TY - JOUR
T1 - Accuracy of the spectral method in estimating fractal/spectral parameters for self-affine roughness profiles
AU - Shirono, T.
AU - Kulatilake, P. H.S.W.
N1 - Funding Information:
Acknowledgements-This research was funded by the U.S. National Science Foundation, Grant Number CMS-9522798. Useful comments provided by an anonymous reviewer are greatly appreciated.
PY - 1997/7
Y1 - 1997/7
N2 - 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, Ks (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, Ks and CD, the non-stationarity of profiles should be removed, if it exists. (c) The parameter combinations D and Ks, 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, Ks and CD. (e) To obtain accurate estimates for D, Ks, 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, Ks and CD.
AB - 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, Ks (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, Ks and CD, the non-stationarity of profiles should be removed, if it exists. (c) The parameter combinations D and Ks, 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, Ks and CD. (e) To obtain accurate estimates for D, Ks, 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, Ks and CD.
UR - https://www.scopus.com/pages/publications/0031187959
UR - https://www.scopus.com/inward/citedby.url?scp=0031187959&partnerID=8YFLogxK
U2 - 10.1016/S0148-9062(96)00068-X
DO - 10.1016/S0148-9062(96)00068-X
M3 - Article
AN - SCOPUS:0031187959
SN - 0148-9062
VL - 34
SP - 789
EP - 804
JO - International journal of rock mechanics and mining sciences & geomechanics abstracts
JF - International journal of rock mechanics and mining sciences & geomechanics abstracts
IS - 5
ER -