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Published online 1 January 2007
Published in Soil Sci Soc Am J 71:15-25 (2007)
DOI: 10.2136/sssaj2006.0132
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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A Multifractal Approach for Assessing the Structural State of Tilled Soils

Christian J. C. Roisin*

Walloon Agricultural Research Centre, Dep. of Crop Production, 4, rue du Bordia, B-5030 Gembloux, Belgium


Figure 1
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  		Fig. 1. View of the apparatus used for the soil strength measurements.

 

Figure 2
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  		Fig. 2. Cropping profiles of the two selected plots and the origin of the five datasets used during the first stage of the study.

 

Figure 3
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  		Fig. 3. Contour maps of the five datasets used during the first stage of the study.

 

Figure 4
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  		Fig. 4. Examples of graphs expressing loge Mq({delta}) versus loge ({delta}): graphs relating to the original datasets supplying the worst and the best coefficient of variation when the moment order |q| = qmax = 10.

 

Figure 5
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  		Fig. 5. Coefficients of correlation associated with the graphs of loge Mq({delta}) versus loge {delta}) for the five datasets used during the first stage of the study and relating to: (a) the original datasets, (b) the wraparound-generated variants supplying {Omega} max, (c) the wraparound-generated variants supplying {Omega} min.

 

Figure 6
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  		Fig. 6. Spectra of fractal dimensions [D(q) curves] for the five datasets used during the first stage of the study and relating to: (a) the original datasets, (b) the wraparound-generated variants supplying {Omega} max, (c) the wraparound-generated variants supplying {Omega} min.

 

Figure 7
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  		Fig. 7. Soil profile in Plot 8 illustrating the undulating bottom of the tilled stratum in a tine-cultivated plot.

 

Figure 8
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  		Fig. 8. Soil profile in Plot 5 showing the two different ploughing depths.

 

Figure 9
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  		Fig. 9. Detail of the structure for depths between 15 and 35 cm in: (a) Plot 5 and (b) Plot 6

 




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Copyright © 2007 by the Soil Science Society of America.