New Applications of the Model of de Wijs in Regional Geochemistry - Agterberg, Frits (Mathematical geology, 2007)
This paper is concerned with the lognormal, and its logbinomial approximation, in connection with a three-parameter version of the model of de Wijs. The three parameters are: overall average element concentration value (ξ), dispersion index (d), and apparent number of subdivisions of the environment (N). Multifractal theory produces new methods for estimating the parameters of this model. In practical applications, the frequency distribution of element concentration values for small rock samples is related to self-similar spatial variability patterns of the element in large regions or segments of the Earth's crust. The approach is illustrated by application to spatial variability of gold and arsenic in glacial till samples from southern Saskatchewan. It is shown that for these two elements the model of de Wijs is satisfied on a regional scale but degree of dispersion decreases rapidly toward the local, sample-size scale. Thus the apparent number of subdivisions (N) is considerably less than would be expected if degree of dispersion were to extend from regional to local scale. A random-cut variant of the model of de Wijs produces an empirical frequency distribution of relative element concentration values that can be related to random dispersion index