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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 4
Nonlin. Processes Geophys., 14, 503–511, 2007
https://doi.org/10.5194/npg-14-503-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: New developments in scaling, scale and nonlinearity in the...

Nonlin. Processes Geophys., 14, 503–511, 2007
https://doi.org/10.5194/npg-14-503-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  14 Aug 2007

14 Aug 2007

Representative elementary area for multifractal analysis of soil porosity using entropy dimension

F. San José Martínez1, F. J. Caniego1, C. García-Gutiérrez1, and R. Espejo2 F. San José Martínez et al.
  • 1Dept. of Applied Mathematics to Agriculture Engineering, E.T.S.I Agrónomos, Technical University of Madrid (UPM), 28040 Madrid, Spain
  • 2Dept. of Pedology, E.T.S.I Agrónomos, Technical University of Madrid (UPM), 28040 Madrid, Spain

Abstract. The notion of representative elementary area (REA) developed to address heterogeneity and scale problems in quantitative soil pedology comes from the notion of representative elementary volume of fluid dynamics in porous media. The REA allows the identification of the minimum area of a soil block section that is required to represent the pedofeature of interest based on its distribution in soil space. In this paper eight samples were imaged with two different techniques: the confocal microscope and the conventional film camera. These techniques provided information about pore sizes between 3.62 μm and 161.98 μm, and between 39.72 μm and 1776.34 μm, respectively. Sixteen of the resulting digital images were then analyzed to investigate the representative elementary area of the multifractal patterns of the spatial distribution of voids related to the micro and macroporosity by means of the entropy dimension. Our results permit the location of the REA region over the domain of the microstructures rendered by the analysis of the microscope images. They also suggest that this region seemingly spans scales of the macrostructures as revealed by the analysis of the camera pictures.

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