A note on the description of surface roughness using fractal dimension

Self‐affine fractals are useful models of the surfaces of rock fractures. The scaling properties of these surfaces are described by two parameters, the fractal dimension and the crossover length. Two methods for estimating the fractal dimension of a profile of a rough surface are compared, the divider method and the spectral method. It is shown that the two methods yield the same results, if the horizontal resolution at which the profile is measured is smaller than the crossover length. However, for resolutions greater than the crossover length, the divider method always gives a fractal dimension close to 1. To guide future work, the crossover length is estimated for typical joint surfaces and for the San Andreas fault. Additionally, a simple method is proposed to obtain the correct fractal dimension without prior knowledge of the crossover length.