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1.
在矿产勘查、矿山设计、生产及管理等各阶段都需要进行资源储量估算的工作。地质统计学方法相对于传统储量估算方法具有明显优势,在资源储量估算中获得了广泛的应用。估值过程中单元块尺寸的合理选择对储量估算结果至关重要,然而,在以往实践中块尺寸通常根据经验或主观判断进行选择,缺乏科学依据。本文在总结前人工作及地质统计学资源储量估算经验的基础上,将块尺寸的选取问题明确地划分为勘探阶段和生产阶段。针对不同阶段的特点,重点讨论了块尺寸与品位、储量、估计精度、选别开采单元的关系,为块尺寸的合理选择提供参考。并以某特大型钼矿为工程背景,进行了深度解析及数据实验,得出了块尺寸不仅影响资源品位分布、矿石量而且影响开采技术经济指标的结论,综合考虑估计精度和选别开采单元,推荐该矿床选择15m×15m×15m的单元块尺寸进行储量估算。 相似文献
2.
Roland Froidevaux 《Mathematical Geology》1984,16(4):327-350
One of the tasks routinely carried out by geostatisticians is the evaluation of global mining reserves corresponding to a given cutoff grade and size of selective mining units. A long with these recovery figures, the geostatistician generally provides an assessment of the global estimation variance, which represents the precision of the overall average grade estimate, when no cutoff is applied. Such a global estimation variance is of limited interest for evaluating mining projects; what is required is the reliability of the estimate of recovered reserves or, in other words, the conditional estimation variance. Unfortunately, classical linear geostatistical methods fail to provide an easy way to estimate this variance. Through the use of simulated deposits (representing various types of regionalization)the present paper reviews and discusses the effects of changes in cutoff grade and selective mining unit size on the conditional estimation variance. It is shown that, when the cutoff grade is applied to a pointsupport (sample-size)distribution, the conditional estimation variance appears to be readily accessible by classical formulas, once the conditional semivariogram is known. However, the evaluation of the conditional estimation variance seems to be less straightforward for the general case when a cutoff is applied to the average grade distribution of selective mining units. Empirical approximation formulas for the conditional estimation variance are tentatively proposed, and their performance in the case of the simulated deposits is shown. The limitations of these approximations are discussed, and possible ways of formalizing the problem suggested. 相似文献
3.
Approximate local confidence intervals are constructed from uncertainty models in the form of the conditional distribution of the random variable Z given values of variables [Zi, i=1,...,n]. When the support of the variable Z is any support other than that of the data, the conditional distributions require a change of support correction. This paper investigates the effect of change of support on the approximate local confidence intervals constructed by cumulative indicator kriging, class indicator kriging, and probability kriging under a variety of conditions. The conditions are generated by three simulated deposits with grade distributions of successively higher degree of skewness; a point support and two different block supports are considered. The paper also compares the confidence intervals obtained from these methods using the most used measures of confidence interval effectiveness. 相似文献
4.
Ali Akbar Daya 《Journal of the Geological Society of India》2014,83(5):567-576
Most significant iron ore deposits in Iran are located in Central Iran Zone. These deposits belong to the Bafq mining district. The Bafq mining district is located in the Early Cambrian Kashmar-Kerman volcanic arc of Central Iran. Linear estimation of regionalized variables (for example by inverse distance weighting or ordinary Kriging) results in relatively high estimation variances, i.e. the estimates have very low precision. Assessment of project economics (or other critical decision making) based on linear estimation is therefore risky. Non-linear estimation methods like disjunctive kriging perform better and the lower estimation variance allows less risky economic decision-making. Another advantage of disjunctive kriging is that it allows estimation of functions of the primary variable, which here is the grade (Fe %) of the ore. In particular it permits estimation of indicator functions defined using thresholds on the primary variable. This paper is devoted to application of disjunctive kriging method in Choghart North Anomaly iron ore deposit in Central Iran, Yazd province, Iran. In this study, the Fe concentration of Choghart North Anomaly iron ore deposit was modelled and estimated. The exploration data consists of borehole samples measuring the Fe concentration. A Gaussian isofactorial model is fitted to these data and disjunctive kriging was used to estimate the regionalized variable (Fe %) at unsampled locations and to assess the probabilities that the actual concentrations exceed a threshold value at a given location. Consequently a three dimensional model of probability of exceeding a threshold value and the estimated value are provided by disjunctive kriging to divide the ore into an economic and uneconomic part on the basis of estimation of indicator functions using thresholds grades defined on point support. The tools and concepts are complemented by a set of computer programs that are applied to the case study. The study showed that disjunctive kriging can be applied successfully for modeling the grade of an ore deposit. Results showed that the correlation between the estimated value and real value at locations close to each other is 81.9%. 相似文献
5.
