共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
在固体矿产矿体圈定中,目前常用内插法的内插计算公式在推导过程中,没有考虑采用最低工业可采品位与最低工业可采米百分率圈定矿体边界的协调性,致使有时不合理地增加或减少部分工业储量。针对这一缺点,本文介绍一个更合理、使用更方便的计算边界点品位与厚度的修正公式。 相似文献
6.
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
7.
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
8.
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
9.
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
10.
Gilles Bourgault 《Mathematical Geosciences》2014,46(7):841-868
A multivariate probability transformation between random variables, known as the Nataf transformation, is shown to be the appropriate transformation for multi-Gaussian kriging. It assumes a diagonal Jacobian matrix for the transformation of the random variables between the original space and the Gaussian space. This allows writing the probability transformation between the local conditional probability density function in the original space and the local conditional Gaussian probability density function in the Gaussian space as a ratio equal to the ratio of their respective marginal distributions. Under stationarity, the marginal distribution in the original space is modeled from the data histogram. The stationary marginal standard Gaussian distribution is obtained from the normal scores of the data and the local conditional Gaussian distribution is modeled from the kriging mean and kriging variance of the normal scores of the data. The equality of ratios of distributions has the same form as the Bayes’ rule and the assumption of stationarity of the data histogram can be re-interpreted as the gathering of the prior distribution. Multi-Gaussian kriging can be re-interpreted as an updating of the data histogram by a Gaussian likelihood. The Bayes’ rule allows for an even more general interpretation of spatial estimation in terms of equality for the ratio of the conditional distribution over the marginal distribution in the original data uncertainty space with the same ratio for a model of uncertainty with a distribution that can be modeled using the mean and variance from direct kriging of the original data values. It is based on the principle of conservation of probability ratio and no transformation is required. The local conditional distribution has a variance that is data dependent. When used in sequential simulation mode, it reproduces histogram and variogram of the data, thus providing a new approach for direct simulation in the original value space. 相似文献
11.
Obtaining accurate geological boundaries and assessing the uncertainty in these limits are critical for effective ore resource and reserve estimation. The uncertainty in the extent of an ore body can be the largest source of uncertainty in ore resource estimation when drilling is sparse. These limits are traditionally interpreted deterministically and it can be difficult to quantify uncertainty in the boundary and its impact on ore tonnage. The proposed methodology is to consider stochastic modeling of the ore boundary with a distance function recoding of the available data. This technique is modified to incorporate non-stationarities in the form of a locally varying anisotropy field used in kriging and sequential Gaussian simulation. Implementing locally varying anisotropy kriging retains the geologically realistic features of a deterministic model while allowing for a stochastic assessment of uncertainty. A case study of a gold deposit in Northern Canada is used to demonstrate the methodology. The proposed technique generates realistic, curvilinear geological boundary models and allows for an assessment of the uncertainty in the model. 相似文献
12.
Generalized sequential kriging (GSK) for heterogeneous cell size: property modeling without matrices
J. A. Vargas-Guzmán 《Computational Geosciences》2010,14(1):207-215
Sequential kriging avoids the use of matrices and resolves the issue of unstable solutions. It allows for stepwise ways to
get joint estimations and cosimulations that are equivalent to the simultaneous solution. The approach is proposed as the
solution for geocellular modeling with variable cell size from heterogeneous structural properties (HSPs) as required for
modeling with structural constraints. Rock properties are controlled by structural domains, regions, and structural geology
parameters. In some cases, rock properties are cross-correlated to formation thickness, curvature of structures, and other
structural attributes. Cell thickness may be proportional to formation thickness and may enter as a conditioning property
in the estimation of rock property parameters for simulation. In addition, cell volume controls the upscaling of covariance
structures (i.e., regularized variograms). Structural properties are priorly modeled. Perturbation response functions (PRFs)
are computed for each cell vs all possible sample point locations to facilitate sequential kriging. Upscaled PRFs are modified
following conditional updating after each new data value is included in the estimation of parameters. Generalized sequential
kriging is expected to become the main tool for real-time spatial modeling of 3D cellular models with HSP. In addition, some
new developments related to the sequential kriging algorithm are included. Sequential kriging can be used for the estimation
of parameters for simulation in the so-called unstructured grids. 相似文献
13.
钻孔孔径变化与矿床类型、钻进孔径、矿化岩性、矿层品位、矿层厚度、冲冼液的性质以及工程切穿矿层的时间有着密切的关系。孔径变化对γ测井解释含量、矿床储量的增减影响甚大。理论和实践证明,专门性的孔径测量,是提高γ测井质量、准确确定矿层品级的重要措施之一,对提高矿床经济效益也具有重要意义。 相似文献
14.
