A fuzzy logic based explicit declustering technique

Abstract

During the spatial estimation of geoscience resource variables, the quantity or quality of minerals and hydrocarbons can be represented by a broad range of properties, including geochemical, geotechnical, or other physical measures. Preferential sampling within the region of interest causes biased global parameters due to clustered sampling patterns. Unbiased sample distribution is essential for conducting conditional simulations to model uncertainty of spatially distributed attributes, e.g. geochemical content of metal or porosity. Therefore, declustering procedures are applied during resource estimation to estimate an unbiased statistical distribution of the measured variables. Traditional techniques such as cell declustering do not consider grade clustering, i.e., the similarity of measured variables within a spatially clustered neighbourhood. This paper presents a declustering technique that explicitly accounts for spatial clustering and the similarity of measured samples' attributes within these spatially clustered samples. In the proposed method, samples were first classified explicitly into spatial and geochemical (grade) clusters using the Fuzzy c-means algorithm. Declustering weights were derived using the Mamdani based Fuzzy Inference System using various T-norm operations. The technique was applied to the publicly available GSLib and Walker Lake datasets. It was shown that the proposed scheme produced more accurate results than those obtained with the traditional declustering technique.