Advanced statistical methods for geochemical mineral exploration

Abstract

The detection and identification of mineralization in geochemical exploration contains many tasks that are strongly linked to statistics. A geochemical exploration project starts with sampling planning in the area under investigation in terms of an optimal sampling design. There are of course also several other considerations that need to be taken into account, most importantly the overall costs for sampling, which limits the number of samples to be collected. Once the samples are available, they are analyzed in a laboratory resulting in “geochemical data”, which are challenging by their nature. Typically, they are compositional and thus multivariate, spatially dependent, they usually come with detection limit issues, and different kinds of uncertainties are inherent in these data. The last point is particularly addressed with statistical quality control procedures, and this provides the basis for selecting the data that are finally used for the subsequent statistical analyses. Besides the data quality considerations, data preprocessing is the following important step. Since values below the lower or above the upper detection limit could affect subsequent multivariate data analyses, it is important to first replace these values by appropriately estimated numbers. While methods accounting for the compositional nature of the geochemical data are available to estimate values below the lower detection limit, a novel method dealing with values exceeding the upper detection limit is proposed. Since this regression based procedure acts in a multivariate sense, it has advantages over existing strategies such as replacing right-censored values simply by a constant. The main statistical task in geochemical exploration is to locate of mineralized zones and to identify the underlying lithogeochemical source. While exploratory data analysis techniques may support this process, they are usually not accounting for the compositional nature of the data. Thus, an unsupervised methodology is introduced which accounts for the log-ratios of all element pairs. Due to the presence of data uncertainties, not the original observations are considered for the log-ratios, but values obtained from smooth fits, derived from Generalized Additive Models (GAMs). A measure incorporating the overall curvature of a log-ratio pair is introduced to rank the pairs, and to indicate pathfinder elements vectoring towards the mineralization. The procedure is developed for cases where samples located on linear transects, and also extended to cases where samples are taken on a plane. Real geochemical exploration data sets are used to demonstrate the performance of the methods.