The spatial distributions of mineralisation

Abstract

The concept of fractal spatial distributions of mineralisation has been widely proposed since Mandelbrot (1965) who emphasised the stable Pareto-Lévy distribution as the relevant distribution. The concept of a fractal is used as a basis for estimating endowment and for erecting exploration models based on self-organised criticality. This paper explores the proposition that the growth kinetics for a mineralising system are reflected in the probability distributions that describe the spatial patterns of mineralisation. We revisit the data sets and ask the question: What are the best fit probability distributions for the spatial distribution of mineralisation? The answer is: members of the Extreme Value Distribution family (Gumbel-, Fréchet- and Weibull-distributions) and not the Pareto distribution. Thus, the spatial distribution of mineralisation is not a fractal although the tails of the distributions can be or resemble power-laws. The standard box counting procedure for a spatial point distribution establishes a nearest neighbour distribution and hence, by definition, the resulting distribution is Weibull and not Pareto. The mass distributions are Fréchet and not Pareto. The extreme end members are Gumbel. We discuss the implications of these distributions for models that generate mineralisation sites within a system and for the underlying thermodynamics.