A Top-Cut Model for Deposits with Heavy-Tailed Grade Distribution     

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   

Spectral Simulation of Isotropic Gaussian Random Fields on a Sphere     

Lantuéjoul  Christian  Freulon  Xavier  Renard  Didier 《Mathematical Geosciences》2019,51(8):999-1020

A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric. This algorithm supposes that the angular power spectrum of the covariance function is explicitly known. Direct analytic calculations are performed for exponential and linear covariance functions. In addition, three families of covariance functions are presented where the calculation of the angular power spectrum is simplified (shot-noise random fields, Yadrenko covariance functions and solutions of certain stochastic partial differential equations). Numerous illustrative examples are given.

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Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework     

Pizzella  Laure  Alais  Robin  Lopez  Simon  Freulon  Xavier  Rivoirard  Jacques 《Mathematical Geosciences》2022,54(1):95-130

Mathematical Geosciences - When too few field measurements are available for the geological modeling of complex folded structures, the results of implicit methods typically exhibit an...  相似文献