Multifractality as a measure of spatial distribution of geochemical patterns

To quantify the spatial distribution of geochemical elements, the multifractality indices for Zn, Cu, Pt, Pd, Cr, Ni, Co, Pb, and As in lake-sediment samples in the Shining Tree area in the Abitibi area of Ontario are determined. The characterization of multifractal distribution patterns is based on the box-counting moment method and involves three functions: a mass exponent function tau(q); Coarse Holder Exponent alpha(q); and fractal dimension spectrum f (alpha(q)). Properties of these functions at different values of q, characterize the spatial distribution of the variable under study. It is shown that the degree of multifractality defined by tau"(1) can be used as a measure of irregularity of geochemical spatial dispersion patterns. The variations of Zn and Cu in the study area are characterized by relatively low degree of multifractality, whereas those for Pt, Pd, Cr, Ni, and Co; and particularly for As and Pb are characterized by higher multifractality indices. In the case of Zn and Cu, singularity spectra are close to a monofractal compared to the ones for As an Pb. The determination of multifractality indices allows us, in a quantitative way, to study the pattern of metal dispersions and link them to different physical processes, such as metal adsorption by organic material or glaciogenic processes.