共查询到20条相似文献，搜索用时 203 毫秒
1.
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
2.
Xavier Emery 《Mathematical Geology》2006,38(7):801-819
Multigaussian kriging aims at estimating the local distributions of regionalized variables and functions of these variables
(transfer or recovery functions) at unsampled locations. In this paper, we focus on the evaluation of the recoverable reserves
in an ore deposit accounting for a change of support and information effect caused by ore/waste misclassifications. Two approaches
are proposed: the multigaussian model with Monte Carlo integration and the discrete Gaussian model. The latter is simpler
to use but requires stronger hypotheses than the former. In each model, ordinary multigaussian kriging gives unbiased estimates
of the recoverable reserves that do not utilize the mean value of the normal score data.
The concepts are illustrated through a case study on a copper deposit which shows that local estimates of the metal content
based on ordinary multigaussian kriging are close to the optimal conditional expectation when the data are abundant and are
not dominated by the global mean when the data are scarce. The two proposed approaches (Monte Carlo integration and discrete
Gaussian model) lead to similar results when compared to two other geostatistical methods: service variables and ordinary
indicator kriging, which show strong deviations from conditional expectation. 相似文献
3.
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
4.
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
5.
This paper presents a modified ordinary kriging technique referred to as the “Area Influence Kriging” (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
6.
G. Verly 《Mathematical Geosciences》1983,15(2):259-286
The performance of the geostatistical techniques of disjunctive kriging and multigaussian kriging for the estimation of local recovered reserves are compared using a simulated deposit. 相似文献
7.
Isobel Clark 《Mathematical Geosciences》1983,15(4):517-536
One traditional method of estimating ore reserves is to allocate the arithmetic mean of local samples to each block or stope within the deposit. Thirty years ago, Krige showed that this method produced a “bias” in the estimates, in that high values were commonly overestimated and low values underestimated. This bias became known as the “regression effect” because it could usually be corrected by an empirical regression relationship derived from previously mined areas. This paper shows how the regression effect can be reconciled with the geostatistical method of kriging and how a simple regression line may be derived before any areas are mined out. The method is similar to kriging with known mean, but acknowledges that the overall mean of the deposit may not be known precisely. 相似文献
8.
The aim of this paper is to present a fast method based on bootstrapping, for simulating recoverable reserves for input to financial Monte Carlo simulations. In mining, the three parameters defining recoverable reserves are the cutoff grade, z, the ore tonnage above cutoff, T, and the metal quantity above cutoff, Q. After introducing the concept of 3-dimensional QTz curves, the statistical technique called bootstrapping is reviewed and applied to a set of South African gold grades. As selective mining is carried out on blocks not points, these curves have to be calculated for blocks. The QTz curves obtained by bootstrapping are compared to those obtained by conditionally simulating the same deposit. The procedure has been extended to incorporate geologists' ideas of the likely size of the ore volume. Lastly, the recoverable reserves obtained by bootstrapping are compared with those obtained by traditional risk analysis (base case ± 10% or 20%). 相似文献
9.
Abdullah Arik 《Geotechnical and Geological Engineering》1990,8(4):305-318
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. 相似文献
10.
For earthquake ground motion studies, the actual ground motion distribution should be reproduced as accurately as possible. For optimal estimation of ground motion, kriging has been shown to provide accurate estimates. Although kriging is accurate for this application, some estimates it provides are underestimates. This has dire consequences for subsequent design for earthquake resistance. Kriging does not provide enough information to allow an analysis of each estimate for underestimation. For such an application, disjunctive kriging is better applied. This advanced technique quantifies the probability that an estimate equals or exceeds particular levels of ground motion. Furthermore, disjunctive kriging can provide improved estimation accuracy when applied for local estimation of ground motion. 相似文献
11.
Abdullah Arik 《Mathematical Geology》2002,34(7):783-796
This paper presents a modified ordinary kriging technique referred to as the Area Influence Kriging (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
12.
