ACCURACY OF THE SPECTRAL METHOD IN ESTIMATING FRACTAL SPECTRAL PARAMETERS FOR SELF-AFFINE ROUGHNESS PROFILES/

Accurate quantification of roughness is important in modeling strength , deformability and fluid flow behaviors of rock joints. Self-affine f ractals seem to have the potential to represent rock joint roughness p rofiles. Both stationary and non-stationary fractional Brownian profil es (self-affine profiles) with known values of fractal dimension, D, a nd input standard deviation, sigma, were generated at different genera tion levels. A few smoothing techniques were used with the spectral me thod to calculate D, and two other spectral parameters K-s (a proporti onality constant; see the text for the details) and CD (the cross-over dimension of the profile) for the fractional Brownian profiles. The e ffects of smoothing, generation level of the profile, seed value used in the generation, non-stationarity of the profile and sigma on the ac curacy of the calculated D were examined using the spectral method. Th e following conclusions were obtained: (a) To obtain accurate estimate s for D, K-s and CD, it seems necessary to have at least 10 data point s per unit length for a profile having a total length of 100 units (th is is equivalent to a generation level of 10). (b) For accurate estima tion of D, K-s and CD, the non-stationarity of profiles should be remo ved, if it exists. (c) The parameter combinations D and K-s (which has the potential to capture scale effects), and D and CD are recommended for quantification of stationary roughness; in addition, extra parame ters are required to quantify the non-stationarity. (d) Both the Parze n and Hanning smoothing techniques seem suitable to use with the spect ral technique to obtain accurate estimates for D, K-s and CD. (e) To o btain accurate estimates for D, K-s, and CD, it is necessary to we a s uitable bandwidth for the Parzen window and a suitable number of inter actions for the Hanning window; this paper provides guidelines to choo se these suitable values. (f) Seed value has negligible effect on the accuracy of estimated D, K-s and CD. (C) 1997 Elsevier Science Ltd.