Methods for geochemical anomaly separation: the geostatistical and multifractal approaches

Separation of geochemical anomalies from background has always been a major concern of exploration geochemistry. The search for methods that can make this analysis quantitative and objective aims not only at the reduction of subjectiveness but also at providing an automatic routine in exploration, assisting the interpretation and production of geochemical maps. This report discusses two methodologies which aim at the same objective of geochemistry anomaly separation: multifractal theory and geostatistics. Geostatistics is a powerful tool for the analysis of regionalized variables, and factorial kriging has been successfully applied to map di¤erent components of a random function in a domain. These components, in geochemical analysis, correspond to the di¤erent average grades in an area, each one related to a given geological structure responsible for the phenomenon. This same problem has also been approached in a di¤erent manner, by means of multifractal modeling. At the present time, a proposed multifractal model is the only ones which aims at giving quantitative values for the anomalous thresholds by means of the relations between areas enclosing a given concentration and concentrations. This model relies on the assumption that the collection of geochemical values follow a multifractal model, i.e. the measured concentrations in a given area are self-similar at any scale. It is also discussed, in relation to the multifractal model, how to prove if a given data set is multifractal or not. However, it has been shown that the model is e¢cient even if such proof fails, which opens a series of questions regarding the true multifractal nature of the model. It is brie‡y discussed that some measurements still need the geostatistical framework in order to be representative and robust, and a comparative study should be performed between multifractal models and factorial kriging. Since it is not proved that the multifractal model is universal, although it is extremely simple to implement and can give very quick results, its combination with factorial kriging could give a very powerful and robust method used in geochemical exploration.