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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 6
Nonlin. Processes Geophys., 15, 881–891, 2008
https://doi.org/10.5194/npg-15-881-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Nonlinear and Scaling Processes in Hydrology and Soil...

Nonlin. Processes Geophys., 15, 881–891, 2008
https://doi.org/10.5194/npg-15-881-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

  25 Nov 2008

25 Nov 2008

Influence of thresholding in mass and entropy dimension of 3-D soil images

A. M. Tarquis1,2, R. J. Heck3, J. B. Grau2, J. Fabregat2, M. E. Sanchez2, and J. M. Antón2 A. M. Tarquis et al.
  • 1C.E.I.G.R.A.M. E.T.S. Ing. Agrónomos (E.T.S.I.A.), Universidad Politécnica de Madrid (U.P.M.), Ciudad Universitaria, s.n. 28040 Madrid, Spain
  • 2Dpto. de Matemática Aplicada a la Ingeniería Agronómica. E.T.S. Ing. Agrónomos, U.P.M., Ciudad Universitaria, s.n. 28040 Madrid, Spain
  • 3Department of Land Resource Science. Ontario Agricultural College, University of Guelph. NIG 2WI, Canada

Abstract. With the advent of modern non-destructive tomography techniques, there have been many attempts to analyze 3-D pore space features mainly concentrating on soil structure. This analysis opens a challenging opportunity to develop techniques for quantifying and describe pore space properties, one of them being fractal analysis.

Undisturbed soil samples were collected from four horizons of Brazilian soil and 3-D images at 45 μm resolution. Four different threshold criteria were used to transform computed tomography (CT) grey-scale imagery into binary imagery (pore/solid) to estimate their mass fractal dimension (Dm) and entropy dimension (D1). Each threshold criteria had a direct influence on the porosity obtained, varying from 8 to 24% in one of the samples, and on the fractal dimensions. Linear scaling was observed over all the cube sizes, however depending on the range of cube sizes used in the analysis, Dm could vary from 3.00 to 2.20, realizing that the threshold influenced mainly the scaling in the smallest cubes (length of size from 1 to 16 voxels).

Dm and D1 showed a logarithmic relation with the apparent porosity in the image, however, the increase of both values respect to porosity defined a characteristic feature for each horizon that can be related to soil texture and depth.

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