共查询到20条相似文献，搜索用时 46 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.
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
3.
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
4.
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
5.
Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions 总被引：5，自引：0，他引：5
Xavier Emery 《Mathematical Geology》2005,37(4):419-445
This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions. 相似文献
6.
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
7.
A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These
transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study
presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured
transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity
maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and
ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated
data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates
to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother
than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even
natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic
information systems (GIS) as basic information for further groundwater study.
Received: 27 August 1999 · Accepted: 22 February 2000 相似文献
8.
Marat. Z. Abzalov 《Mathematical Geology》2006,38(4):393-411
Recoverable mineralisation at a given mining selectivity is traditionally modelled from sparse data grids by non-linear geostatistical techniques such as Uniform Conditioning. This method estimates the tonnage and grade of mineralisation which can be extracted as small selective minable blocks from large blocks (panels), whose grade is modelled by Ordinary Kriging. Uniform Conditioning technique estimates the proportions of recoverable mineralisation in each panel without specifying the actual locations of the economically extractable blocks. This inability to predict a spatial location of the recoverable mineralisation is a major disadvantage of the conventional Uniform Conditioning method. A new approach, called Localised Uniform Conditioning, has been developed to overcome this limitation. This method applies the grade–tonnage relationships modelled by the Uniform Conditioning technique to the spatial grade distribution patterns approximated by direct kriging of the small blocks from the sparse data grid. This approach estimates localised selective mining units grades conforming to the proper grade–tonnage curves obtained by the Uniform Conditioning method as well as maintaining the relative spatial grade distribution pattern indicated by the directly kriged small block grades. The advantage of this approach is essentially dependent upon the data available for ranking the small blocks within a panel in increasing order of their grade. Ordinary Kriging of the small blocks can be used for their ranking providing the kriged estimates produce a meaningful indication of the relative grade pattern. Where the data is sparse and not close to a panel, or their distribution is characterised by a strong short-range variability, the advantages of using the Localised Uniform Conditioning approach are more limited. 相似文献
9.
Xavier Emery 《Mathematical Geology》2007,39(6):607-623
Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging.
In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random
field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant
over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the
random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian
random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended
to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for
conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging. 相似文献
10.
Empirical Maximum Likelihood Kriging: The General Case 总被引：4，自引：0，他引：4
Although linear kriging is a distribution-free spatial interpolator, its efficiency is maximal only when the experimental data follow a Gaussian distribution. Transformation of the data to normality has thus always been appealing. The idea is to transform the experimental data to normal scores, krige values in the “Gaussian domain” and then back-transform the estimates and uncertainty measures to the “original domain.” An additional advantage of the Gaussian transform is that spatial variability is easier to model from the normal scores because the transformation reduces effects of extreme values. There are, however, difficulties with this methodology, particularly, choosing the transformation to be used and back-transforming the estimates in such a way as to ensure that the estimation is conditionally unbiased. The problem has been solved for cases in which the experimental data follow some particular type of distribution. In general, however, it is not possible to verify distributional assumptions on the basis of experimental histograms calculated from relatively few data and where the uncertainty is such that several distributional models could fit equally well. For the general case, we propose an empirical maximum likelihood method in which transformation to normality is via the empirical probability distribution function. Although the Gaussian domain simple kriging estimate is identical to the maximum likelihood estimate, we propose use of the latter, in the form of a likelihood profile, to solve the problem of conditional unbiasedness in the back-transformed estimates. Conditional unbiasedness is achieved by adopting a Bayesian procedure in which the likelihood profile is the posterior distribution of the unknown value to be estimated and the mean of the posterior distribution is the conditionally unbiased estimate. The likelihood profile also provides several ways of assessing the uncertainty of the estimation. Point estimates, interval estimates, and uncertainty measures can be calculated from the posterior distribution. 相似文献
11.
Restricted kriging for mixture of grade models 总被引：2，自引：0，他引：2
A modified type of kriging, referred to as restricted kriging (RK), is proposed in this study. The method incorporates constraints on different grade classes to restrict the influence of the samples having different likelihoods in estimation. RK is motivated by the estimation of mineral reserves when grades have highly skewed distributions. Ordinary kriging tends to produce an overly smoothed interpolated surface by underestimating high grades and overestimating low grades. The fact that ordinary kriging gives a uniform prior treatment to all samples independent of their values is a major factor associated with this smoothing effect. The new approach differentiates each grade portion by preselected cutoffs. RK is developed for a single cutoff and then extended into a general form for any finite number of cutoffs. Restricted cokriging (RCK) is also formulated to simultaneously estimate a set of random functions with restriction conditions. Methods are suggested for determination of the probabilities of occurrence of different grade portions. Finally, the new approach is demonstrated on a case study of an epithermal gold deposit. 相似文献
12.
