A Novel Multifractal Method for Geochemical Element Distribution Analysis

Abstract

Accurately analysis of the multifractal characteristics of geochemical element distribution is crucial for identifying geochemical anomalies and meaningful element associations. However, the most commonly used multifractal method, i.e., the method of moments, may generate different multifractal spectra for a single element distribution due to variations in the range of moment orders. This is because multifractals and their control mechanisms are not well defined. Fractal topography provides a basis for defining multifractals and clarifies the physical meaning of the singularity index. Therefore, a multifractal analysis method based on fractal topography is proposed to generate a unified multifractal spectrum and give new insight into the singularity analysis of element distribution. The similarities and distinctions between the two methods were evaluated using the de Wijs model. The distributions of two multifractal spectra are shown to be fundamentally consistent. The novel method, nevertheless, utilizes fewer statistics and presents a simplified criterion for element enrichment or depletion. To demonstrate its application, Cu geochemical distribution in the Zhongdian area, China, was used as a case study. Based on the comparison results of the two approaches, the proposed novel approach proves beneficial for accurately characterizing the heterogeneity of geochemical element distribution while maintaining a consistent range of the singularity index. The singularity index distribution map at a fine scale provides a comprehensively detailed zonation of geochemical anomalies and, at different scales, it can effectively reveal and interpret the variation of element distribution.