Models for Support and Information Effects: A Comparative Study 总被引：1，自引：0，他引：1
The recoverable reserves in an ore deposit depend on several factors, in particular the size of the selective mining units (support effect) and the misclassifications when sending these units to mill or dump according to their estimated grade (information effect). Both effects imply a loss of selectivity and have to be correctly forecasted. In this work, several models are reviewed and applied to a synthetic ore deposit characterized by a highly skewed grade histogram and a spatial connectivity of high grades. The affine correction, mosaic correction, and discrete Gaussian model are compared when assessing the global recoverable reserves, whereas local estimations are performed by indicator kriging with affine correction, bigaussian disjunctive kriging, and multigaussian conditional expectation. Despite their convenience and simplicity, distribution-free methods like affine correction or indicator kriging have a poorer accuracy than the other methods. In the global framework, the discrete Gaussian model is a better alternative and is based on mild assumptions. Local estimations are not accurate and may be improved by resorting to a more suitable parametric model or to conditional simulations. 相似文献
6.
Xavier Emery 《Mathematical Geology》2007,39(2):205-223
This work deals with a family of geostatistical models used in application fields concerned with a change of support, such
as mineral resources evaluation and polluted soil management. Three models are examined: the discrete Gaussian, Hermitian
and Laguerrian models, which rely on a transformation of the variable of interest (mineral grade or pollutant concentration)
defined on point and block supports into variables with Gaussian or gamma univariate distributions and isofactorial bivariate
distributions. The focus is given to the relationships between the transformed variables at both supports, and to the conditions
that these relationships imply on the model parameters. Additionally, guidelines are given for improving the variogram analysis
of the transformed variables and for validating the change-of-support model. 相似文献
7.
Xavier Emery 《Mathematical Geology》2005,37(3):295-319
Multigaussian kriging is used in geostatistical applications to assess the recoverable reserves in ore deposits, or the probability for a contaminant to exceed a critical threshold. However, in general, the estimates have to be calculated by a numerical integration (Monte Carlo approach). In this paper, we propose analytical expressions to compute the multigaussian kriging estimator and its estimation variance, thanks to polynomial expansions. Three extensions are then considered, which are essential for mining and environmental applications: accounting for an unknown and locally varying mean (local stationarity), accounting for a block-support correction, and estimating spatial averages. All these extensions can be combined; they generalize several known techniques like ordinary lognormal kriging and uniform conditioning by a Gaussian value. An application of the concepts to a porphyry copper deposit shows that the proposed “ordinary multigaussian kriging” approach leads to more realistic estimates of the recoverable reserves than the conventional methods (disjunctive and simple multigaussian krigings), in particular in the nonmineralized undersampled areas. 相似文献
8.
依据河南省鲁山—宝丰韩梁地区铝土矿的地质特征,利用Surpac 6.3矿业软件建立了该矿区的地质数据库及地层、矿体、断层和地表模型,形象表达了矿区的地形地貌和矿体的产状及空间关系。推断出矿床形成的环境和成因,应用块体模型和距离幂次反比法对矿体的品位分布和资源量进行了动态估算,表明块体估算资源量的方法可靠准确,提高了储量估算的效率,为勘查工作提供了可靠的参考和科学依据。 相似文献
9.
