research is expanded upon to provide considerably more detail on Gauss quadrature for approximating the areal or volumetric integral for block-sample covariance. A 4 × 4 Gauss point rule is shown to be optimal for this procedure. Moreover, pseudo-computer algorithms are presented to show how to implement Gauss quadrature in existing computer programs which perform block kriging.     

Analysis and Estimation of Natural Processes with Nonhomogeneous Spatial Variation Using Secondary Information

Natural processes encountered in mining, hydrogeologic, environmental, etc. applications usually are poorly known because of scarcity of data over the area of interest. Therefore, stochastic estimation techniques are the tool of choice for a careful accounting of the heterogeneity and uncertainty involved. Within such a framework, a better utilization of all available data concerning the process of interest and all other natural processes related to it, is of primary importance. Because many natural processes show complicated spatial trends, the hypothesis of spatial homogeneity cannot be invoked always, and the more general theory of intrinsic spatial random fields should be employed. Efficient use of secondary information in terms of the intrinsic model requires that suitable permissibility criteria for the generalized covariances and cross-covariances are satisfied. A set of permissibility criteria are presented for the situation of two intrinsic random fields. These criteria are more general and comprehensive than the ones currently available in the geostatistical literature. A constrained least-square technique is implemented for the inference of the generalized covariance and cross-covariance parameters, and a synthetic example is used to illustrate the methodology. The numerical results show that the use of secondary information can lead to significant reductions in the estimation errors.     

Spatial analyses of groundwater levels using universal kriging

For water levels, generally a non-stationary variable, the technique of universal kriging is applied in preference to ordinary kriging as the interpolation method. Each set of data in every sector can fit different empirical semivariogram models since they have different spatial structures. These models can be classified as circular, spherical, tetraspherical, pentaspherical, exponential, gaussian, rational quadratic, hole effect, K-bessel, J-bessel and stable. This study aims to determine which of these empirical semivariogram models will be best matched with the experimental models obtained from groundwater-table values collected from Mustafakemalpasa left bank irrigation scheme in 2002. The model having the least error was selected by comparing the observed water-table values with the values predicted by empirical semivariogram models. It was determined that the rational quadratic empirical semivariogram model is the best fitted model for the studied irrigation area.