共查询到20条相似文献，搜索用时 321 毫秒
1.
James R. Carr 《Mathematical Geology》1994,26(5):605-621
Consideration of order relations is key to indicator kriging, indicator cokriging, and probability kriging, especially for the latter two methods wherein the additional modeling of cross-covariance contributes to an increased chance of violating order relations. Herein, Gaussian-type curves are fit to estimates of the cumulative distribution function (cdf) at data quantiles to: (1) yield smoothed estimates of the cdf; and (2) to correct for violations of order relations (i.e., to correct for situations wherein the estimate of the cdf for a larger quantile is less than that for a smaller quantile). Smoothed estimates of the cdf are sought as a means to improve the approximation to the integral equation for the expected value of the regionalized variable in probability kriging. Experiments show that this smoothing yields slightly improved estimation of the expected value (in probability kriging). Another experiment, one that uses the same variogram for all indicator functions, does not yield improved estimates.Presented at the 25th Anniversary Meeting of the IAMG, Prague, Czech Republic, October 10–15, 1993. 相似文献
2.
Comparative performance of indicator algorithms for modeling conditional probability distribution functions 总被引：1，自引：0，他引：1
P. Goovaerts 《Mathematical Geology》1994,26(3):389-411
This paper compares the performance of four algorithms (full indicator cokriging. adjacent cutoffs indicator cokriging, multiple indicator kriging, median indicator kriging) for modeling conditional cumulative distribution functions (ccdf).The latter three algorithms are approximations to the theoretically better full indicator cokriging in the sense that they disregard cross-covariances between some indicator variables or they consider that all covariances are proportional to the same function. Comparative performance is assessed using a reference soil data set that includes 2649 locations at which both topsoil copper and cobalt were measured. For all practical purposes, indicator cokriging does not perform better than the other simpler algorithms which involve less variogram modeling effort and smaller computational cost. Furthermore, the number of order relation deviations is found to be higher for cokriging algorithms, especially when constraints on the kriging weights are applied. 相似文献
3.
Mapping by simple indicator kriging 总被引：3，自引：0，他引：3
Andrew R. Solow 《Mathematical Geology》1986,18(3):335-352
The problem of predicting the type of an unsampled point in a two-type map is addressed using a procedure called simple indicator kriging. This procedure estimates the conditional probability that the point is of one type or the other given the types of sample points. Simple indicator kriging is applied to examples of certain map models. It is shown to perform well, and in some cases to be exact in a specified sense. Use of simple indicator kriging to estimate multivariate normal quandrant probabilities is explored. 相似文献
4.
C. Lajaunie 《Mathematical Geology》1990,22(1):123-144
Approximate local confidence intervals can be produced by nonlinear methods designed to estimate indicator variables. The most precise of these methods, the conditional expectation, can only be used in practice in the multi-Gaussian context. Theoretically, less efficient methods have to be used in more general cases. The methods considered here are indicator kriging, probability kriging (indicator-rank co-kriging), and disjunctive kriging (indicator co-kriging). The properties of these estimators are studied in this paper in the multi-Gaussian context, for this allows a more detailed study than under more general models. Conditional distribution approximation is first studied. Exact results are given for mean squared errors and conditional bias. Then conditional quantile estimators are compared empirically. Finally, confidence intervals are compared from the points of view of bias and precision. 相似文献
5.
Direct Sequential Simulation and Cosimulation 总被引：7，自引：0，他引：7
Amilcar Soares 《Mathematical Geology》2001,33(8):911-926
Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of N
v variables without any transformation. A set of examples of direct simulation and cosimulation are presented. 相似文献
6.
Eevaliisa Laine 《Mathematical Geology》1996,28(4):477-499
The Ryytimaa dolomite formation in western Finland is mined for fertilizing purposes in agriculture. Ordinary kriging, indicator kriging, and indicator principal components simulation were used to map the dolomite quality. The fertilizing properties depend on the relative amounts of MgO and neutralizing CaO in dolomite. Based on the chemical composition the dolomite is divided into six quality classes according to the Finnish legislation. This quality classification is only partially in accordance with the three populations inferred from the distributions of the MgO, CaO, and neutralizing CaO contents. These populations probably represent compositionally different dolomite layers, now forming complicated fold interference structures that are visible on the kriged maps. The mapping of the quality, and thus, selective mining of the dolomite deposit is possible using the quality classification based on the three populations. In contrast, selective mining of the dolomite based on the legislation is difficult—at least with techniques used in this study. 相似文献
7.
