Accuracy of the spectral method in estimating fractal/spectral parameters for self-affine roughness profiles

Self-affine fractals seem to have the potential to represent rock joint roughness profiles. Both stationary and non-stationary fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, and input standard deviation, σ, were generated at different generation levels. A few smoothing techiques were used. The following conclusions were obtained: (a) To obtain accurate estimates for D, K_s (spectral parameters) and CD (cross-over profile dimension), it seems necessary to have at least 10 data points per unit length for a profile having a total length of 100 units. (b) For accurate estimation of D, K_s and CD, the non-stationarity of profiles should be removed, if it exists. (c) The parameter combinations D and K_s, and D and CD are recommended for quantification of stationary roughness; in addition, extra parameters are required to quantify the non-stationarity. (d) Both the Parzen and Hanning smoothing techniques seem suitable to use with the spectral technique to obtain accurate estimates for D, K_s and CD. (e) To obtain accurate estimates for D, K_s, and CD, it is necessary to use a suitable bandwidth for the Parzen window and a suitable number of iterations for the Hanning window; this paper provides guidelines to choose these suitable values. (f) Seed value has negligible effect on the accuracy of estimated D, K_s and CD.