Identification of the Nonlinear Distributions of Elements with Multifractal: A Case Study of the Er'renshan Ore Field, NW China

Abstract

Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements. However, these surveys often involve compositional data, the weight concentrations, which do not meet the requirements of statistical methods due to the closure effect. In this study, we applied an integrated approach combining compositional data, multifractal, and multivariate statistical analyses to identify the nonlinear complexity of the spatial distributions of elemental concentrations in the Er'renshan ore field. Initially, the raw concentrations were transformed into log-ratios following the principles of composition data theory to alleviate the impact of the closure effect. Multifractal analysis was then conducted to characterise the nonlinear complexity of the concentration distributions. Furthermore, principal component analysis (PCA) and factor analysis (FA) were applied to identify spurious correlations and the potential factors controlling the distribution patterns. The results demonstrate that: a) the raw data are biased, while the log-ratio data are unbiased and more reliable; b) the spatial distributions of elemental concentrations exhibit nonlinear complexity; and c) the elemental distribution in the study area is largely controlled by structural factors.

Keywords

nonlinear complexity / compositional data / fractal / multivariate statistical analysis / element distribution

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2025 Geological Society of China