共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
P. S. N. Murthy 《Mathematical Geology》1989,21(4):443-461
This paper presents the results of disjunctive kriging applied to a supergene iron ore deposit of Bailadila Range of India. Disjunctive kriging is applied firstly to compare estimates of the blocks by ordinary kriging and secondly to estimate benchwise local recoverable reserves of the orebody. Good agreement exists between block estimates by ordinary kriging and disjunctive kriging except for peripheral blocks with less borehole information. Estimation of benchwise reserves shows that the behavior of the distribution of grades is different in various benches. The study shows that disjunctive kriging can be applied successfully for estimation of local recoverable reserves in the case of a good grade hematite iron ore deposit. 相似文献
5.
I. C. Lemmer 《Mathematical Geology》1986,18(7):589-604
For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name mononodal cutoff is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished). 相似文献
6.
Guocheng Pan 《Mathematical Geology》1994,26(1):135-155
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. 相似文献
7.
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
8.
A. G. Journel 《Mathematical Geology》1977,9(6):563-586
In the last few years, an increasing number of practical studies using so-called kriging estimation procedures have been published. Various terms, such as universal kriging, lognormal kriging, ordinary kriging, etc., are used to define different estimation procedures, leaving a certain confusion about what kriging really is. The object of this paper is to show what is the common backbone of all these estimation procedures, thus justifying the common name of kriging procedures. The word kriging (in French krigeage) is a concise and convenient term to designate the classical procedure of selecting, within agiven class of possible estimators, the estimator with a minimum estimation variance (i.e., the estimator which leads to a minimum variance of the resulting estimation error). This estimation variance can be seen as a squared distance between the unknown value and its estimator; the process of minimization of this distance can then be seen as the projection of the unknown value onto the space within which the search for an estimator is carried out. 相似文献
9.
A. G. Journel 《Mathematical Geology》1986,18(3):269-286
Traditional interpolation algorithms, including krigings, do not account for inequality-type data less subjective qualitative information. Soft kriging formalism allows a coding of both hard data and constraint intervals as prior cumulative distribution functions (cdfs) which are interpolated into posterior cdfs. Non-Gaussian confidence intervals and various optimal estimates then are derived. A synthetic case study is presented. 相似文献
10.
We evaluate the performance and statistical accuracy of the fast Fourier transform method for unconditional and conditional simulation. The method is applied under difficult but realistic circumstances of a large field (1001 by 1001 points) with abundant conditioning criteria and a band limited, anisotropic, fractal-based statistical characterization (the von Kármán model). The simple Fourier unconditional simulation is conducted by Fourier transform of the amplitude spectrum model, sampled on a discrete grid, multiplied by a random phase spectrum. Although computationally efficient, this method failed to adequately match the intended statistical model at small scales because of sinc-function convolution. Attempts to alleviate this problem through the covariance method (computing the amplitude spectrum by taking the square root of the discrete Fourier transform of the covariance function) created artifacts and spurious high wavenumber content. A modified Fourier method, consisting of pre-aliasing the wavenumber spectrum, satisfactorily remedies sinc smoothing. Conditional simulations using Fourier-based methods require several processing stages, including a smooth interpolation of the differential between conditioning data and an unconditional simulation. Although kriging is the ideal method for this step, it can take prohibitively long where the number of conditions is large. Here we develop a fast, approximate kriging methodology, consisting of coarse kriging followed by faster methods of interpolation. Though less accurate than full kriging, this fast kriging does not produce visually evident artifacts or adversely affect the a posteriori statistics of the Fourier conditional simulation. 相似文献
11.
On the condition number of covariance matrices in kriging, estimation, and simulation of random fields 总被引：1，自引：0，他引：1
The numerical stability of linear systems arising in kriging, estimation, and simulation of random fields, is studied analytically and numerically. In the state-space formulation of kriging, as developed here, the stability of the kriging system depends on the condition number of the prior, stationary covariance matrix. The same is true for conditional random field generation by the superposition method, which is based on kriging, and the multivariate Gaussian method, which requires factoring a covariance matrix. A large condition number corresponds to an ill-conditioned, numerically unstable system. In the case of stationary covariance matrices and uniform grids, as occurs in kriging of uniformly sampled data, the degree of ill-conditioning generally increases indefinitely with sampling density and, to a limit, with domain size. The precise behavior is, however, highly sensitive to the underlying covariance model. Detailed analytical and numerical results are given for five one-dimensional covariance models: (1) hole-exponential, (2) exponential, (3) linear-exponential, (4) hole-Gaussian, and (5) Gaussian. This list reflects an approximate ranking of the models, from best to worst conditioned. The methods developed in this work can be used to analyze other covariance models. Examples of such representative analyses, conducted in this work, include the spherical and periodic hole-effect (hole-sinusoidal) covariance models. The effect of small-scale variability (nugget) is addressed and extensions to irregular sampling schemes and higher dimensional spaces are discussed. 相似文献
12.
