Log selfsimilarity of continuous soil Particle-size distributions estimated using random multiplicative cascades
Log selfsimilarity of continuous soil Particle-size distributions estimated using random multiplicative cascades
复制标题
连续土壤的对数自相似性 使用随机乘法级联估计的粒度分布
DOI：
10.1346/ccmn.2008.0560308
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
C. García
中科院分区：
文献类型：
--
作者：
M. Martín;C. García
粒度分布（PSD）是土壤的基本性质，通常以离散的粘土、粉土和砂的百分比报告。使用另一个属性从这种糟糕的描述中有效地生成连续PSD的模型和方法对于预测和理解在自然界中普遍存在的碎片化分布将是非常有用的。土壤PSD的幂律意味着尺度不变性（或自相似性），这一特性已被证明在PSD描述中很有用。这项工作是基于两个新的想法在建模PSD：（1）PSD的自相似性的概念;（2）数学工具来计算分形分布的特定土壤PSD使用少量的实际纹理数据。基于这些想法，一个随机的，乘法级联模型的开发依赖于规模不变性的规律性称为“对数自相似性”。该模型允许从常见的纹理数据的中间粒度值的估计。使用等效输入，这种新的建模方法进行了检查，使用土壤数据和土壤PSD数据的自相似模型相比，提供了很大的改善结果。在92.94%的情况下，对数自相似模型的Kolmogorov-Smirnov D统计量小于自相似模型。平均误差是自相似模型的0.74倍。所提出的方法允许测量的异质性指数，H，定义使用Hölder指数，这有利于土壤质地类的定量表征。平均H值范围从粉砂质地的0.381到桑迪壤土质地的0.838，所有质地类别的方差<0.034。该索引还可以用于区分同一纹理类别内的纹理。这些结果表明，该模型及其参数可能是有用的估计其他土壤物理性质和开发新的土壤PSD土壤传递函数。这种建模方法，沿着其潜在的应用，可能会扩展到细粒矿物和材料的研究。
Particle-size distribution (PSD) is a fundamental soil property usually reported as discrete clay, silt, and sand percentages. Models and methods to effectively generate a continuous PSD from such poor descriptions using another property would be extremely useful to predict and understand in fragmented distributions, which are ubiquitous in nature. Power laws for soil PSDs imply scale invariance (or selfsimilarity), a property which has proven useful in PSD description. This work is based on two novel ideas in modeling PSDs: (1) the concept of selfsimilarity in PSDs; and (2) mathematical tools to calculate fractal distributions for specific soil PSDs using few actual texture data. Based on these ideas, a random, multiplicative cascade model was developed that relies on a regularity of scale invariance called ‘log-selfsimilarity.’ The model allows the estimation of intermediate particle size values from common texture data. Using equivalent inputs, this new modeling approach was checked using soil data and shown to provide greatly improved results in comparison to the selfsimilar model for soil PSD data. The Kolmogorov-Smirnov D-statistic for the log-selfsimilar model was smaller than the selfsimilar model in 92.94% of cases. The average error was 0.74 times that of the selfsimilar model. The proposed method allows measurement of a heterogeneity index, H, defined using Hölder exponents, which facilitates quantitative characterization of soil textural classes. The average H value ranged from 0.381 for silt texture to 0.838 for sandy loam texture, with a variance of <0.034 for all textural classes. The index can also be used to distinguish textures within the same textural class. These results strongly suggest that the model and its parameters might be useful in estimating other soil physical properties and in developing new soil PSD pedotransfer functions. This modeling approach, along with its potential applications, might be extended to fine-grained mineral and material studies.