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.     

EXCEL在地质样品标签设计打印及样品管理中的应用

本文根据地质矿产岩石和化探样品管理的实际情况,利用现代化的管理经验,不断探索新方法,改进样品标签手写的管理模式,使得样品管理程序化,规范化,提高检测进度,降低差错率。     

Quantifying sample bias in clast fabric measurements

Sampling elongate clasts that protrude from a planar face for clast macro‐fabric analysis introduces a bias into reconstructed fabrics because clasts aligned perpendicular to the sampling face are over‐represented relative to those aligned parallel to the face. This study develops a probability‐based mathematical analysis to quantify sample bias for a variety of clast shapes and population fabrics, including isotropic, clustered and girdled fabric styles. Bias is expressed in terms of sample eigenvalues and eigenvectors relative to those of the parent population. Results indicate that sampling always has the effect of artificially drawing fabrics towards perpendicularity to the sampling face relative to the populations from which they are drawn. This rotation generally has the effect of artificially strengthening population fabrics, by up to 30% in the case of very weakly clustered or girdled populations. However, fabric strengthening is by no means universal and sampling alters different parent populations in different, sometimes complex, ways: the analysis in this paper identifies situations where sampling can strengthen or weaken parent fabrics, where it can rotate parent fabrics (by up to 90° in the case of a very weak population fabric), and where it can even change the style of a population fabric. For example, near‐isotropic population fabrics can appear clustered; weakly clustered and weakly girdled population fabrics can appear isotropic; weakly clustered population fabrics can appear weakly girdled; and girdled population fabrics can appear clustered. Overall, this analysis indicates that weakly orientated population fabrics are most susceptible to bias. Thus, a weakly clustered population fabric aligned parallel to a sample face is particularly susceptible to major sample bias in both fabric strength (artificially overestimated) and orientation (artificially rotated perpendicular to the face). Bias can be reduced either by sampling all the clasts from a cube‐shaped block of sediment excavated from the face, or by sampling equal numbers of clasts from the three orthogonal faces of the same sedimentary unit.     

取样扰动对固结系数的影响研究

在软土工程中,地基土的固结系数是重要参数。目前固结系数的选取主要根据室内固结试验得到的沉降与时间曲线得到。但已有的研究成果表明,室内试验获得的固结系数远低于现场资料反演得到的固结系数,取样扰动是一个重要的影响因素。根据Hong & Onitsuka的扰动度定义,推导了取样扰动对固结系数的影响,并引用了大量的试样数据验证了分析的合理性。     

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.     

释光年代学样品前处理流程

释光测年是第四纪年代学中应用较广泛的重要测年方法。释光技术的发展经历了热释光(Thermoluminescence,简写TL)阶段到光释光(Optically Stimulated Luminescence,简写OSL)阶段,测年研究的载体矿物主要是长石和石英。因测试目的不同,前处理方法有一定的差异。本文主要在前人工作的基础上,针对沉积物、陶瓷、暴露岩石三种释光测年样品的长石或石英获取方法进行总结,以期对释光测年样品前处理起到参考作用。     

Variance as a function of sample support size

The effect of sample support size on variance is examined and evaluated. Results based on variograms and geostatistics are compared to the classical relationship developed by H. F. Smith in 1938; that is, that the variance is reduced fromV ₁ toV ₁ /n ^b as the support area increases from I ton plots for uniformity trials. The exponentb is between zero and one. Theoretical results are based on use of auxiliary functions and account for the size and shape of the sample support and the overall field geometry. Results are given in terms of approximations by rational functions for ease of calculation. Experimental results for uniformity trials, infiltration measurements, and spectral data from satellites are compared to theoretical and empirical results. Applications include not only uniformity trials, but also measurement theory.     

Lunar sample 14425: Not a lunar tektite

Energy-dispersive x-ray analysis of a polished section of lunar sample 14425 shows, in contradiction to a previous report, that it has a composition similar to Apollo 14 breccias, but not to high-magnesium microtektites. The glass is homogeneous, but the bead contains numerous metallic spherules up to 0.7 mm in diameter. The metal in the spherules is iron with up to 16 wt.% Ni and 9 wt.% P and small amounts of S and Si. The high phosphorus content indicates the presence of a fine-grained phosphide phase in the metal. All of the metallic spherules have an associated sulphide phase. The composition of the glass bead and the presence of numerous Ni-Fe spherules with an associated sulphide phase indicates that the bead was formed by impact melting of surficial deposits at the Apollo 14 site.     