Masoud Monjezi Majid Rajabalizadeh Kashani Mohammad Ataei 《Arabian Journal of Geosciences》2013,6(1):123-128
Grade estimation is very important in designing open pits. In the process of grade estimation, underestimation can result in loss of economic ore, whereas overestimation would unnecessarily increase stripping ratio. Normally, kriging method, which suffers from underestimation and/or overestimation due to smoothing effect, is used for grade estimation. To overcome drawbacks of the kriging method, more efficient techniques such as conditional simulation can be applied. In this paper, utilizing sequential Gaussian conditional simulation, grade models were constructed for Sungun copper deposit situated in the North West of Iran. According to the obtained results, it was observed that conditional simulation can effectively cope with the weakness of kriging method. Also, it was observed that as compared to the kriging method, grade distribution, resulted from the conditional simulation, is almost identical to that of the real exploration data. Accordingly, using conditional simulation, the amount of mineable ore was significantly increased, and also, average net present value as the mines’ most important economic indicator was improved by 40%. 相似文献
13.
P. Fabbri 《Mathematical Geology》2001,33(6):745-760
In the geothermal Euganean area (Veneto region, NE Italy) water temperatures range from 60 to 86°C. The aquifer considered is rocky and the production wells in this study have a depth ranging from 300 to 500 m. For exploitation purposes, it is important to identify zones with a high probability that the temperature is more than 80°C and zones with a high probability that the temperature is less than 70°C. First, variographic analysis was conducted from 186 temperature data of thermal ground waters. This analysis gave results that are consistent with the main regional tectonic structure, the NW-SE trending Schio-Vicenza fault system. Then indicator variograms of the second, fifth, and eighth decile were compared to identify the spatial continuity at different thresholds. The unacceptability of a multigaussian hypothesis of the random function and the necessity to know the cumulative distribution function in any location, suggested the use of a nonparametric geostatistical procedure such as indicator kriging. Thus, indicator variograms at the cutoffs of 65, 70, 73, 75, 78, 80, 82, and 84°C were analyzed, fitted, and used during the indicator kriging procedure. Finally, probability maps were derived from postprocessing indicator kriging results. These maps identified scarcely exploited areas with a high probability of the temperature being higher than 80°C, between 70 and 80°C and areas with high probability of the temperature being below 70°C. 相似文献
14.
Interval-valued random functions and the kriging of intervals 总被引：1，自引：0，他引：1
Phil Diamond 《Mathematical Geology》1988,20(3):145-165
Estimation procedures using data that include some values known to lie within certain intervals are usually regarded as problems of constrained optimization. A different approach is used here. Intervals are treated as elements of a positive cone, obeying the arithmetic of interval analysis, and positive interval-valued random functions are discussed. A kriging formalism for interval-valued data is developed. It provides estimates that are themselves intervals. In this context, the condition that kriging weights be positive is seen to arise in a natural way. A numerical example is given, and the extension to universal kriging is sketched. 相似文献
15.
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
16.
Xavier Emery 《Mathematical Geology》2002,34(1):79-100
This paper presents a conditional simulation procedure that overcomes the limits of gaussian models and enables one to simulate regionalized variables with highly asymmetrical histograms or with partial or total connectivity of extreme values. The philosophy of the method is similar to that of sequential indicator technique, but it is more accurate because it is based on a complete bivariate model by means of an isofactorial law. The resulting simulations, which can be continuous or categorical, not only honor measured values at data points, but also reproduce the mono and bivariate laws of the random function associated to the regionalized variable, that is, every one or two-point statistic: histogram, variogram, indicator variograms. The sequential isofactorial method can also be adapted to conditional simulation of block values, without resorting to point–support simulations. 相似文献
17.
In this study, machine learning methods such as neural networks, random forests, and Gaussian processes are applied to the estimation of copper grade in a mineral deposit. The performance of these methods is compared to geostatistical techniques, such as ordinary kriging and indicator kriging. To ensure that these comparisons are realistic and relevant, the predictive accuracy is estimated on test instances located in drill holes that are different from the training data. The results of an extensive empirical study in the Sarcheshmeh porphyry copper deposit in Southeastern Iran illustrate that specially designed Gaussian processes with a symmetric standardization of the spatial location inputs and an anisotropic kernel yield the most accurate predictions. Furthermore, significant improvements are obtained when, besides location, information on the rock type is included in the set of predictor variables. This observation highlights the importance of carrying out detailed studies of the geological composition of the deposit to obtain more accurate ore grade predictions. 相似文献
18.
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
19.
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
20.
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