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On Some Simplifications of Cokriging Neighborhood 总被引：2，自引：0，他引：2
Jacques Rivoirard 《Mathematical Geology》2004,36(8):899-915
Choosing the cokriging neighborhood is often difficult. A poor choice, ignoring influent data, can result in a loss of information as well as in artifacts in simulations based on cokriging. Then it is convenient to use if possible, or to refer to models that lead to simplified cokriging neighborhood. We essentially consider the case of two stationary variables, a target variable and an auxiliary one. By examining possible simplifications, we set up a list of models (essentially models with residuals) that, in general or under specific configurations, lead to simplifications of cokriging neighborhood. Collocated, dislocated, and other types of neighborhood are identified, that are optimal in some models and configurations. Possible extensions to cokriging with unknown means, and to more variables, are included. 相似文献
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Jacques Rivoirard Claude Demange Xavier Freulon Aurélie Lécureuil Nicolas Bellot 《Mathematical Geosciences》2013,45(8):967-982
In some ore deposits, the grade distribution is heavy-tailed and high values make the inference of first- and second-order statistics nonrobust. In the case of gold data, high values are usually cut and the block estimation is performed using truncated grades. With this method, a part of the deposit is omitted, resulting in a potential bias on resources figures. Ad-hoc corrections can be applied on the final figures to take into account the tail of the grade distribution, but no theoretical guidelines are available. A geostatistical model has been developed to handle high values based on the assumption that for high grade zones, the only tangible information is the geometry. The grade variable z can be split into three parts: the truncated grade ( $\operatorname{Min} (z, z_{\mathrm{e}})$ where z e is the top-cut grade), a weighted indicator above top-cut grade (1{z≥z e}), and a residual. Within this framework, the residual is poorly structured, and in most cases is a pure nugget-effect. Moreover, it has no spatial correlation with the truncated grade and the indicator above top-cut grade. This decomposition makes the variographic study more robust because variables (indicator and truncated grade) do not keep high grade values. The underlying hypotheses can be tested on experimental indicator variograms and the top-cut grade can be justified. Finally, the estimation is based on a truncated grade and indicator cokriging. The model is applied to blast holes from a gold deposit and on a simulated example. Both cases illustrate the benefits of keeping the high values in the estimation process via an appropriate mathematical model. 相似文献
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Which Models for Collocated Cokriging? 总被引：1，自引：0，他引：1
Jacques Rivoirard 《Mathematical Geology》2001,33(2):117-131
When a target variable is sparsely sampled, compared to a densely sampled auxiliary variable, cokriging requires simplifications. In its strict sense, collocated cokriging makes use of the auxiliary variable only at the current point where the target variable is to be estimated; in the multicollocated form, it also makes use of the auxiliary variable at all points where the target variable is available. This paper looks for the models that support these collocated cokrigings, i.e., the models in which the simplification resulting from the collocated forms does not result in any loss of information. In these models, the cross-structure between the two variables is shown to be proportional to the structure of the auxiliary variable, not to the structure of the target variable as is often assumed (except, of course, when all structures are proportional). The target variable depends on the auxiliary variable and on a spatially uncorrelated residual. Collocated cokriging simplifies to the simple method, which consists in kriging this residual. The strictly collocated cokriging corresponds to the particular case where the residual has a pure nugget structure, but it is then reduced to the single regression at the target point. Except for this trivial case, there are no models in which strictly collocated cokriging is exactly a cokriging. 相似文献
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J. Rivoirard 《Mathematical Geology》1987,19(8):851-856
In the stationary case, two parameters are especially interesting when choosing the kriging neighborhood: weight of the mean, which shows how kriging depends on the neighborhood, and slope of the regression, which indicates if the neighborhood is large enough. 相似文献
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A review of lognormal estimators forin situ reserves 总被引：1，自引：0，他引：1
Jacques Rivoirard 《Mathematical Geosciences》1990,22(2):213-221
The term “lognormal kriging” does not correspond to a single well defined estimator. In fact, several types of lognormal estimators forin situ reserves are available, and this may cause confusion. These estimators are based on different assumptions—that is, different models. This paper presents a review of these estimators. 相似文献
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