共查询到20条相似文献，搜索用时 15 毫秒
1.
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. 相似文献
2.
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
3.
The presence of geological units with different grade characteristics mostly leads to problems during the grade modeling process. In special cases, if the area under study has units with small thickness and low grade with respect to the dominant unit of the area, it is difficult to reproduce different grade contents in these units in the simulated grade models because of the low thickness and lack of data in these units. In this study, the local moment constraints method, based on the definition of soft conditioning data reflecting geological knowledge, is investigated for improving simulated grade models under the mentioned conditions. This method is applied for grade simulation at the 1,750 m level of Sungun porphyry copper mine. The studied area is divided into two rock type domains: Sungun porphyry and Dyke. The Sungun porphyry unit is the dominant rock type in the considered area and has, on average, a higher copper grade, while dykes discontinue Sungun porphyry rock units sporadically and most of them are barren of mineralization. It is demonstrated that the use of soft conditioning data makes the simulated grade model closer to reality and improves the reproduction of grade contents considering the rock type units in the area. In the next step, the results obtained from conditional simulation are used for mineral resources classification. To this end, the conditional coefficient of variation is chosen as a criterion for measuring uncertainty and for defining the resources classes. Then, it is shown that uncertainty can be considerably reduced in the prepared models if soft data are considered; as a result, an increase in measured resource classification is observed. 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.
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
6.
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
7.
Comparison of kriging techniques in a space-time context 总被引：1，自引：0，他引：1
Patrick Bogaert 《Mathematical Geology》1996,28(1):73-86
Space-time processes constitute a particular class, requiring suitable tools in order to predict values in time and space, such as a space-time variogram or covariance function. The space-time co-variance function is defined and linked to the Linear Model of Coregionalization under second-order space-time stationarity. Simple and ordinary space-time kriging systems are compared to simple and ordinary cokriging and their differences for unbiasedness conditions are underlined. The ordinary space-time kriging estimation then is applied to simulated data. Prediction variances and prediction errors are compared with those for ordinary kriging and cokriging under different unbiasedness conditions using a cross-validation. The results show that space-time kriging tend to produce lower prediction variances and prediction errors that kriging and cokriging. 相似文献
8.
Analysis and Estimation of Multi-unit Deposits: Application to a Porphyry Copper Deposit 总被引：1，自引：1，他引：0
Serge Antoine Séguret 《Mathematical Geosciences》2013,45(8):927-947
This work concerns mineral deposits consisting of geological bodies whose metal grades have different characteristics in terms of distribution and variogram, which means that estimating grades by ordinary kriging may produce unrealistic spatial continuity. This paper proposes a method based on the indicators of the geological objects (hereafter called units) and their product with the metal grade. This is illustrated by an application to a porphyry copper deposit. The aim of this paper is essentially to promote the use of variogram ratios to analyze and characterize deposits. 相似文献
9.
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
10.
11.
Measures of Parameter Uncertainty in Geostatistical Estimation and Geostatistical Optimal Design 总被引：4，自引：2，他引：2
Wolfgang Nowak 《Mathematical Geosciences》2010,42(2):199-221
Studies of site exploration, data assimilation, or geostatistical inversion measure parameter uncertainty in order to assess
the optimality of a suggested scheme. This study reviews and discusses measures for parameter uncertainty in spatial estimation.
Most measures originate from alphabetic criteria in optimal design and were transferred to geostatistical estimation. Further
rather intuitive measures can be found in the geostatistical literature, and some new measures will be suggested in this study.
It is shown how these measures relate to the optimality alphabet and to relative entropy. Issues of physical and statistical
significance are addressed whenever they arise. Computational feasibility and efficient ways to evaluate the above measures
are discussed in this paper, and an illustrative synthetic case study is provided. A major conclusion is that the mean estimation
variance and the averaged conditional integral scale are a powerful duo for characterizing conditional parameter uncertainty,
with direct correspondence to the well-understood optimality alphabet. This study is based on cokriging generalized to uncertain
mean and trends because it is the most general representative of linear spatial estimation within the Bayesian framework.
Generalization to kriging and quasi-linear schemes is straightforward. Options for application to non-Gaussian and non-linear
problems are discussed. 相似文献
12.
Ore grade is the most important source of uncertainty in a mining operation which plays an important role to classify run-of-mine (ROM) material into ore and waste parcels. As a widely used method, kriging estimator is used to estimate the grade of ore blocks. In conventional mining practices, if the estimated grade of a parcel is above the cut-off grade, this parcel is classified as ore, otherwise, is labelled as a waste parcel. An alternative approach is to simultaneously consider the grade of parcels and the economic consequences of sending parcels to destinations by applying simulation-based methods. In this study, kriging and simulation-based methods including loss and profit functions are applied on a real-world case study to classify ore/waste material based on the initial exploration data. Then, the actual known data, collected from blast holes samples, are compared with the estimated results in order to validate the performance of the presented methods. Outcomes show that simulation-based methods can perform better and show more adjustability with real data. 相似文献
13.