基于样本熵理论的自适应小波消噪分析方法

小波消噪方法的核心问题是阈值的选择及确定.依据样本熵的特性,将样本熵与小波分析方法耦合起来,提出了一种自适应确定阈值的小波消噪分析方法.该方法计算了不同阈值对应噪声序列的样本熵值,得到阈值与样本熵值之间的关系曲线,当样本熵值达到最大时,此时阈值为所求阈值.通过算例加以验证分析,结果表明,自适应小波消噪分析方法能较好地实现水文序列的信噪分离,其消噪结果符合序列本身的特性及评价指标的要求,这为合理确定阈值提供了一种新的途径和方法.     

The updated kriging variance and optimal sample design

A number of criteria based on kriging variance calculations may be used for infill sampling design in geologic site characterization. Searching for the best new sample locations from a set of candidate locations can result in excessive computation time if these criteria and the naive rekriging are used. The relative updated kriging estimate and variance for universal kriging estimation are demonstrated as a simple kriging estimate and variance, respectively. The updated kriging variance is demonstrated as the multiplication of two kriging variances. Using these updated kriging variance equations can increase the computational speed for selecting the best new sample locations. The application results for oil rock thickness in an oilfield indicate that minimizing the average relative updated kriging variance is a useful alternative to the other criteria based on kriging variance in optimal infill sampling design for geologic site characterization.     

区域地下水污染调查取样点布设量化分配方法

在区域尺度、有限样品的地下水污染调查中,密度控制可以计算区域总样品数量,但取样点布设应综合考虑地质环境、人类活动等方面的差异性。目前,样点布设主要依赖技术人员经验,存在较强的不确定性,如何科学布设取样点是需要解决的一个科学问题。针对这个问题,文章基于实际工作创建了“区域预分配、单元再优选”的解决方法。在区域上,基于层次分析法构建量化分配模型,以背景控制因素和潜在污染因素建立分配因子组合,运用指数标度量化定性因子、标度函数计算定量因子,通过矩阵运算获取每个分配单元的样品预分配数量;在单元内,按照分段控制、条件优选的方法提高取样点针对性和代表性。利用构建的分配方法,以拉萨河流域地下水水质调查为案例进行了取样点布设分配应用,确定了各单元样品分配数量。结果表明:考虑背景控制和潜在污染的层次分析模型及量化计算平衡了拉萨河流域不同分配单元对样品的实际需求,解决了城关区面积小样品需求多、当雄县面积大样品需求少等问题;分段控制、条件优选的方法明确了分配单元内取样点选择依据。本方法的构建为地下水污染调查取样点布设提供了必要的方法支撑。     

A Precambrian core sample from the Altiplano/Bolivia

Drilling in the Bolivian Altiplano discovered the Precambrian basement at 2.744 m of depth, Paleozoic strata lacking. The core is composed of hornblende meta-granite (hornblende granoblastite), in the upper part of biotite meta-granite (biotite granoblastite). Radiometric dating provides evidence for a Grenvillian magmatic or anatectic rock formation (1.050±100 my) and a later metamorphic event of 530±30 my in age.

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Zusammenfassung In einem Bohraufschluß vom Altiplano in Bolivien wurde in 2.744 m Teufe unter tertiärer und kretazischer Bedeckung das präkambrische Basement angetroffen. Der präkambrische Bohrkern besteht teils aus Hornblende-Meta-Granit (Hornblende-Kalifeldspat-Quarz-Plagioklas-Gneis), teils aus Biotit-Meta-Granit (Biotit-Kalifeldspat-Quarz-Plagioklas-Gneis). Nach Rb-Sr Datierung dürfte das Bildungsalter etwa 1.050±100 my betragen, eine Aufheizungsperiode um 530±30 my ist nach K-Ar Analyse zu vermuten.

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Résumé Lors d'un forage dans l'Altiplano bolivien le substratum précambrien a été rencontré à une profondeur de 2.744 m. La couverture sédimentaire comprend des couches tertiaires et crétaciques. La carotte précambrienne se compose d'un micro-granite gneissique de l'assemblage hornblende — feldspath potassique — quartz — plagioclase et d'un microgranite gneissique de biotite — feldspath potassique — quartz — plagioclase. L'âge de constitution de la roche est d'après l'analyse Rb-Sr de 1.050 ± 100 my. L'analyse K-Ar laisse supposer une transformation métamorphique de 530 ± 30 my.

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- , 2744 . — ( - -- —, - (- -- -). - 1050 ± 100 , , - , 530 ± 30 .

     

Toward a definition of a mineral sample in geology

Summary Any rock may be regarded as an aggregate of mineral species frequency distributions, thus opening up a new method of analyzing the problems of the nature of these discrete distributions.Based on theorems in mathematical probability, a subrock sample is defined as a probability sample under the conditions that every mineral species' distribution function in this subrock converges probabilistically to one and the same distributions the nature of which is immaterial at this point.For obvious reasons, the situation is excluded if the sample size approaches infinity, i.e., Chebyshev's theorem (Chebyshev, 1867).     

