A direct divider method for self-affine fractal profiles and surfaces

Abstract

Many profiles and surfaces of interest in geology and geophysics can be modelled by self-affine fractals. The divider method was the first method introduced in fractal analysis, is generally suitable for self-similar fractals, and has been adapted by Brown [1987] using a multi-step approach to estimate the fractal dimension of self-affine profiles. Here, we improve the method in order to be a 1-step technique, but showing also that it is in practice another form of the variance method. Then, we generalise the divider method to self-affine fractal surfaces. The method is tested with application to synthetic one- and two-dimensional functions of known fractal dimension.