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首页> 外文期刊>Applied Mathematical Modelling >Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements
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Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements

机译：比较MIE和FRAUNHOFER模型从激光衍射测量计算的土壤粒度分布的多分术特征

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摘要

Particle size distribution (PSD) is a basic soil property, closely related to main soil physical and chemical attributes. Soil PSD determined by laser diffraction (LD) may provide additional information to soil texture determined by traditional methods. In turn, LD may be implemented using either Mie or Fraunhofer calculation methods, based on different assumptions. The multifractal approach has been demonstrated to be useful for characterizing the inner structure of soil PSD. We analysed the PSDs of 18 soil horizons sampled on the most characteristic soil types from Argentina with a wide range of textural classes, from clayey to sandy, mainly developed over loess material. Our aims were to assess the multifractality between PSDs computed using either Mie scattering or Fraunhofer diffraction models, and to compare the scaling properties and multifractal behavior of PSDs from soils with contrasting textures. Fraunhofer model provided PSD curves, which were shifted toward coarser particles compared to those obtained with Mie model. Regardless calculation method, all the PSDs studied displayed a well-defined multifractal structure, as shown by singularity, f(α) versus α, and by Renyi spectra, D_qvs q. Moreover, all singularity spectra were strong asymmetric, right deviating curves, which is consistent with a greater heterogeneity of the low values of volume frequencies for all the PSDs analysed. Soil PSDs computed by Fraunhofer model showed higher asymmetry than those computed by Mie model for 16 out of 18 horizons studied; this suggests that scaling heterogeneity mainly depends on the support length, which is larger for the PSDs computed by Mie. In addition, other features of the PSDs stemming from soil processes such as weathering intensity of loess materials may also influence multifractality. Stronger correlations were found between multifractal parameters from PSDs calculated by the two models for the most positive q moments of singularity and Renyi spectra, i.e. α_(10), D_(10), than for those gathered from the central and negative q moments. The entropy dimension, D_1, significantly (P<0.05) increased with increasing clay content, in contrast to previous findings; this may be due either to differences in the inner structure of various PSD data sets compared, or to shortcomings of standard PSD measurement and calculation procedures.
机译：粒度分布（PSD）是一种基本土壤，与主要土壤物理和化学属性密切相关。通过激光衍射（LD）确定的土壤PSD可以向通过传统方法确定的土壤质地提供额外的信息。反过来，可以使用基于不同假设的MIE或FRAUNHOFER计算方法来实现LD。已经证明了多法分泌方法是用于表征土壤PSD的内部结构的用途。我们分析了来自阿根廷最具特色土壤类型的18种土壤视野的PSDS，来自克莱恩到桑迪的广泛的纹理课程，主要是在黄土材料上开发的。我们的目标是评估使用MIE散射或FRAUNHOFER衍射模型计算的PSD之间的多重性，并比较来自纹理纹理的土壤的PSD的缩放性质和多重术行为。 Fraunhofer模型提供了PSD曲线，与MIE模型获得的那些相比，PSD曲线向较粗糙的颗粒移位。无论计算方法如何，所研究的所有PSD都显示出明确定义的多重分术结构，如奇点，F（α）与α所示，并由renyi光谱，D_QVS Q.此外，所有奇点光谱都是强不对称的，右偏离曲线，其与分析所有PSD的体积频率低值的更大的异质性一致。由Fraunhofer模型计算的土壤PSD显示比Mie模型计算的更高的不对称，其中16个由18个地平线中学完成的。这表明缩放异质性主要取决于支持长度，这对于由MIE计算的PSD更大。另外，PSD的其他特征源于土壤过程，如黄土材料的耐候强度，也可能影响多重性。由两个模型计算的PSD的多法变性参数与奇异性Q矩和仁维光谱的最阳性Q矩数计算的PSD之间的相关性相比，即（10），D_（10），而不是从中央和负数Q时刻收集的PS。与以前的发现相比，熵尺寸D_1显着（p <0.05）随着粘土含量的增加而增加;这可能是由于各种PSD数据集的内部结构的差异，或者与标准PSD测量和计算过程的缺点。

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