随机模拟是地质统计方法的重要内容。在矿石品位估计方法中克里格方法作为一种无偏估计方法,常被用于矿石品位的估计。但克里格法估值存在平滑效应。作者在分析序贯高斯模拟和普通克里格法基本原理的基础上,运用序贯高斯模拟方法和普通克里格方法对某铁矿体内全铁(TFe)品位进行估计,给出了品位估计结果模型。研究从勘探线方向、垂直勘探线方向和竖直方向分别计算变差函数,对球状模型、指数模型、高斯模型的变差函数拟合效果进行了优选,结果表明球型模型拟合效果最好。针对序贯模拟和克里格品位估值效果进行了分析,结果显示:序贯高斯模拟结果在品位分布形态上更接近样品品位分布形态,其平滑效应更小;克里格方法估计与序贯高斯模拟方法相比仅在品位均值方面更接近样本品位均值。因此,认为序贯高斯模拟方法可以更好地刻画矿体内品位分布状态。 相似文献
15.
The postprocessing algorithm introduced by Yao for imposing the spectral amplitudes of a target covariance model is shown to be efficient in correcting the smoothing effect of estimation maps, whether obtained by kriging or any other interpolation technique. As opposed to stochastic simulation, Yao's algorithm yields a unique map starting from an original, typically smooth, estimation map. Most importantly it is shown that reproduction of a covariance/semivariogram model (global accuracy) is necessarily obtained at the cost of local accuracy reduction and increase in conditional bias. When working on one location at a time, kriging remains the most accurate (in the least squared error sense) estimator. However, kriging estimates should only be listed, not mapped, since they do not reflect the correct (target) spatial autocorrelation. This mismatch in spatial autocorrelation can be corrected via stochastic simulation, or can be imposed a posteriori via Yao's algorithm. 相似文献
16.
Looking at kriging problems with huge numbers of estimation points and measurements, computational power and storage capacities
often pose heavy limitations to the maximum manageable problem size. In the past, a list of FFT-based algorithms for matrix
operations have been developed. They allow extremely fast convolution, superposition and inversion of covariance matrices
under certain conditions. If adequately used in kriging problems, these algorithms lead to drastic speedup and reductions
in storage requirements without changing the kriging estimator. However, they require second-order stationary covariance functions,
estimation on regular grids, and the measurements must also form a regular grid. In this study, we show how to alleviate these
rather heavy and many times unrealistic restrictions. Stationarity can be generalized to intrinsicity and beyond, if decomposing
kriging problems into the sum of a stationary problem and a formally decoupled regression task. We use universal kriging,
because it covers arbitrary forms of unknown drift and all cases of generalized covariance functions. Even more general, we
use an extension to uncertain rather than unknown drift coefficients. The sampling locations may now be irregular, but must
form a subset of the estimation grid. Finally, we present asymptotically exact but fast approximations to the estimation variance
and point out application to conditional simulation, cokriging and sequential kriging. The drastic gain in computational and
storage efficiency is demonstrated in test cases. Especially high-resolution and data-rich fields such as rainfall interpolation
from radar measurements or seismic or other geophysical inversion can benefit from these improvements. 相似文献
17.
《Applied Geochemistry》2005,20(1):157-168
In monitoring a minor geochemical element in groundwater or soils, a background population of values below the instrumental detection limit is frequently present. When those values are found in the monitoring process, they are assigned to the detection limit which, in some cases, generates a probability mass in the probability density function of the variable at that value (the minimum value that can be detected). Such background values could distort both the estimation of the variable at nonsampled locations and the inference of the spatial structure of variability of the variable. Two important problems are the delineation of areas where the variable is above the detection limit and the estimation of the magnitude of the variables inside those areas. The importance of these issues in geochemical prospecting or in environmental sciences, in general related with contamination and environmental monitoring, is obvious. In this paper the authors describe the two-step procedure of indicator kriging and ordinary kriging and compare it with empirical maximum likelihood kriging. The first approach consists of using a binary indicator variable for estimating the probability of a location being above the detection limit, plus ordinary kriging conditional to the location being above the detection limit. An estimation variance, however, is not available for that estimator. Empirical maximum likelihood kriging, which was designed to deal with skew distributions, can also deal with an atom at the origin of the distribution. The method uses a Bayesian approach to kriging and gives intermittency in the form of a probability map, its estimates providing a realistic assessment of their estimation variance. The pros and cons of each method are discussed and illustrated using a large dataset of As concentration in groundwater. The results of the two methods are compared by cross-validation. 相似文献
18.
Components of geostatistical estimation, developed as a method for ore deposit assessment, are discussed in detail. The assumption that spatial observations can be treated as a stochastic process is judged to be an inappropriate model for natural data. Problems of semivariogram formulation are reviewed, and this method is considered to be inadequate for estimating the function being sought. Characteristics of bivariate interpolation are summarized, highlighting kriging limitations as an interpolation method. Limitations are similar to those of inverse distance weighted observations interpolation. Attention is drawn to the local bias of kriging and misplaced claims that it is an “optimal” interpolation method. The so-called “estimation variance,” interpreted as providing confidence limits for estimation of mining blocks, is shown to be meaningless as an index of local variation. The claim that geostatistics constitutes a “new science” is examined in detail. Such novelties as exist in the method are shown to transgress accepted principles of scientific inference. Stochastic modeling in general is discussed, and purposes of the approach emphasized. For the purpose of detailed quantitative assessment it can provide only prediction qualified by hypothesis at best. Such an approach should play no part in ore deposit assessment where the need is for local detailed inventories; these can only be achieved properly through local deterministic methods, where prediction is purely deductive. 相似文献
19.
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
20.
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