Shahab Shahbeik Peyman Afzal Parviz Moarefvand Mania Qumarsy 《Arabian Journal of Geosciences》2014,7(9):3693-3704
Estimation of mineral resources and reserves with low values of error is essential in mineral exploration. The aim of this study is to compare inverse distance weighted (IDW) and ordinary kriging (OK) methods based on error estimation in the Dardevey iron ore deposit, NE Iran. Anisotropic ellipsoid and variograms were calculated and generated for estimation of Fe distribution by both methods. Density, continuity of ore and waste, the number of points involved, and the discretization factor in the estimation of ore and waste boundaries were determined and the resource estimated by IDW and OK methods. Estimation errors were classified based on JORC standard, and both methods were compared due to distribution of error estimation. Results obtained by the study indicate that error estimation of OK method is less than IDW method and that the results of OK method are reliable. 相似文献
13.
V. Kameshwara Rao C. R. Rao A. C. Narayana 《Journal of the Geological Society of India》2014,83(5):549-554
Conventional methods of ore deposit estimates are time consuming, whereas geostatistical methods provide quick and reliable estimates with minimum variance. Geostatistical tools, semi-variograms and kriging, have been used for estimation of grades of an iron ore deposit in the present study. In order to model the deposit and estimate grade, 4537 samples collected from 93 boreholes were used in the study. 3-D data have been converted to 2-D for analyzing the variation of Fe within the boreholes. For each borehole, the weighted mean of Fe grade and its coefficient of variation (CV) are calculated and further analysis is carried out for these two variables. Semi-variogram model suggests that the deposit extends over a zone of influence up to 700 m. Grade maps of kriged estimates reveal that the iron ore deposit is distributed in three distinct zones. 相似文献
14.
15.
克里格法在离子吸附型稀土矿勘查储量估算中的应用 总被引：1，自引：1，他引：0
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。 相似文献
16.
17.
Six different geostatistical estimators (linear kriging, lognormal kriging, and disjunctive kriging, each with and without a nonbias, i.e., universality condition) were compared using data from a polymetallic deposit in Algeria. The differences between estimators with and without the nonbias condition were far more pronounced than between the different kriging methods. This highlights the importance of choosing an appropriate stationarity model for the data. The criterion concerning kriging weight of the mean in simple kriging, proposed by Remacre (1984, 1987) and Rivoirard (1984) was found to be helpful for determining blocks where the choice of the stationarity hypothesis was critical. 相似文献
18.
Xavier Emery 《Mathematical Geology》2003,35(6):699-718
This paper presents a methodology for assessing local probability distributions by disjunctive kriging when the available data set contains some imprecise measurements, like noisy or soft information or interval constraints. The basic idea consists in replacing the set of imprecise data by a set of pseudohard data simulated from their posterior distribution; an iterative algorithm based on the Gibbs sampler is proposed to achieve such a simulation step. The whole procedure is repeated many times and the final result is the average of the disjunctive kriging estimates computed from each simulated data set. Being data-independent, the kriging weights need to be calculated only once, which enables fast computing. The simulation procedure requires encoding each datum as a pre-posterior distribution and assuming a Markov property to allow the updating of pre-posterior distributions into posterior ones. Although it suffers some imperfections, disjunctive kriging turns out to be a much more flexible approach than conditional expectation, because of the vast class of models that allows its computation, namely isofactorial models. 相似文献
19.
砂岩型铀矿是绿色经济可采的重要能源矿种,目前是世界上重要的铀矿勘探类型之一。二连盆地芒来铀矿床、鄂尔多斯盆地纳岭沟铀矿床铀矿体多呈板状产出,板状铀矿体成因备受关注。为研究砂岩型铀矿内部U、Ra和铀镭平衡系数（Kp）分布的垂向分布规律,本文以二连盆地芒来铀矿床为例,采用具有网格精度高优点的克里格插值法研究U、Ra和Kp垂向分布规律,分别利用放射性样品分析数据和定量伽马测井五点式反褶积法反演U含量数据,通过克里格法精细刻画砂岩型矿体中U、Ra和Kp分布的垂向分布规律。研究发现,该矿床板状矿体内部具有卷状的特征,Kp分布形态可以用来判断含氧含铀水的运移方向以及氧化强弱。该方法对研究铀矿体形态、铀矿成矿规律和后续地浸开采具有重要意义。 相似文献
20.
Reducing the Impact of Outliers in Ore Reserves Estimation 总被引：1，自引：0，他引：1
Joao Felipe Costa 《Mathematical Geology》2003,35(3):323-345
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. 相似文献