Fractal and Multifractal Properties of Geochemical Fields

Abstract

A fractal model, introduced by De Wijs to study the distribution, redistribution, or enrichment/depletion of element concentrations in a region, has become widely accepted. This paper uses it to simulate various geochemical fields for element concentration values. The frequency distribution and spatial pattern of the simulated values or “concentrations” are analyzed by the method of moments and the concentration–area (C–A) model. The spatial pattern of the original De Wijs model is shown to be intrinsically characterized by ∩-shaped and symmetrical multifractal spectrum curves, whose center and width change systematically with the enrichment factors set in the simulation. The corresponding frequency distribution pattern on the log–log plot of frequency versus concentrations is called simple continuous multifractal (SCM) by the authors. In other experiments, when a De Wijs model is locally superimposed by another De Wijs model of different enrichment factors, the symmetry of the multifractal spectrum graph is broken and a different pattern of frequency distribution is found. It is referred to as highly accumulated continuous multifractals (HACM). Concentrations of 12 elements in 1448 rock samples from Shaoguan district, North Guangdong Province, South China, and 12 oil/gas indexes in surface soils from Sangtamu region, Tarim Basin, Northwest China, have been applied. The real geochemical fields, both metallic and oil/gas, are found to be remarkably compatible to those simulated patterns of De Wijs models with backgrounds of various enrichment and different degrees of superimposition, indicating that the frequency and spatial distribution patterns revealed by the authors are most possibly universal features of geochemical fields. It is particularly interesting to note that the major geochemical indicators of oil/gas geochemical fields are closer to the results of De Wijs models with a small enrichment factor, either with or without local superimposition, whereas those of the metallic geochemical field correspond more closely to De Wijs models with a background field of larger enrichment factors. The results obtained herein potentially have important implications in mineral and oil/gas resource assessment.