Based on a detailed statistical analysis of chemical data published in the scientific literature, estimates were made of the minimum amounts of recoverable Ge contained within sulphidic zinc ores and coals, given current processing technologies. It is expected that at least 119 kt (～7 kt in zinc ores and ～112 kt in coal) of recoverable germanium exist within proven reserves (at present stage of knowledge) at grades in excess of 100 ppm in sphalerite and 200 ppm in coal, while at least 440 kt (～50 kt in zinc ores and ～390 kt in coal) should become recoverable in the future, being associated to coal reserves at 8–200 ppm Ge and zinc resources containing in excess of 100 ppm Ge in sphalerite. Mississippi Valley Type (MVT) deposits are expected to be the most important hosts of germanium-rich sphalerite, while both brown and hard coals are expected to be equally important as hosts of germanium. The approach taken in this publication shows that reliable minimum estimates for the availability of by-product metals lacking suitable reserve/resource data may be attained by using robust statistical methods and geochemical data published in the scientific literature 相似文献
13.
When do we need a trend model in kriging? 总被引：1，自引：0，他引：1
Under usual estimation practice with local search windows for data and for interpolation situations, universal kriging and ordinary kriging yield the same estimates, using a data set with apparent trend, for both the unknown attribute and its trend component. Modeling the trend matters only in extrapolation situations. Because conditions of the case study presented arise most frequently in practice, the simpler ordinary kriging is the preferred option. 相似文献
14.
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
15.
Jorge Kazuo Yamamoto 《Mathematical Geology》2000,32(4):489-509
This paper presents an interpolation variance as an alternative to the measure of the reliability of ordinary kriging estimates. Contrary to the traditional kriging variance, the interpolation variance is data-values dependent, variogram dependent, and a measure of local accuracy. Natural phenomena are not homogeneous; therefore, local variability as expressed through data values must be recognized for a correct assessment of uncertainty. The interpolation variance is simply the weighted average of the squared differences between data values and the retained estimate. Ordinary kriging or simple kriging variances are the expected values of interpolation variances; therefore, these traditional homoscedastic estimation variances cannot properly measure local data dispersion. More precisely, the interpolation variance is an estimate of the local conditional variance, when the ordinary kriging weights are interpreted as conditional probabilities associated to the n neighboring data. This interpretation is valid if, and only if, all ordinary kriging weights are positive or constrained to be such. Extensive tests illustrate that the interpolation variance is a useful alternative to the traditional kriging variance. 相似文献
16.
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
17.
Compensating for estimation smoothing in kriging 总被引：2，自引：0，他引：2
Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator—compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-ft2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well—better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. 相似文献
18.
Correcting the Smoothing Effect of Ordinary Kriging Estimates 总被引：2，自引：0，他引：2
Jorge Kazuo Yamamoto 《Mathematical Geology》2005,37(1):69-94
The smoothing effect of ordinary kriging is a well-known dangerous effect associated with this estimation technique. Consequently kriging estimates do not reproduce both histogram and semivariogram model of sample data. A four-step procedure for correcting the smoothing effect of ordinary kriging estimates is shown to be efficient for the reproduction of histogram and semivariogram without loss of local accuracy. Furthermore, this procedure provides a unique map sharing both local and global accuracies. Ordinary kriging with a proper correction for smoothing effect can be revitalized as a reliable estimation method that allows a better use of the available information. 相似文献
19.
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
20.
Estimating Freshwater Acidification Critical Load Exceedance Data for Great Britain Using Space-Varying Relationship Models 总被引：1，自引：0，他引：1
In this study, two distinct sets of analyses are conducted on a freshwater acidification critical load dataset, with the objective of assessing the quality of various models in estimating critical load exceedance data. Relationships between contextual catchment and critical load data are known to vary across space; as such, we cater for this in our model choice. Firstly, ordinary kriging (OK), multiple linear regression (MLR), geographically weighted regression (GWR), simple kriging with GWR-derived local means (SKlm-GWR), and kriging with an external drift (KED) are used to predict critical loads (and exceedances). Here, models that cater for space-varying relationships (GWR; SKlm-GWR; KED using local neighbourhoods) make more accurate predictions than those that do not (MLR; KED using a global neighbourhood), as well as in comparison to OK. Secondly, as the chosen predictors are not suited to providing useable estimates of critical load exceedance risk, they are replaced with indicator kriging (IK) models. Here, an IK model that is newly adapted to cater for space-varying relationships performs better than those that are not adapted in this way. However, when site misclassification rates are found using either exceedance predictions or estimates of exceedance risk, rates are intolerably high, reflecting much underlying noise in the data. 相似文献