Spatial Variation of Fractal Parameters and Its Geological Implications

Sung, Quo-Cheng; Chen, Y. C.; Chao, P. C.

doi:10.3319/tao.1998.9.4.655(t)

Cited by 19 publications

(26 citation statements)

References 13 publications

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“…The accuracy of the digital elevation model could also be an influential factor in scale-dependent variation and directional bias of fractal dimension. Nevertheless, the angled variograms are picking up detail that is not visible in a contour plot and might extract the anisotropy of the terrain feature that reflects the regional structures of valleys and ridges (Klinkenberg and Goodchild, 1992;Sung et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

“…Cheng et al (1999a,b) divide the study area of the entire Taiwan Island into different sizes of units and find a good estimation of the fractal dimension with a unit size as small as 1280 Â 1280 m 2 (32 rows by 32 columns). In an empirical approach, Sung et al (1998) suggested 30 by 30 be the smallest data matrix from which one can obtain about 80% accuracy in estimating the surface fractal dimension. Referring to the conventional DEMs of Taiwan, the smallest spatial unit is therefore about 1.2 by 1.2 km for estimating the fractal parameters of the landscape surface.…”

Section: Introductionmentioning

confidence: 99%

“…However, it follows that a failure to accept the possibility of multifractal behavior is almost certain to result in an incomplete understanding of the real nature of the surface. Another problem with limited sizes is that surface anisotropy might be induced by taking limited data for estimating the D of a profile in certain directions (Sung et al, 1998). The accuracy of the digital elevation model could also be an influential factor in scale-dependent variation and directional bias of fractal dimension.…”

Section: Introductionmentioning

confidence: 99%

“…Cheng et al (1999b) find that the self-similar dimensions of different geographic regions of Taiwan Island are close to 2.0 in the plains, 2.25 -2.5 in the Foothills, and 2.75 in the Central Mountain Range. However, a different approach was taken by applying the variogram method for estimating the self-affine dimensions from the same DEM of Taiwan Island (Sung and Tsaan, 1992;Sung et al, 1998). Sung et al (1998) find that the coastal plains is characterized by a high fractal dimension (2.5 -2.8) and a low c, while terrain on the sedimentary rocks in the imbricate fold-and-thrust belt are characterized by a low fractal dimension (2.2 -2.4) and a high c. It implies that elevations in the coastal plains vary more frequently in the short range than in the long range and vice versa in the mountain range.…”

Section: Introductionmentioning

confidence: 99%

“…However, a different approach was taken by applying the variogram method for estimating the self-affine dimensions from the same DEM of Taiwan Island (Sung and Tsaan, 1992;Sung et al, 1998). Sung et al (1998) find that the coastal plains is characterized by a high fractal dimension (2.5 -2.8) and a low c, while terrain on the sedimentary rocks in the imbricate fold-and-thrust belt are characterized by a low fractal dimension (2.2 -2.4) and a high c. It implies that elevations in the coastal plains vary more frequently in the short range than in the long range and vice versa in the mountain range. They also demonstrate that the fractal characteristics of topographic surfaces in different tectonic provinces of this young orogenic mountain belt are distinct and directionally biased with respect to the direction of plate convergence (Sung and Tsaan, 1992;Sung et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

Sung

Chen

2004

Geomorphology

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

Sung

Chen

2004

Geomorphology

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The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

Liucci

Melelli

2017

Earth Surf Processes Landf

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Landscape topography widely exhibits fractal structure. Because of the complexity of relief geometry this structure is not homogeneous in space, and the study of its spatial characteristics represents a powerful method for investigating the interrelationships between landforms and underlying processes. We explore these interrelationships using the digital elevation model (DEM) of an area located in central Italy, where landscape topography is strongly linked to its geological evolution, being characterized by alternating intermountain basins and mountain ranges trending NW–SE. A modified version of the method based on the standard deviation of relief elevations is used to evaluate the fractal parameters of relief after tiling the DEM in spatial units characterized by homogeneous fractal geometry, and statistical methods in conjunction with spatial analysis techniques are applied to the resulting terrain datasets. Both the lowest and (to a lesser extent) the highest values of fractal dimension are found to follow the ridge‐and‐valley trend. Low fractal dimension is observed in the mountain ranges characterized by massive strata of limestone, and along the fault scarps defining the contact between the intermountain basins and the surrounding slopes, where sediment deposition prevails. High fractal dimension is observed in regions characterized by highly erodible terrigenous lithology, and in areas where tectonic activity favors erosional processes mainly by rivers. The analysis of the (fractal) power law parameters also suggests that each major lithological complex has its own characteristic fractal signature. These results provide new insights into the link between the fractal properties of topography and the tectonic, lithological, and geomorphological features of the area, and show that the analysis approach proposed is useful to depict key aspects about the geomorphological and geological setting of an area, using only a DEM. Copyright © 2017 John Wiley & Sons, Ltd.

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Description of soil micro‐topography and fractional wetted area under runoff using fractal dimensions

García‐Serrana

Gulliver

Nieber

2018

Earth Surf Processes Landf

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Understanding the connections between the micro‐topography of a surface and the patterns of shallow overland flow is important to the study of runoff and infiltration processes. In slopes with micro‐topographic features parallel to the flow, water tends to concentrate in channels and only a fraction of the slope contributes to the overland flow. This study aimed to formulate the relevance of the fractal approach for understanding the relation of surface roughness to overland flow patterns. Laboratory experiments of simulated runoff over a bare soil slope were used to test the efficacy of two fractal parameters (fractal dimension [FD] and vertical intercept [VIC] from the Fourier power spectrum method) to describe how main surface micro‐topographic features can influence runoff, infiltration and erosion processes. The fractal parameters behaved differently for the distinctive initial surface treatments (smooth, three rills, and five rills). The anisotropy of the surface was evident based on the change of the fractal parameters with direction. The rose plots of the fractal parameters provided important information about the magnitude of the concentrated flow erosion of a surface and its main direction; in the direction perpendicular to the rills, the FD values were lower and the VIC greater. The minimum FD decreased and the maximum VIC increased with runoff time. A linear relationship between the infiltration depth and the percentage of wetted area was observed. Furthermore, a relationship between the fraction of wetted area and the fractal parameters has been developed, indicating that vertical variations (VIC) in roughness had more impact on fraction of wetted area than horizontal variations (FD) of the surface. Finally, a decrease in the minimum FD and an increase in the maximum VIC were related to greater scour volumes. The scour volume of an initially smooth surface seems to be well‐represented by a power relationship with the maximum VIC. By defining indicators of rill erosion and associating them with flow patterns through these fractal parameters, a better description of shallow overland flow can be achieved. © 2018 John Wiley & Sons, Ltd.

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Spatial Variation of Fractal Parameters and Its Geological Implications

Cited by 19 publications

References 13 publications

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

Description of soil micro‐topography and fractional wetted area under runoff using fractal dimensions

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