Multifractal characterization of soil pore systems

Soil Science Society of America Journal

Volumn 67, Issue 5, 2003, Pages 1361-1369

  Posadas, Adolfo N D ^a,b   Giménez, Daniel ^c   Quiroz, Roberto ^a   Protz, Richard ^d  

^a INTERNATIONAL POTATO CENTER   (Peru)

^b UNIVERSIDAD NACIONAL MAYOR DE SAN MARCOS   (Peru)

^c RUTGERS UNIVERSITY   (United States)

^d UNIVERSITY OF GUELPH   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; FRACTALS; PORE SIZE; POROSITY;

SOIL STRUCTURE;

SOIL MECHANICS;

FRACTAL ANALYSIS; IMAGE ANALYSIS; PORE SPACE; SOIL STRUCTURE; SPATIAL DISTRIBUTION;

EID: 0141792094     PISSN: 03615995     EISSN: None     Source Type: Journal    
DOI: 10.2136/sssaj2003.1361     Document Type: Article

References (50)

1. Anderson, A.N., A.B. McBratney, and E.A. FitzPatrick. 1996. Soil mass, surface, and spectral fractal dimensions estimated from thin section photographs. Soil. Sci. Soc. Am. J. 60:962-969.
2. Bouma, J., A. Jongerius, O. Boersma, A. Jager, and D. Schoonderbeek. 1977. The function of different types of macropores during saturated flow through four swelling soil horizons. Soil Sci. Soc. Am. J. 41:945-950.
3. Brewer, R. 1979. Relationships between particle size, fabric and other factors in some Australian soils. Aust. J. Soil Res. 17:29-41.
4. Callen, H.B. 1985. Thermodynamics and an introduction to thermostatistics. 2nd ed. John Wiley & Sons, New York.
5. Caniego, F.J., M.A. Martín, and F. San José. 2001. Singularity features of pore-size soil distribution: Singularity strength analysis and entropy spectrum. Fractals 9:305-316.
6. Cheng, Q., and F.P. Agterberg. 1996. Multifractal modeling and spatial statistics. Math. Geol. 28:1-16.
7. Cheng, Q. 1999. Multifractality and spatial statistics, Comput. Geosci. 25:949-961.
8. Chhabra, A.B., C. Meneveu, R.V. Jensen, and K.R. Sreenivasan. 1989. Direct determination of the f (α) singularity spectrum and its application to fully developed turbulence. Phys. Rev. A 40:5284-5294.
9. Chhabra, A.B., and R.V. Jensen. 1989. Direct determination of the f(α) singularity spectrum. Phys. Rev. Lett. 62:1327-1330.
10. Dexter, A.R. 1976. Internal structure of tilled soil. J. Soil Sci. 27:267-278.
11. Dexter, A.R. 1977. A statistical measure of the structure of tilled soil. J. Agric. Eng. Res. 22:101-104.
12. Droogers, P., A. Stein, J. Bouma, and G. de Boer. 1998. Parameters for describing soil macroporosity derived from staining patterns. Geoderma 83:293-308.
13. Eswaran, H., and C. Banos. 1976. Related distribution patterns in soils and their significance. An. Edaf. Agriobiol. 35:33-45.
14. Evertsz, C.J.G., and B.B. Mandelbrot. 1992. Multifractal measures. p. 921-953. In H.-O. Peitgen et al. (ed.). Chaos and Fractals. New Frontiers of Science. Springer-Verlag, New York.
15. Feder, J. 1988. Fractals. Plenum Press, New York.
16. Folorunso, O.A., C.E. Puente, D.E. Rolston, and J.E. Pinzon. 1994. Statistical and fractal evaluation of the spatial characteristics of soil surface strength. Soil Sci. Soc. Am. J. 58:284-294.
17. Frisch, U., and G. Parisi. 1985. Fully developed turbulence and intermittency. p. 84. In M. Ghil et al. (ed.). Turbulence and preditability in geophysical flows and climate dynamics. North-Holland, NY.
18. Garboczi, E.J., D.P. Bentz, and N.S. Martys. 1999. Digital images and computer modelling. p. 1-41. In P-Z Wong (ed.). Experimental methods for porous media. Academic Press, San Diego, CA.
19. Giménez, D., R.R. Allmaras, E.A. Nater, and D.R. Huggins. 1997. Fractal dimensions for volume and surface of interaggregate pores - Scale effects. Geoderma 77:19-38.
20. Goenadi, D.H., and K.H. Tan. 1989. Relationship of soil fabric and particle-size distribution in a Davison soil. Soil Sci. 147:264-269.
21. Grout, H., A.M. Tarquis, and M.R. Wiesner. 1998. Multifractal analysis of particle size distributions in soil. Environ. Sci. Technol. 32:1176-1182.
