Ninth International Geostatistics Congress, Oslo, Norway
June 11 – 15, 2012


Mining 5

Abstract No.:



MAF Decomposition of Compositional Data to Estimate Grades in Iron Ore Deposits


M N M Boezio, federal university of rio grande do sul (BR)
L A Abichequer, federal university of rio grande do sul (BR)
J F C L Costa, federal university of rio grande do sul (BR)


Products from iron ore deposits are defined by iron and contaminants grades and also grain sizes.

Furthermore, the data sets constitute regionalized compositions, in which each part carries information that is relative to a total, provided both by the mass balances for each attribute among granulometric partitions and in each granulometric partition among attributes of interest.

In this context, transformation of simplicial coordinates into the real space through the isometric log-ratio transform (ilr) makes it possible to use the classical approach of ordinary cokriging of the balances, and then back-transform them into the simplex.

However, implementing cokriging for multiple variables has the known disadvantage of modeling the corregionalization, where the difficulties in satisfying the positive definiteness conditions and the lack of adherence of the models, increases with the number of variables.

An approach to override the difficulties related to modelling the LMC is to decompose the multiple correlated random functions through orthogonal factors with no spatial correlation. Thus, there is no need of modelling the coregionalization: each factor can be independently modeled and treated as an independent variable.

The decomposition through Min/Max Autocorrelation Factors (MAF) has the advantage, when compared with the classical decomposition in principal components, of decorrelating variables for separation vectors different from zero.

In this work, decomposition through MAF is implemented over the isometric log-ratio transformations, in order to estimate multiple variables that constitute a regionalized composition, with results that satisfy the original considered balances and that provide adequate results (reproduction of global and local mean, no negative values within the data values interval).

Results obtained combining both the compositional data approach and MAF decomposition, proved to better when compared to the ones obtained through cokriging of raw data. The MAF decomposition, in addition, eases the computational and operational efforts of modeling the corregionalization.




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