Estimation of some mineral deposits involves chemical species or a granulometric mass balance that constitute a closed constant sum (e.g., 100%). Data that add up to a constant are known as compositional data (CODA). Classical geostatistical estimation methods (e.g., kriging) are not satisfactory when CODA are used, since bias is expected when estimated mean block values are back-transformed to the original space. CODA methods use nonlinear transformations, and when the transformed data are interpolated, they cannot be returned directly to the space of the original data. If these averages are back-transformed using the inverse function, bias is generated. To avoid this bias, this article proposes geostatistical simulation of the isometric logratio ratio (ilr) transformations back-transforming point simulated values (instead of block estimations), with the averaging being postponed to the end of the process. The results show that, in addition to maintaining the mass balance and the correlations among the variables, the means (E-types) of the simulations satisfactorily reproduce the statistical characteristics of the grades without any sort of bias. A complete case study of a major bauxite deposit illustrates the methodology.
The geological modeling of stratiform deposits can become very complex, often making use of geological envelopes of small thickness and requiring the use of subblocks (based on Cartesian coordinates) to produce a coherent block model. However, geological events after the formation of the deposit (folds, faults, etc.) can change the direction of spatial continuity of certain attributes, with the mixing of samples belonging to different formation eras (in the case of stratiform deposits) in the same elevation. This study presents a solution for deposits with stratigraphic grades combined with samples of different origins. The solution is a two-dimensional estimate obtained by accumulating the thicknesses of P 2 O 5 in a phosphate deposit (as compared to traditional statistical analysis in three dimensions).Keywords: accumulation, ordinary kriging, phosphate. (dobras, falhas, etc.)
Resumo
A modelagem geológica de depósitos estratiformes pode-se tornar muito complexa, muitas vezes fazendo uso de envelopes geológicos de pequena espessura e exigindo o uso de sub-blocos (com base em coordenadas cartesianas) para produzir um modelo de blocos coerente. No entanto, eventos geológicos após a formação do depósito
All available data should be used to build a geostatistical model. In underground mining, data have different support volumes: drillhole data are defined at a quasi-point support, while production data represent tonnes of ore mined during a period of time (stopes). Due to the support difference, production data are frequently ignored to update the block grade model. We propose a block kriging approach to combine these two sources of information (point and volumetric support data). A synthetic underground mining case is presented. Two estimation scenarios are evaluated: the first considers only drillhole data, while the second considers both drillhole and production data. Results show that the use of production data improves grade estimation. The improvement is more pronounced where diamond drillholes are sparsely located.
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