Bounding the required sample size for geologic site characterization

The proposed objective of limited sample geologic site characterization is to minimize the chance of unknown and unexpected extremes. This problem proves to be extremely difficult when the data are spatially correlated. A generalization of the classical one-sided nonparametric tolerance interval, based upon the statistical concept of associated random variables, establishes a rigorous, almost distribution-free, tool for computing the minimum required sample size for site characterization. An upper bound on the required number of samples follows from a heuristic measure for the quantity of information in a spatially dependent sample; the measure presented is the equivalent number of uncorrelated samples and is calculated using an estimated variogram. An empirical check of the upper and lower bounds, using more than 2 million simulations and seven real data sets produces a heuristic rule for quantifying the required number of samples.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

Impact of sample size on geotechnical probabilistic model identification

This paper aims to investigate the impact of sample size on geotechnical probabilistic model identification. First, the copula approach is presented to model the bivariate distribution of geotechnical parameters. Thereafter, the AIC scores are adopted to identify the best-fit marginal distribution and copula. Second, the variation of AIC scores because of small sample size is investigated using simulated data. Finally, the impact of the variation of AIC scores on identification of the best-fit marginal distribution and copula is examined. The minimum sample sizes for geotechnical data are also suggested to obtain a correct identification of the probabilistic models. The results indicate that the AIC scores estimated from a small sample exhibit large variation. The variation of the AIC scores has a significant impact on probabilistic model identification. The marginal distributions and copulas have a low percentage of correct identification when sample size is small. The percentages of correct identification for the marginal distributions and copulas increase with increasing sample size. The correlation coefficient between geotechnical parameters has a much larger impact on probabilistic model identification than the COV of geotechnical parameters. The suggested minimum sample sizes for geotechnical data are useful for guiding practical geotechnical site investigation.     

凝析气藏流体样品恢复方法研究

在综合凝析气藏流体相态特性资料及现场测试报告的基础上，总结出凝析气藏流体样品恢复的3种方法：①常规的分离器油气样品在露点压力下配样的样品恢复法；②重质组份添加法配样的样品恢复法；③凝析气藏油环平衡气样品恢复法．结合凝析气藏流体相态特性讨论了此3种样品恢复法的适用性，针对较为特殊的带油环凝析气藏——大张坨凝析气藏，采用第3种方法进行了样品恢复的实例计算，验证了该方法的适用性．     

Utilization of sample disturbance for dating a marl deposit

Summary Values of the low-amplitude shear modulus, G _o, of a marl underlying the city of Kalamata, Greece, obtained by in situ crosshole and laboratory resonant column techniques are presented in the paper. It was found that the laboratory values were lower than their field counterparts and the difference was considered to be the result of (i) the temporary stress release following sampling and (ii) the mechanical disturbance associated with specimen preparation. By utilizing previous experimental results relating the field versus laboratory difference in the value of G _o to the age of the clay deposit, it became possible to estimate the age of the particular marl which was found to agree with the geologically expected age of the deposit. The approach taken in this study may, upon further improvement, become a useful technique for dating geological materials, especially those possessing cohesion.     

平果铝土矿样品加工粒度的研究

为使样品加工粒度200目的过筛率平均达到98％以上，满足X荧光分析对样品粒度的基本要求，在实验过程中发现了饭颗粒存在并影响着过筛率，通过分析饭颗粒的成因，找出了有效抑制饭颗粒的办法——加入酒精在一定的条件下能抑制饭颗粒的产生并能保证样品加工粒度达到200目过筛率平均在98％以上。     

Pegmatoid objects in a sample of the Kaidun meteorite

We report the results of textural and mineralogical investigations of fragment #d(3–8)B of the Kaidun meteorite. The fragment is represented by six polished thin sections obtained by sequential sawing of a meteorite sample. Its main mineral is magnesian olivine; pyroxenes, augite and enstatite, are less abundant. The minor minerals are Fe-Ni sulfides, and the accessory minerals are chromian magnetite and apatite. The minerals show highly variable compositions. Several lithological types of material were distinguished on the basis of texture and composition. A characteristic feature is the presence of fractures, whose walls are enriched in olivine and, occasionally, sulfides. Some fractures contain relatively large euhedral crystals of zoned olivine. Olivines occurring on the walls of fractures and within fractures show a negative correlation between Mg# values and nickel content. The fragment has been subjected to multiple impact events. The material of the fragment bears evidence for intense multistage metasomatic alteration with the influx of olivine material and formation of pegmatoid-type segregations. This process has never previously been observed in meteorites, but is quite common in terrestrial massifs. The results of this study are in good agreement with our hypothesis that Phobos is the parent body of the Kaidun meteorite and indicate a possible Martian origin for Kaidun fragment #d(3–8)B.