Evaluating the geological properties of a mineral deposit is a fundamental task for mine planning and it requires an assessment of reserve parameters such as thickness and grade. This paper presents a linguistic model for estimating bauxite thickness within a deposit in a fuzzy environment using indicator geostatistics and fuzzy modeling. The proposed model consists of two main stages: determining the orebody boundary and estimating the thickness. In order to estimate the thickness, a rule‐based fuzzy inference mechanism has been developed based on data statistics. Results and performance of the model have been compared with that of a well‐known conventional technique, geostatistics (kriging), and it is shown that the proposed model has bigger estimation power. In addition, the fuzzy approach is more flexible than the kriging approach. The fuzzy methodology used in the present paper is convenient for modeling reserve parameters. 相似文献
14.
This study compares kriging and maximum entropy estimators for spatial estimation and monitoring network design. For second-order
stationary random fields (a subset of Gaussian fields) the estimators and their associated interpolation error variances are
identical. Simple lognormal kriging differs from the lognormal maximum entropy estimator, however, in both mathematical formulation
and estimation error variances. Two numerical examples are described that compare the two estimators. Simple lognormal kriging
yields systematically higher estimates and smoother interpolation surfaces compared to those produced by the lognormal maximum
entropy estimator. The second empirical comparison applies kriging and entropy-based models to the problem of optimizing groundwater
monitoring network design, using six alternative objective functions. The maximum entropy-based sampling design approach is
shown to be the more computationally efficient of the two. 相似文献
16.
试论固体矿产资源／储量经济分类原理 总被引：1，自引：0，他引：1
以矿山企业生产情况分类为基础,讨论了固体矿产资源／储量经济分类原理。矿山企业有盈利生产、亏损生产、关闭三种主要生产情况,这决定了其所使用的资源／储量有经济的,边际经济的、次边际经济的三种。文章从经济学和利润最大化要求的角度提出了资源／储量分类的方法,建立了求最低边际品位和最低经济品位的公式。用最低经济品位区分经济储量和边际经济储量,用最低边际品位区分边际经济储量和次边际经济资源量。 相似文献
17.
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
18.
Optimally locating additional drill holes in three dimensions using grade and simulated annealing 总被引：2，自引：0，他引：2
Saeed Soltani Mohammadi Ardeshir Hezarkhani A. Erhan Tercan 《Journal of the Geological Society of India》2012,80(5):700-706
Average kriging variance is a standard tool used in optimization of the location of additional drill holes. However, this tool cannot distinguish between areas with different priorities. This limitation could be eliminated by using weighted average kriging variance. This paper extends the problem of optimal location to three dimensional cases, use grade as a weight and search optimum locations by simulated annealing. Weighted average kriging variance is used as objective function. The method is applied to a copper deposit. Results have shown that weighting of the estimation variance with ??grade?? is effective only when the difference among the grades estimated for different blocks is considerable. 相似文献
19.
20.
《地学前缘(英文版)》2022,13(6):101435
The past two decades have seen a rapid adoption of artificial intelligence methods applied to mineral exploration. More recently, the easier acquisition of some types of data has inspired a broad literature that has examined many machine learning and modelling techniques that combine exploration criteria, or ‘features’, to generate predictions for mineral prospectivity. Central to the design of prospectivity models is a ‘mineral system’, a conceptual model describing the key geological elements that control the timing and location of economic mineralisation. The mineral systems model defines what constitutes a training set, which features represent geological evidence of mineralisation, how features are engineered and what modelling methods are used. Mineral systems are knowledge-driven conceptual models, thus all parameter choices are subject to human biases and opinion so alternative models are possible. However, the effect of alternative mineral systems models on prospectivity is rarely compared despite the potential to heavily influence final predictions. In this study, we focus on the effect of conceptual uncertainty on Fe ore prospectivity models in the Hamersley region, Western Australia. Four important considerations are tested. (1) Five different supergene and hypogene conceptual mineral systems models guide the inputs for five forest-based classification prospectivity models model. (2) To represent conceptual uncertainty, the predictions are then combined for prospectivity model comparison. (3) Representation of three-dimensional objects as two-dimensional features are tested to address commonly ignored thickness of geological units. (4) The training dataset is composed of known economic mineralisation sites (deposits) as ‘positive’ examples, and exploration drilling data providing ‘negative’ sampling locations. Each of the spatial predictions are assessed using independent performance metrics common to AI-based classification methods and subjected to geological plausibility testing. We find that different conceptual mineral systems produce significantly different spatial predictions, thus conceptual uncertainty must be recognised. A benefit to recognising and modelling different conceptual models is that robust and geologically plausible predictions can be made that may guide mineral discovery. 相似文献