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Fractal Analysis of Karst Landscapes

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Abstract

Fractal analysis has, for some time, been used to evaluate the roughness of both natural and engineered surfaces. Since the introduction of fractal geometry, evidence of the universality of fractal forms in nature has increased, and many applications have been found for fractal analysis. The purpose of this work is to study the relationships between karst geological features and landscape roughness in order to extract information on karst landscape evolution and the interaction between lithological, geomorphological and tectonic processes and karst terrain complexity. As a means of achieving this, the fractal analysis of a high-relief karst system using a high-resolution digital elevation model is presented. The local fractal dimension of the topography is calculated within a moving window from the variogram of terrain profiles. It has been found that the fractal dimension is not related to slope, and that a fractal dimension of 2.3, suggested as an upper limit on surface roughness based on arguments of surface fragility, is also a practical limit for fractal dimensions of karst terrains. The methodology is applied to the high-relief Mediterranean karst of the Sierra de las Nieves in Southern Spain where two different areas of karst evolution and development have been identified.

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Acknowledgements

This work was supported by research project CGL2015-71510-R of the Ministerio de Economía, Industria y Competitividad of Spain. We thank two anonymous reviewers and the journal’s Editor-in-Chief for their constructive comments that have significantly helped to improve the final version of the paper.

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Authors and Affiliations

  1. Instituto Geológico y Minero de España (IGME), Ríos Rosas 23, 28001, Madrid, Spain

    Eulogio Pardo-Igúzquiza

  2. Faculty of Engineering, Computer and Mathematical Sciences, The University of Adelaide, Adelaide, Australia

    Peter A. Dowd

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  1. Eulogio Pardo-Igúzquiza
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  2. Peter A. Dowd
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Correspondence to Eulogio Pardo-Igúzquiza.

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Pardo-Igúzquiza, E., Dowd, P.A. Fractal Analysis of Karst Landscapes. Math Geosci 52, 543–563 (2020). https://doi.org/10.1007/s11004-019-09803-x

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