变异函数在兰坪铅锌矿北厂矿段中的应用

变异函数是地质统计学的核心内容和基本工具,利用其成果可较好地研究一个矿床区域化变量的基本特征,通过变量的随机性反映变量结构性.本文应用变异函数理论和三维矿业软件SURPAC,对兰坪铅锌矿北厂矿段Pb,Zn品位进行变异函数的拟合和结构分析,基本反应矿体空间变化规律,为该矿储量计算、生产勘探和合理开发提供科学依据.     

指示变异函数在裂隙介质渗透性参数空间分布规律研究中的应用

简要介绍了变异函数和指示变异函数的概念,以拉西瓦水电站坝址区右岸花岗岩体裂隙介质渗透性研究为例,利用一般统计法、变异函数和指示变异函数的方法分析了单位吸水量数据。结果表明,指示变异函数能够很好地表征裂隙介质的非均质和各向异性特征,特别是极端值（极端大或极端小）的空间连续性程度,是进行裂隙介质渗透性研究的有效工具。     

变异函数在个旧锡矿X号矿体中的应用

变异函数是地质统计学的核心和基本工具。它既能描述区域化变量的空间结构性变化，又能描述其随机性变化，而且它的计算还是许多其它地质统计学计算的基础。在阐述了地质统计学原理和变异函数理论研究的基础上，根据个旧锡矿X号矿体的地质特征，对该矿体Sn品位进行了变异函数的模拟和结构分析，并在此基础上进行了地质解释。     

变异函数在都龙锡多金属矿床的应用

变异函数是地质统计学的核心和基本工具.它既能描述区域化变量的空间结构性变化,又能描述其随机性变化,变异函数分析是许多其它地质统计学计算的基础.文章在阐述了地质统计学原理和变异函数理论研究的基础上,运用Surpac矿业软件,根据都龙锡多金属矿床主矿体的产出特征,对该矿区锡、锌品位进行了变异函数分析,并对分析结果进行了地质解释.     

三维Kriging方法中的变异函数套合

三维属性建模是利用有限的采样数据, 通过插值或模拟的方法来重构地学属性在三维空间中的分布.将Kriging方法推广到三维空间, 从而演化为三维Kriging方法, 可以为三维属性建模提供可靠的手段.而三维Kriging方法面临的一大难题就是各向异性变异函数的套合.提出了一种简单通用的三维空间变异函数的套合方法.该方法以空间坐标基的变换为基础, 在套合时充分考虑轴向上变异差异的影响, 并由此提出各向异性变化率的概念; 论证了套合方法的可行性, 并通过地下水水质三维属性建模的实例对该方法进行了有效的验证.      

土壤空间变异研究中的定量分析

 系统地介绍了用地质统计学方法定童地研究土攘空间变异性的基本原理和方法以及这一领域目前研究的几个重点问题，并简单介绍了我国在这方面的研究现状。     

Kriging插值方法在地层模型生成中的应用

为了建立三维数字地层,采用了一种适合城市工程地质和岩土工程特点的地层数据模型-基于钻孔信息的3棱柱模型。由于钻孔之间的距离稀疏程度、方向、数据值存在差异,钻孔以外未知的地质特性需要插值和推断,传统的数理统计方法无法很好地解决空间样本点的选取、空间估值和2组以上空间数据的关系等问题。借鉴地质统计学的Kriging方法给出一种距离加权插值算法,即先根据空间数据得到统计特征,再根据统计特征进行插值。通过对地层模型插值结果的观察,得出该算法可以获得良好的插值效果。     

空间分析技术在地球化学异常分区统计中的应用

以MAPGIS为平台,介绍了对区域化探分区、分类进行解释的方法,通过运用空间分析技术可自动、高效完成数据准备工作,为异常地质解释提供了目的性、针对性更强的数据处理成果。     

二元插值函数在地下水位计算中的应用

地下水位值接关系到地下水流数值模拟的精度,在传统地下水位计算中常常用一元线性行值法,实际上,地下水面是一连续变化的曲面,按传统方法计算,不符合客观实际,影响数值模拟的精度,本文着重介绍了二元插值函数计算地下水位的原因及其评价方法,并将此方法运用到中国科学院长春地理研究所国家“九五”农业科技攻关大安试验示范区地下水位计算工作中,证明其具有较高的实际应用价值。     

变异函数在马关都龙曼家寨锡锌多金属矿床中的应用

变异函数是地质统计学的核心内容和基本工具,它既能描述区域化变量的空间结构性变化,又能描述其随机性变化.本文在阐述了变异函数理论研究的基础上,依据都龙锡锌矿体的地质特征,运用变异函数,对该矿床Sn、Zn品位进行了变异函数的模拟和结构分析,为该矿床的储量计算和生产勘探提供了科学依据.     