22. Halsey, T.C., M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman. 1986. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A 33:1141-1151.
23. Hentschel, H.G.E., and I. Procaccia. 1983. The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8:435-444.
24. Holden, N.M. 2001. Description and classification of soil structure using distance transform data. Eur. J. Soil Sci. 52:529-545.
25. Horgan, G.W. 1998. Mathematical morphology for analysing soil structure from images. Eur. J. Soil Sci. 49:161-173.
26. Horgan, G.W. 1999. An investigation on the geometric influences on pore space diffusion. Geoderma 88:55-71.
27. Jim, C.Y. 1988. A classification of soil microfabrics. Geoderma 41:315-325.
28. Korvin, G. 1992. Fractal methods in the earth science. Elsevier, Amsterdam.
29. Kravchenko, A., C.W. Boast, and D.G. Bullock. 1999. Multifractal analysis of soil spatial variability. Agron. J. 91:1033-1041.
30. Lipiec, J., R. Hatano, and A. Słowińska-Jurkiewicz. 1998. The fractal dimension of pore distribution patterns in variously-compacted soils. Soil Tillage Res. 47:61-66.
31. Loehle, C., and B.-L. Li. 1996. Statistical properties of ecological and geological fractals. Ecol. Modell. 85:271-284.
32. Mandelbrot, B.B. 1982. The fractal geometry of nature. 2nd ed. W.H. Freeman and Co., New York.
33. Martín, M.A., and E. Montero. 2002. Laser diffraction and multifractal analysis for the characterization of dry soil volume-size distribution. Soil Tillage Res. 64:113-123.
34. Meakin, P. 1991. Fractal aggregates in geophysics. Rev. Geophys. 29:317-354.
35. Meneveau, C., and K.R. Sreenivasan. 1991. The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224:429-484.
36. Moran, C.J., and A.B. McBratney. 1997. A two-dimensional fuzzy random model of soil pore structure. Math. Geol. 29:755-777.
37. Muller, J., and J.L. McCauley. 1992. Implication of fractal geometry for fluid flow properties of sedimentary rocks. Transp. Porous Media 8:133-147.
38. Pachepsky, Ya., V. Yakovchenko, M.C. Rabenhorst, C. Pooley, and L.J. Sikora. 1996. Fractal parameters of pore surfaces as derived from micromorphological data: Effect of long term management practices. Geoderma 74:305-319.
39. Pagliai, M., and M. De Nobili. 1993. Relationships between soil porosity, root development and soil enzyme activity in cultivated soils. Geoderma 56:243-256.
40. Posadas, A., D. Giménez, M. Bittelli, C.M.P. Vaz, and M. Flury. 2001. Multifractal characterization of soil particle-size distributions. Soil Sci. Soc. Am. J. 65:1361-1367.
41. Rasband, W. 1993. NIH-Image v. 1.52. An image processing system for the Macintosh. U.S. National Institute of Health, NTIS, Springfield, VA.
42. Ringrose-Voase, A.J. 1987. A scheme for the quantitative description of soil macrostructure by image analysis. J. Soil Sci. 38:343-356.
43. Ringrose-Voase, A.J., and P. Bullock. 1984. The automatic recognition and measurement of soil pore types by image analysis and computer programs. J. Soil Sci. 35:673-684.
44. Saucier, A., and J. Muller. 1999. Textural analysis of disordered materials with multifractals. Physica A 267:221-238.
45. Shannon, C.E., and W. Weaver. 1949. The Mathematical Theory of Communication. University of Illinois Press. Urbana, IL.
46. Stanley, H.E., and P. Meakin. 1988. Multifractal phenomena in physics and chemistry. Nature 335:405-409.
47. VandenBygaart, A.J., and R. Protz. 1999. The representative elementary area (REA) in studies of quantitative soil micromorphology. Geoderma 89:333-346.
48. Vicsek, T. 1992. Fractal growth phenomena. 2nd ed. Word Scientific Publishing Co., Singapore.
49. Vogel, H.-J., and K. Roth. 2001. Quantitative morphology and network representation of soil pore structure. Adv. Water Resour. 24:233-242.
50. Voss, R.F. 1988. Fractals in nature: From characterization to simulation. p. 21-69. In H.-O. Peitgen and D. Saupe (ed.). The Science of Fractal Images. Springer-Verlag, New York.