Multidimensional Self-Affine Distribution With Application in Geochemistry

摘要

In this paper, we present the conception of the multidimensional self-affine distribution and show that the multidimensional self-affine distribution possesses the fractal property of scale-invariance under truncation, which means that theoretical study of fractals has expanded from univariate cases to multivariate cases. Application of the multidimensional self-affine distribution is illustrated by means of geochemical Au and Ag elements data sets. The fractal dimension is a parameter which can quantitatively explain the variation of geochemical elements data on some orientation. This method is applied to Au data and Ag data, but also suited for other geochemical elements data or geological data. Theory of multivariate fractal can be applied for the study of change courses of fractal system, that is, fractal dynamics.