Estimation of statistical parameters for censored lognormal hydraulic conductivity measurements

Field tests of hydraulic conductivity (e.g., injection test, pumping test, etc.) in low permeability formations are subject to censoring due to the detection limit of the instruments used. An iterative method of estimating the mean and variance of hydraulic conductivity data with a presumed log-normal distribution function is presented. This method accounts for the data that are actually below the lower detection limit (called truncated data) and thus gives distribution parameters that are more representative for the underlying distribution. The proposed method is then tested on two simulated normally distributed random datasets having different variances. The results show that the means and variances estimated by the proposed method are very accurate. Finally, the method is used to estimate the mean and variance of hydraulic conductivity data from single hole water injection tests in a fractured geological formation.     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

大别杂岩中混合岩的矿物空间分布研究

介绍了矿物空间分布研究的基本原理及两种统计方法(接触频数法和线切法)。作者对混合岩矿物空间分布的研究表明:(1)前人提出的统计方法存在方法上的缺陷和应用上的局限性,作者推导出矿物接触类型的概率公式;(2)部分浅色体中矿物显示聚集分布的特征,而绝大部分的浅色体中矿物具有分散分布的特点。结合质量平衡和地球化学研究认为:大别杂岩中主体混合岩成因机制是重熔和交代作用。     

Distribution and mode of occurrences of radionuclides in phosphogypsum from the Aqaba and Eshidiya fertilizer plants, Jordan

Phosphogypsum is a waste by-product of the phosphate fertilizer industry that has relatively high concentrations of some U decay-series radionuclides such as ^226Ra and ^210Pb. The distribution and environmental mobility of radionuclides in phosphogypsum are an important concern because this gypsum by-product is used for wallboard, in agriculture and as a soil amendment. This study determined the distribution of ^226Ra, ^210Pb, within phosphogypsum stacks of varying age and among three size fractions （coarse： 〈0.212 mm; medium： 0.212-0.053 mm; fine： 〈0.053 mm）, in phosphogypsum derived from Aqaba and Eshidiya fertilizer plants. The results indicated that ^226Ra and ^210Pb were generally uniformly distributed in phosphogypsum stacks and showed no significant difference in the concentration of these elements with the age of stack. In the Aqaba phosphogypsum ^226Ra was slightly 10% enriched in the coarse fraction, while ^210Pb was 10% enriched in the free size fraction. In the Eshidiya phosphogypsum ^226Ra and ^210Pb contents were both relatively enriched （10%） in the fine size fraction.     

A Practical Procedure for the Measurement of Fragmentation by Blasting by Image Analysis

Summary. The operation of a digital image analysis system in a limestone quarry is described. The calibration of the system, required in order to obtain moderately reliable fragmentation values, is done from muckpile sieving data by tuning the image analysis software settings so that the fragmentation curve obtained matches as close as possible the sieving. The sieving data have also been used to extend the fragment size distribution curves measured to sizes below the system’s optical resolution and to process the results in terms of fragmented rock, discounting the material coming from a loose overburden (natural fines) that is cast together with the fragmented rock. Automatic and manual operation modes of the image analysis are compared. The total fragmentation of a blast is obtained from the analysis of twenty photographs; a criterion for the elimination of outlier photographs has been adopted using a robust statistic. The limitations of the measurement system due to sampling, image processing and fines corrections are discussed and the errors estimated whenever possible. An analysis of consistency of the results based on the known amount of natural fines is made. Blasts with large differences in the amount of fines require a differentiated treatment, as the fine sizes tend to be the more underestimated in the image analysis as they become more abundant; this has been accomplished by means of a variable fines adjustment factor. Despite of the unavoidable errors and the large dispersion always associated with large-scale rock blasting data, the system is sensitive to relative changes in fragmentation.     

The log-normal distribution for hydraulic conductivity of compacted clays: Two or three parameters?

Risk and uncertainty assessments for waste containment systems employing clay barriers often include spatial variability in the hydraulic conductivity as part of the analysis. The two-parameter log-normal distribution is often used to describe the spatial variability, but for compacted clays the three-parameter form can be more appropriate. A statistical hypothesis test was developed that can be used to determine if the two- or three-parameter form of the log-normal distribution is more appropriate. The test is based on a likelihood ratio, comparing likelihood functions for the two- and three-parameter forms at their maximums. Likelihood functions are used assuming that a data set can be segregated into a set of distinct groups of hydraulic conductivities. A step-by-step calculation procedure is described and the test is applied to data collected from 45 sites.     

山西霍山植物群落主要层LAI垂直分布规律

在山西霍山七里峪林场，采用间接的光学测量方法对沿着海拔分布的植物群落主要层叶面积指数（LAI）进行了测量，从不同的角度对LAI的垂直分布规律进行分析。结果表明：1．海拔不同，LAI表现出很大的差异，海拔1750m左右的LAI值大于较高与较低海拔的；对LAI和海拔之间的关系进行回归，得到LAI分布的拟合方程：y=b0＋b1x＋b2x^2＋b3x^3（R=0．712，P〈0．01）。2．同一海拔样带，阴坡LAI均大于阳坡，但对同种种群来说，阴坡树种平均胸径并不一定均大于阳坡。3．植被类型LAI比较表现为：低山针叶林〈低山灌丛〈落叶阔叶林〈落叶针叶林〈常绿针叶林；而主要群系LAI比较表现为：油松林（0．38）〈落叶松林（0．78）〈山杨林及其混交林（1．09）〈白桦林（2．00）〈辽东栎林及其混交林（3．73）。4．典型群落LAI值变化分析和人工林与天然林以，比较表明，LAI值在一定海拔达到最大值，这对于山西霍山人工林栽培和丰产林培育等具有重要意义。