Estimating the average concentration of minor and trace elements in surficial sediments using fractal methods

The methods chosen to calculate the average value of the concentration for any geochemical element should depend on the probability distribution of the element abundance data. In this study, a fractal-based method was introduced to estimate the mean concentrations of geochemical elements that follow fractal frequency distributions. The fractal-based method has been tested on two abundance datasets for Ag, As, Au, Cu, Pb, Zn, Ce, Cr, and U from 529 floodplain sediment samples in China and from 10,927 stream sediment samples in Zhejiang Province, China. We compared the fractal method with other methods, including the arithmetic averaging, geometric averaging, and median, and found that there exist large discrepancies among these averages. The results show that the average calculated using the fractal-based method is always smaller than the arithmetic average and also generally smaller than the geometric mean and the median. The discrepancies may be attributed to the fact that the datasets follow a fractal distribution rather than a normal or a lognormal distribution. This study indicates that calculated arithmetic mean, geometric mean, or median may overestimate the average concentrations for elements that follow a fractal distribution.