Lattice model for approximate self-affine soil profiles. (English) Zbl 0978.86009
Summary: A modelling of the soil structure and surface roughness by means of the fractal growth concepts is presented. Two parameters are used to control the model: the fragmentation dimension, \(D_f\), and the maximum mass of the deposited aggregates, \(M_{\max}\). The fragmentation dimension is related to the particle size distribution through the relation \(N(r\geqslant R)\sim R^{D_f}\), where \(N(r\geqslant R)\) is the accumulative number of particles with radius greater than \(R\). The size of the deposited aggregate is chosen following the power law above, and the morphology of the aggregate is random selected using a bond percolation algorithm. The deposition rules are the same used in the model of solid-on-solid deposition with surface relaxation. A comparison of the model with real data shows that the Hurst exponent, \(H\), measured via semivariogram method and detrended fluctuation analysis, agrees in statistical sense with the simulated profiles.
MSC:
| 86A99 | Geophysics |
References:
| [1] | Dietler, G.; Zhang, Yi.-Ch., Physica A, 191, 213 (1992) |
| [2] | Matsushita, M.; Ouchi, Sh., Physica D, 38, 246 (1989) |
| [3] | Martin, M. A.; Taguas, F. J., Proc. R. Soc. London A, 454, 1457-1468 (1998) · Zbl 0916.28009 |
| [4] | Yordanov, O. I.; Guissard, A., Physica A, 238, 49-65 (1997) |
| [5] | Perfect, E.; Kay, B. D., Soil Till. Res., 36, 1-20 (1996) |
| [6] | Giménez, D.; Perfect, E.; Rawls, W. J.; Pachepsky, Ya., Eng. Geol., 48, 161-183 (1997) |
| [7] | J.G. Vivas Miranda, Analysis Fractal del Microrelieve del Suelo, Tesis de Doctorado, Univ. da Coruña, 2000.; J.G. Vivas Miranda, Analysis Fractal del Microrelieve del Suelo, Tesis de Doctorado, Univ. da Coruña, 2000. |
| [8] | Chadoeuf, J.; Goulard, M.; Garcia-Sanchez, L., Microsc. Microanal. Microstruct., 7, 557-563 (1996) |
| [9] | Perrier, E.; Bird, N.; Rieu, M., Geoderma, 88, 137-164 (1998) |
| [10] | Barabásie, A.-L.; Stanley, H. E., Fractal Concepts in Surface Growth (1995), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0838.58023 |
| [11] | Tyler, S. W.; Wheatcraft, S. W., Soil Sci. Soc. Am. J., 53, 362-369 (1992) |
| [12] | Giménez, D.; Allmaras, R. R.; Huggins, D. R.; Nater, E. A., Geoderma, 86, 261-278 (1998) |
| [13] | Nemes, A.; Wösten, J. H.M.; Lilly, A.; Oude Voshaar, J. H., Geoderma, 90, 187-202 (1999) |
| [14] | Moreira, J. G.; Kamphorst Leal da Silva, J.; Ollifson Kamphorst, S., J. Phys. A, 27, 8079 (1994) · Zbl 0835.28004 |
| [15] | Vivas Miranda, J. G.; Paz González, A., Cad. Lab. Xeol. de Laxe, 23, 121-136 (1998) |
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