中国辽宁典型风成黄土分维区间选取研究

Selecting Fragmentation Fractal Scaling Range for Typical Eolian Loess-paleosol in Liaoning, China

应用分形理论中的幂指函数关系法,选取粒径R区间为无标度区,使用线性回归(linear regression)和分段线性回归(piecewise linear regression)来确定辽宁典型风成黄土837个样品粒度分维的无标度区。统计分析结果表明:一元分维的粒度分维值介于1.446~2.027,决定系数均大于0.900,确定无标度区为0.1~54.4μm;二元分维得到节点平均值为7.64μm±1.21μm(CV=15.87%),决定系数在0.978~0.999之间变化,变异系数为0.438%,确定无标度区为0.1~7.64μm(F_2)和7.64~54.4μm(F_1),且分维值D_(F1)>D_(F2)。二元分维值与一元分维值差异较大,从另一个侧面表明即使是同一个研究对象,选取不同标度区范围,得到的分维值及其决定系数也不同,因此,使用分维模型前要注意无标度区的选取。分维值包含着土壤发生与沉积环境信息,深入解译分维值信息有助于理解黄土-古土壤的土壤发生过程。

Based on the theory of fragmentation fractal dimension, particle size data of 837 loess samples from LOP （the lower part of Chaoyang section） in Liaoning were analyzed using linear regression and piecewise linear regression to select appropriate scaling range for loess in this area. For the single fragmentation fractal dimension, values of fractal dimensions （DF） are between 1.446 and 2.027 with determination coefficient more than 0.900. The scaling range of 0.1-54.4μm was determined. While two scaling range of 0.1-7.64μm （F2） and 7.64-54.4 μm （F0 were obtained by a cutoff of 7.64 μm±1.21μm （CV=15.870%） using piecewise linear regression. The high coefficient of determination ranges from 0.978 to 0.999 with coefficient of variation for 0.438%. Furthermore, the DF1 is greater than DF2. The Dr values from piecewise fractal are different from the single fractal dimension. This suggests that DF values could be different due to different scaling range selected for specific loess. Therefore, appropriate scaling range should be selected first before using fractal models. Due to the possible relationship with loess pedogenesis and deposition environment, interpreting DF values is helpful for understanding loess pedogenesis and deposition environment.