Importance of Orthogonalization Algorithm in Modeling Conditional Distributions by Orthogonal Transformed Indicator Methods 总被引：1，自引：0，他引：1
A. E. Tercan 《Mathematical Geology》1999,31(2):155-173
The orthogonal transformed indicator approach to conditional cumulative distribution functions is based on the decomposition of the indicator variogram matrix as a matrix product. This paper explores the manner in which the decomposition algorithm affects the conditional cumulative distribution function as estimated by orthogonal transformed indicator kriging. Five decomposition algorithms are considered: spectral, Cholesky, symmetric, Cholesky-spectral, and simultaneous decompositions. Impact of the algorithms on spatial orthogonality and order relations problems is examined and their performances together with indicator kriging are compared using a real dataset. 相似文献
8.
以多重分形理论为基础,对中天山乌拉斯台地区铜多金属元素的岩屑测量数据,采用C-A法获得铜多金属的异常下限值,将其作为阈值进行指示克里格插值,绘制研究区的铜多金属地球化学异常图。研究显示,基于该方法获得的Cu矿化异常高值区主要集中在华力西早期第三侵入次的石英闪长岩和花岗闪长岩岩体中,受北西向和次级北东向断裂构造控制明显,该异常区可以作为寻找热液型铜多金属矿产的重要远景区。该方法对于地球化学数据空间变异性强烈的地区,较之普通克里格插值法具有更好的地球化学异常识别能力和高值信息重建能力,所得结果的最高累计频率值范围与已知矿化点的空间位置吻合度更高,在地球化学异常信息提取工作中具有推广意义。 相似文献
9.
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
10.
Indicator Simulation Accounting for Multiple-Point Statistics 总被引：7，自引：0，他引：7
Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine. 相似文献
11.
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
12.
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
13.
含水层渗透性空间分布的指示克立格估值 总被引：3，自引：0，他引：3
详细介绍了指示克立格估值计算的理论和方法。以指示变异函数为基本工具分析了华北某地区第四系含水层渗透性空间分布的结构特征,结果表明该地区含水层渗透性存在明显的各向异性特征。水平方向上,X轴方向的相关性较Y轴方向的好,Z轴的相关性最差。用指示克立格法对未采样点处进行估值,估值结果显示含水层渗透性由山前向滨海逐渐变低,在垂直方向上,渗透性变化不明显,浅部比深部略好;同时给出了估计精度,并认为对估计精度不高的区域可通过增加适当的工程加以控制。最后用交叉验证法对估值结果进行了检验,证明建立的指示变异函数模型合理且估值效果较好。这一实际应用表明指示克立格法可以很好地描述第四系含水层渗透性的空间分布规律。 相似文献
14.
The indicator kriging (IK) is one of the most efficient nonparametric methods in geo-statistics. The order relation problem in the conditional cumulative distribution values obtained by IK is the most severe drawback of it. The correction of order relation deviations is an essential and important part of IK approach. A monotone regression was proposed as a new correction method which could minimize the deviation from original quintiles value, although, ensuring all order relations. 相似文献
15.
Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities. 相似文献
16.
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
17.
Indicator cokriging is an alternative to disjunctive kriging for estimation of spatial distributions. One way to determine which of these techniques is more accurate for estimation of spatial distributions is to apply each to a particular type of data. A procedure is developed for evaluation of disjunctive kriging and indicator cokriging for such an application. Application of this procedure to earthquake ground motion data found disjunctive kriging to be at least as accurate as indicator cokriging for estimation of spatial distributions of peak horizontal acceleration. Indicator cokriging was superior for all other types of earthquake ground motion data. 相似文献
18.
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
19.
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
20.
《Applied Geochemistry》1999,14(1):133-145
Three univariate geostatistical methods of estimation are applied to a geochemical data set. The studied methods are: ordinary kriging (cross-validation), factorial kriging, and indicator kriging. These techniques use the probabilistic and spatial behaviour of geochemical variables, giving a tool for identifying potential anomalous areas to locate mineralization. Ordinary kriging is easy to apply and to interpret the results. It has the advantage of using the same experimental grid points for its estimates, and no additional grid points are needed. Factorial kriging decomposes the raw variable into as many components as there are identified structures in the variogram. This, however, is a complex method and its application is more difficult than that of ordinary or indicator kriging. The main advantages of indicator kriging are that data are used by their rank order, being more robust about outlier values, and that the presentation of results is simple. Nevertheless, indicator kriging is incapable of separating anomalous values and the high values from the background, which have a behaviour different to the anomaly. In this work, the results of the application of these 3 kriging methods to a set of mineral exploration data obtained from a geochemical survey carried out in NW Spain are presented. This area is characterised by the presence of Au mineral occurrences. The kriging methods were applied to As, considered as a pathfinder of Au in this area. Numerical treatment of Au is not applicable, because it presents most values equal to the detection limit, and a series of extreme values. The results of the application of ordinary kriging, factorial kriging and indicator kriging to As make possible the location of a series of rich values, sited along a N–S shear zone, considered a structure related to the presence of Au. 相似文献