Application of fractal and multifractal analysis on Blue Nile drainage patterns in the morphostructural analysis of the Ethiopian highlands, Ethiopia

Abstract

Fractal geometry methods provide a quantitative description of complex landscape networks, such as drainage patterns. This article focuses on the determination of the fractal dimension ( F D) and Renyi multifractal spectrum ( F Dα) of drainage patterns of the Blue Nile Basin in the Ethiopian Highlands. The Ethiopian Highlands are one of the most tectonically influenced areas in the world. The spatial distribution of drainage patterns reflects a decreasing influence of tectonics with increasing distance from the Main Ethiopian Rift (MER) to the center of the Ethiopian Highlands. The novelty of the paper is given by the calculation of F D and F Dα of drainage patterns as a part of morphostructural analysis. We analyzed how the values of F D and F Dα in each of 145 local drainage patterns changed depending on the changes of tectonic influences on landscape formation. Our methodologies provided a way of distinguishing the morphologies of tectonic and non-tectonic drainage patterns using the fractal/multifractal technique. The results of the study show that old dendritic drainage patterns located in the western part with low tectonic activity and an absence of faults had the lowest F D and F Dαvalues. The opening up of the MER and the neotectonic uplift of the Ethiopian Highlands accelerated the development of drainage patterns by activating river erosion and river piracy. Dendritic drainage patterns of the volcanic platforms have changed to young deep cut trellis patterns, and their F D and F Dα values are increased. Accelerating Quaternary uplift created the recent high landscape in the eastern part of the Blue Nile Basin, where the tectonic activities correspond to the MER. This young Quaternary landscape is characterized by prevailing deep and narrow valleys, and the presence of morphodynamic phenomena (erosion, landslides, earthquakes), where the trellis drainage patterns have the highest F D and F Dα.values.

Structural Characteristics of Endorheic Rivers in the Tarim Basin

“…As is illustrated in Figure 8, significant differences in R B , F D , and D D between the two basins are observed, which further confirm the vulnerability of endorheic rivers characterized with less branching, imperfect developed, and sparser network structures. It should be noted that the multifractal spectra, composed with a sequence of generalized F D with different scaling exponents, could been used for a more detailed description of internal fractal structure in river networks [53]. As an extension of F D , significant distinction of multifractal spectra between the endorheic and exorheic rivers could also be expected and worth exploring in the following analysis.…”

Multifractal Characteristics of Uranium Grade Distribution and Spatial Regularities in a Sandstone-Type Uranium Deposit in Xinjiang, China

“…Shen [33] investigated the fractal characteristics and geological significance of the gold grade distribution of a gold mine in Xinjiang in detail. Kusák [34] discussed how to describe the drainage patterns of the Blue Nile Basin in Ethiopia using the fractal method. The geochemical distribution patterns and migration characteristics of the major and trace elements can be demonstrated well by the multifractal method and multifractal parameters [35].…”