Marzeihe Shademan Khakestar Hassan Madani Hossein Hassani Parvizz Moarefvand 《Journal of the Geological Society of India》2013,81(4):581-585
Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine reserve estimation. In kriging, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of the search space can have a significant impact on the outcome of the kriging estimate. In particular, too restrictive neighbourhood, can result in serious conditional bias. Kriging is commonly described as a ‘minimum variance estimator’ but this is only true when the neighbourhood is properly selected. Arbitrary decisions about search space are highly risky. The criteria to consider when evaluating a particular kriging neighbourhood are the slope of the regression of the ‘true’ and ‘estimated’ block grades, the number of kriging negative weights and the kriging variance. Search radius is one of the most important parameters of search volume which often is determined on the basis of influence of the variogram. In this paper the above-mentioned parameters are used to determine optimal search radius. 相似文献
10.
Forecasting of recoverable reserves aims to predict the tonnages and grades that will be recovered at the time of mining. The main concern in this forecasting is the imprecision in the selection of ore/waste resulting from both the so-called information effect or information that becomes available during grade control, and the support effect or mining selectivity during mining. Existing approaches to recoverable reserve estimation account for mining selectivity; however, they largely ignore the information effects from future data becoming available through grade control practices. An application at the Morila gold deposit, Mali, is utilized in this paper to document a new simulation-based approach for recoverable reserve forecasting that incorporates the potential effects of future grade control data. This accounts for the information effect as well as changes in data quantity and quality over time. In addition, the case study at the Morila mine elucidates the use of a newer, very efficient, and practical alternative to traditional simulation techniques. This direct block simulation method forecasts recoverable reserves directly into the selective mining unit (support) size under consideration. The case study demonstrates the practical uncertainty assessment of the recoverable reserves within the deposit, so that expected inaccuracies in the selection of ore /waste can be accounted for. This allows for fully informed mining decisions to be made that incorporate the effects of information and selectivity while quantifying the potential impact of uncertainty on the mine operation and its final economic outcome. 相似文献
11.
地质统计学在多金属矿床储量计算中的应用研究 总被引：5，自引：1，他引：5
借助国际矿业软件Surpac建立了矿床地质数据库,筛选出矿体内钻孔样品数据并对其进行组合.根据组合样的统计分布特征,应用地质统计学理论建立了品位参数变异规律的数学模型,采用加权多项式回归法自动拟合求得实验变异函数,经交叉验证,优选出理想的实验变异函数参数值.根据理想的实验变异函数参数值,采用普通克立格法对矿体金属元素品位进行了估值,运用估值结果分别按各金属元素和中段进行了储量计算,并与矿山实际勘探获得的储量进行了对比.结果表明,所建模型可靠,计算结果准确,可用于辅助地质及采矿工程师进行资源评估、采矿设计及计划编制等工作. 相似文献
12.
Conclusions The foregoing discussion indicates that geostatistical estimation of ore deposits is not local; it is not objective; it is not sensitive to local data trends; and it is not unrestrained by the range of data values.Kriging, as an interpolation method, is a variant of IDW least squares linear fit. As such, it suffers from the limitations of all IDW linear interpolation methods that employ only data values.The estimation variance, currently used to calculate the confidence limits of values for individual mining blocks, is hypothetical and globally derived. It is more closely related to sampling density than to local variation in the data set.Geostatistical methods, of course, have a real place in ore deposit assessment, e.g. global, comparative evaluation to assist decisions on development and investment. What is questioned here is the validity of employing a global method to assess detail (mining blocks) within an ore deposit. 相似文献
13.
Nonparametric estimation of spatial distributions 总被引：4，自引：0，他引：4
A. G. Journel 《Mathematical Geosciences》1983,15(3):445-468
The indicator approach, whereby the data are used through their rank order, allows a nonparametric approach to the data bivariate distribution. Such rich structural information allows a nonparametric risk-qualified, estimation of local and global spatial distributions. 相似文献
14.
Non-stationary Geostatistical Modeling Based on Distance Weighted Statistics and Distributions 总被引：3，自引：0，他引：3
A common assumption in geostatistics is that the underlying joint distribution of possible values of a geological attribute at different locations is stationary within a homogeneous domain. This joint distribution is commonly modeled as multi-Gaussian, with correlations defined by a stationary covariance function. This results in attribute maps that fail to reproduce local changes in the mean, in the variance and, particularly, in the spatial continuity. The proposed alternative is to build local distributions, variograms, and correlograms. These are inferred by weighting the samples depending on their distance to selected locations. The local distributions are locally transformed into Gaussian distributions embedding information on the local histogram. The distance weighted experimental variograms and correlograms are able to adapt to local changes in the direction and range of spatial continuity. The automatically fitted local variogram models and the local Gaussian transformation parameters are used in spatial estimation algorithms assuming local stationarity. The resulting maps are rich in nonstationary spatial features. The proposed process implies a higher computational effort than traditional stationary techniques, but if data availability allows for a reliable inference of the local distributions and statistics, a higher accuracy of estimates can be achieved. 相似文献
15.
