Abstract: |
Linear kriging methods fail to estimate local grades and local reserves for highly skewed variables due to three reasons: it uses only part of the available data information, it has no physical principles associated with the mathematical proceedings to minimize the problems, and it works on the continuous spectrum while data are discrete because of the limited precision of any equipment. The techniques commonly used up to now to solve the highly skewed variables estimation problems were unsuccessful, unless mathematical rigor is abandoned. Even the method of multiple indicator kriging is not satisfactory. This paper presents a new framework, the Field Parametric Geostatistics (FPG) that transforms noisy variograms into well-behaved variograms and justifies mathematically empirical procedures commonly used, as trimming or capping arbitrarily very high values. As a first step a consistent theory is built, with solid premises and rigorous mathematical procedures. The theory is based upon two underlying axioms. These axioms are associated to grade continuity and data representativeness. The method deals with both distribution function and spatial arrangement, consequently all the available information is used simultaneously. The fundamental point is that when dealing with quasi-point variables such as grade, there is an underlying assumption that all the samples have the same influence or representativeness, thus yielding non-parametric variograms, as the grade distribution is not taken into account. In FPG these point variables are transformed and replaced by macroscopic robust variables. The method, when applied to non-skewed variables, yields similar results to classic kriging. In this paper a summary of FPG estimation theory is presented and its evaluation techniques are shown through examples, which results are compared to results obtained by usual techniques. |