Exact formulas for approximating variogram function integrals

The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.     

Some exact sampling distributions for variogram estimators

For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.     

Robust estimation of the variogram: I

It is a matter of common experience that ore values often do not follow the normal (or lognormal) distributions assumed for them, but, instead, follow some other heavier-tailed distribution. In this paper we discuss the robust estimation of the variogram when the distribution is normal-like in the central region but heavier than normal in the tails. It is shown that the use of a fourth-root transformation with or without the use of M-estimation yields stable robust estimates of the variogram.Visiting Scientist, NRIMS, during the period in which this work was carried out.     

The variogram sill and the sample variance

The relationship between the sill of the variogram and the sample variance is explored. The common practice of using the sample variance as an estimate of the variogram sill is questioned, and a conceptual framework for determining the appropriateness of this heuristic is constructed.     

General polygonal variogram functions: Evaluation of estimation variance integrals

The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a general polygonal function the requisite integrals may be easily computed by a closed form representation of simple integrals. This paper provides the integration formulas for two-dimensional variogram functions whose domain is represented as a finite collection of rectangles. The integration formulas essential for a fully developed polygonal approach to an extensive statistical evaluation of geostatistical quantities are presented.     

Fitting matrix-valued variogram models by simultaneous diagonalization (Part II: Application)

As an application, we demonstrate a proposed variogram modeling scheme using a spatial data set. Because the scheme relies on a procedure for simultaneously diagonalizing several matrices, we briefly describe the FG and least-squares algorithms. The model obtained by our scheme is used to cokrige the data. In addition, the proposed scheme is compared to more traditional methods.     

Multivariable variogram and its application to the linear model of coregionalization

In this article, we present the multivariable variogram, which is defined in a way similar to that of the traditional variogram, by the expected value of a distance, squared, in a space withp dimensions. Combined with the linear model of coregionalization, this tool provides a way for finding the elementary variograms that characterize the different spatial scales contained in a set of data withp variables. In the case in which the number of elementary components is less than or equal to the number of variables, it is possible, by means of nonlinear regression of variograms and cross-variograms, to estimate the coregionalization parameters directly in order to obtain the elementary variables themselves, either by cokriging or by direct matrix inversion. This new tool greatly simplifies the procedure proposed by Matheron (1982) and Wackernagel (1985). The search for the elementary variograms is carried out using only one variogram (multivariable), as opposed to thep(p + 1)/2 required by the Matheron approach. Direct estimation of the linear coregionalization model parameters involves the creation of semipositive definite coregionalization matrices of rank 1.     

Distribution of kriging error and stationarity of the variogram in a coal property

If a particular distribution for kriging error may be assumed, confidence intervals can be estimated and contract risk can be assessed. Contract risk is defined as the probability that a block grade will exceed some specified limit. In coal mining, this specified limit will be set in a coal sales agreement. A key assumption necessary to implement the geostatistical model is that of local stationarity in the variogram. In a typical project, data limitations prevent a detailed examination of the stationarity assumption. In this paper, the distribution of kriging error and scale of variogram stationarity are examined for a coal property in northern West Virginia.     

Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body

Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.     

The variogram method for a fractal model of a rock joint surface

The variogram method can be used to make a fractal model of a rock joint surface. However, it has been found that the range of lag satisfying the power law is very small, that is, less than about 10% of the profile length. The cause of this has been investigated mathematically. The main cause of this problem is due to the fact that the profile length is assumed infinite for the theory, but it is finite for the actual calculation. This discrepancy between the actual calculation and the theory yields a significant error and causes the problem when the lag is large. To confirm the validity of this conclusion, it has been demonstrated that the range of lag satisfying the power law increases with an increase in the profile length by applying the variogram method to profiles cut from a long profile. In addition, the range of lag was investigated mathematically and it has been clarified that the range of lag increases with an increase in the fractal dimension. These results suggest that the profile length, the sampling interval and the removal of the linear trend are items to which we must pay attention when we use the variogram method.