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Requirements for accurate quantification of self-affine roughness using the variogram method

机译：使用变异函数法精确量化自仿射粗糙度的要求

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Both stationary and non-stationary fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, input standard deviation, sigma, and data density, d, were generated. For different values of the input parameter of the variogram method (lag distance, h), D and another associated fractal parameter ii, were calculated for the aforementioned profiles. It was found that sigma has no effect on calculated D. The estimated ii, was found to increase with D, sigma and d according to the equation K-v = 2.0 x 10(-5) d(0.35)sigma(0.95)D(14.5). The parameter K-v seems to have potential to capture the scale effect of roughness profiles. Suitable ranges for h were estimated to obtain computed D within +/- 10% of the D used for the generation and also to satisfy a power functional relation between the variogram and ii. Results indicated the importance of removal of nonstationarity of profiles to obtain accurate estimates for the fractal parameters. It was found that at least two parameters are required to quantify stationary roughness; the parameters D and K-v are suggested for use with the variogram method. In addition, one or more parameters should be used to quantify the non-stationary part of roughness, if it exists; at the basic level, the mean inclination/declination angle of the surface in the direction considered can be used to represent the non-stationarity. A new concept of feature size range of a roughness profile is introduced in this paper. The feature size range depends on d, D and sigma. The suitable h range to use with the variogram method to produce accurate fractal parameter values for a roughness profile was found to depend on both d and D. It is shown that the feature size range of a roughness profile plays an important role in obtaining accurate roughness parameter values with both the divider and the variogram methods. The minimum suitable h was found to increase with decreasing d and increasing D. Procedures are given in this paper to estimate a suitable h range for a given natural rock joint profile to use with the variogram method to estimate D and K-v accurately for the profile. (C) 1998 Elsevier Science Ltd. All rights reserved. [References: 28]
机译：生成具有已知分形维数D，输入标准偏差sigma和数据密度d的固定和非固定分数布朗轮廓（自仿射轮廓）。对于变异函数法的输入参数的不同值（滞后距离，h），对于上述轮廓计算了D和另一个相关的分形参数ii。发现sigma对计算的D没有影响。根据方程Kv = 2.0 x 10（-5）d（0.35）sigma（0.95）D（14.5），估计的ii随着D，sigma和d的增加而增加。 ）。参数K-v似乎具有捕获粗糙度轮廓的比例效应的潜力。估计h的合适范围以获得计算的D，该D在用于生成的D的+/- 10％内，并且还满足变异函数和ii之间的幂函数关系。结果表明，去除轮廓的非平稳性对于获得分形参数的准确估计非常重要。已经发现至少需要两个参数来量化固定粗糙度。建议将参数D和K-v与变异函数法一起使用。另外，应使用一个或多个参数来量化粗糙度的非平稳部分（如果存在）;在基本水平上，表面在所考虑方向上的平均倾斜/倾斜角可用于表示非平稳性。本文介绍了粗糙度轮廓特征尺寸范围的新概念。特征尺寸范围取决于d，D和sigma。发现使用变异函数法为粗糙度轮廓生成准确的分形参数值的合适h范围取决于d和D。这表明，粗糙度轮廓的特征尺寸范围在获得准确粗糙度中起着重要作用。除法和变异函数方法的参数值。发现最小合适的h随着d的减小和D的增大而增加。本文给出了程序来估计给定天然岩石节理剖面的合适h范围，并与变异函数法一起使用，以准确估计该剖面的D和K-v。 （C）1998 Elsevier ScienceLtd。保留所有权利。 [参考：28]

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