陕北黄土丘陵沟壑区土壤粒径分布分形特征

Fractal Characteristics of Soil Particle Size Distributions in Gully-Hilly Regions of the Loess Plateau,North of Shaanxi,China

将激光衍射技术和分形分析结合,多重分形分析应用多重分形参数Rényi维数谱,研究土壤粒径分布(PSD)分形特征。结果表明:土壤PSD分形维数D在2.28～2.47之间,D与土壤黏粒含量线性相关。计算黏粒、粉粒和砂粒分形维数D黏粒、D粉粒和D砂粒,三者之间存在D黏粒<D粉粒<D砂粒的关系,分别用D黏粒、D粉粒和D砂粒计算分裂概率,发现小团粒具有较小的分裂概率。因此,分裂概率具有尺度依赖性,并随着土壤粒径的减小而降低。多重分形分析表明,由PSD获取的Rényi维数谱为反S型递减函数,与理论的多重分形Rényi维数谱相似,说明土壤PSD具有多重分形特征。

Fractal analysis and laser diffractometry were combined to characterize the fractal of soil particle size distribution （PSD） through Renyi dimension spectra in the multifrectal system. The results indicated that the monofractal dimension of soil PSD in various land-uses ranged from 2.28 to 2.47 and had a significant linear regression with the content of soil clay. Dclay, Dsilt and Dsand were calculated and they were in an order of Dclay〈 Dsilt 〈 Dsand. Probability of fragmentation were calculated using Dclay, Dsilt and Dsand, and smaller particles always had a lower probability of fragmentation with respect to larger particles. Therefore, it appears clearly that the probability of fragmentation is scale dependent and it decreases with the decrease of particle sizes. Multifractal analyses showed Rdnyi dimensions spectra generated by PSDs were similar to those obtained for theoretical multifractal properties and PSDs had multifractal properties.