An investigation into the application of fractals for rock roughness estimation

Profiles of naturally fractured surfaces of three sedimentary rock samples were plotted from the measured data using a mechanical profilometer. Fractal dimension of these profiles were computed and statistical F-test indicates that fractal dimension (FD) values can be used as a parameter for distinguishing the rock types. The comparison between FD values and a commonly used profile-roughness parameter called the Mayer's $Z_2$ parameter shows the superiority of the FD values as roughness estimator. Two-dimensional fractal roughness parameters of the same naturally fractured rock surfaces were also studied from their scanning electron microscopic (SEM) images at various magnification levels. The most suitable level of magnification of the SEM images for the study of the 2-D fractal roughness parameter was identified. The values of 2-D fractal roughness parameter for three different rocks were also compared using different methods of fractal dimensioning.