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. 相似文献
16.
Seismic hazard assessment under complex source size distribution of mining-induced seismicity 总被引：1，自引：0，他引：1
It is well-documented that a variety of factors controlling the rockmass fracturing process in mines often results in a complexity of mining event size distribution. In such cases, the estimation of the probability functions of source size parameterizations, with the use of presently known distribution models, brings about an unacceptable and systematic over- or underestimation of the seismic hazard parameters. It is, therefore, recommended that the non-parametric, kernel estimators of the event size distribution functions, be applied to stationary hazard studies in mining seismicity.These data-driven estimators, adapted to seismic source size characterization, accurately fit all kinds of data underlying distributions, regardless of their complexity. Recently, the non-parametric approach to size characterization was supported by a special method of uncertainty analysis based on resampling techniques. At present, it is a fully developed method, which provides point and interval estimates of size distribution functions and related hazard parameters. Two examples of its use in studying mining seismic data are presented and discussed in this paper. The analyzed data sets were recorded in two different copper mines in Poland. The smoothed bootstrap test for multimodality, which is a specialized tool for investigating the shapes of probability densities, provided highly significant proof that in both cases the probability densities of source size parameterization were complex thus implied the superiority of the non-parametric estimation to the classic, model-based approach in the studied cases. The data were then used to construct non-parametric, kernel estimates of the source size cumulative distribution function (CDF), the exceedance probability and the mean return period. Furthermore, confidence intervals for these quantities were also estimated. The intervals for CDF were narrow, showing that the procedures of non-parametric estimation and resampling based uncertainty analysis were precise. Due to the fact that the mean return period is very sensitive to values of the CDF, in particular for larger events sizes, the uncertainty of the return period estimates was not insignificant but remained manageable. The point and interval estimates of source size CDF and hazard parameters so obtained were compared with the respective point estimates achieved from the inappropriate in the case of complex magnitude distributions, model-based approach. 相似文献
17.
Direct Sequential Simulation and Cosimulation 总被引：7，自引：0，他引：7
Amilcar Soares 《Mathematical Geology》2001,33(8):911-926
Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of N
v variables without any transformation. A set of examples of direct simulation and cosimulation are presented. 相似文献
18.
Kateri Guertin 《Mathematical Geology》1987,19(5):407-423
A nonlinear correction functionK(Z*) is proposed to transform any initial linear grade estimatorZ* into a conditional unbiased estimatorZ**=K(Z*) with reduced conditional estimation variance. Such a corrected estimator allows more accurate prediction of ore reserves at any level of selection performed during the mine lifetime. The correction is based upon an analytical or isofactorial representation of a bivariate distribution model of true gradeZ and its estimatorZ*. This correction model allows derivation of conditional estimation variances for both estimatorsZ* andZ** and provides a solution to the problem of change of support. A case study is presented and performance of the proposed correction model is evaluated in terms of actual conditional bias and mean squared errors. Results obtained stress the practical importance of the correction model in selective mining operations. 相似文献
19.
Georges Verly 《Mathematical Geology》2005,37(5):451-475
For a mining operation, minimizing misclassification of ore and waste during grade control is of critical importance. This paper reviews grade control procedures for classifying ore and waste that are based on estimation and conditional simulation approaches. The similarities and differences of the procedures are first discussed in the light of an example. Subsequently, several case studies, including actual operating mines, are presented. The theoretical review shows that conditional simulation is generally better than estimation for ore and waste classification, especially when the profit value of a block is a nonlinear function of the grade of the block. The case studies, however, indicate that, in the context of daily grade control, the value of conditional simulation over good estimation is relatively low compared to the value of improving general practices at mine sites. 相似文献