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Erosional Development of the Ethiopian Plateau of Northeast Africa from a Fractal Analysis of Topography

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Fractals in Petroleum Geology and Earth Processes

Abstract

Sculpting of the Earth’s surface by flowing water is apparent even to a casual observer, yet we know surprisingly little in a quantitative way about how the process of erosion actually occurs over a wide range of length and time scales. Earth’s surface topography at any particular time represents the combined effects of tectonism on one hand, and erosion/depositional processes on the other. Given this situation, it makes sense to study erosion in settings where we can estimate the tectonic component of the topography.

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References

  • Asfaw, B., Ebinger, C., Harding, D., and WoldeGabriel, G., Space-based imagery in paleoanthropological research: an Ethiopian example, National Geographic Res. 6, 418–434 (1990).

    Google Scholar 

  • Berry, M. V., and Hanney, J. H., Topography of random surfaces, Nature 273, 573 (1978).

    Article  ADS  Google Scholar 

  • Brown, S. R., A note on the description of surface roughness using fractal dimension, Geophys. Res. Lett. 14, 1095–1098 (1987).

    Article  ADS  Google Scholar 

  • Brown, S. R., and Scholz, C. H., Broad bandwidth study of the topography of natural rock surfaces, J. Geophys. Res. 90, 12575–12582 (1985).

    Article  ADS  Google Scholar 

  • Chase, C. G., Fluvial landsculpting and the fractal dimension of topography, Geomorphol. 5, 39–57 (1992).

    Article  ADS  Google Scholar 

  • Ebinger, C. J., Bechtel, T. D., Forsyth, D. W., and Bowin, C.O., Effective elastic plate thickness beneath the East African and Afar Plateaux and dynamic compensation of the uplifts, J. Geophys. Res. 94, 2883–2901 (1989).

    Article  ADS  Google Scholar 

  • Ebinger, C. J., Karner, G. D., and Weissel, J. K., Mechanical strength of extended continental lithosphere: Constraints from the western Rift System, East Africa, Tectonics 10, 1239–1258 (1991).

    Article  ADS  Google Scholar 

  • Feder, J., Fractals, Plenum Press, New York (1988).

    MATH  Google Scholar 

  • Fox, C. G., and Hayes, D. E., Quantitative methods for analyzing the roughness of the seafloor, Rev. Geophys. Space Phys. 23, 1–48 (1985).

    Article  Google Scholar 

  • Gilbert, L. E., Are topographic data sets fractal? Pure Appl. Geophys. 131, 241–254 (1989).

    Article  ADS  Google Scholar 

  • Goff, J. A., and Jordan, T. H., Stochastic modeling of seafloor morphology: inversion of Sea Beam data for second-order statistics, J. Geophys. Res. 93, 13589–13608 (1988).

    Article  ADS  Google Scholar 

  • Huang, J., and Turcotte, D. L., Fractal mapping of digitized images: Application to the topography of Arizona and comparisons with synthetic images, J. Geophys. Res. 94, 7491–7495 (1989).

    Article  ADS  Google Scholar 

  • Kazmin, V., Explanation of the geological map of Ethiopia (plus 1:2M geological map). Bulletin No. 1, Ministry of Mines, Energy and Water Resources, Geological Survey of Ethiopia (1975).

    Google Scholar 

  • Kelley, A. D., Malin, M. D., and Nielson, G. M., Terrain simulation using a model of stream erosion, Computer Graphics 22, 263–268 (1988).

    Article  Google Scholar 

  • Kleiner, B., and Graedel, T. E., Exploratory data analysis in the geophysical sciences, Rev. Geophys. Space Phys. 18, 699–717 (1980).

    Article  ADS  Google Scholar 

  • Klinkenberg, B., and Goodchild, M. F., The fractal properties of topography; A comparison of methods, Earth Surface Processes and Landforms 17, 217–234 (1992).

    Article  ADS  Google Scholar 

  • Lavallee, D., Lovejoy, S., Schertzer, D., and Ladoy, P., Nonlinear variability of landscape topography: Multifractal analysis and simulation, in: Fractals in Geography (L. De Cola, and N. Lam, eds.), Prentice-Hall, New York, pp. 158–192 (1993).

    Google Scholar 

  • Malinverno, A., A simple method to estimate the fractal dimension of a self-affine series, Geophys. Res. Lett. 17, 1953–1956 (1990).

    Article  ADS  Google Scholar 

  • Mandelbrot, B. B., The Fractal Geometry of Nature, W.H. Freeman, New York (1983).

    Google Scholar 

  • Mandelbrot, B. B., Fractal landscapes without creases and with rivers, in: The Science of Fractal Images (H. O. Peitgen, and D. Saupe, eds.), Springer-Verlag, New York, pp. 243–260 (1988).

    Google Scholar 

  • Mark, D. M., and Aronson, P.B., Scale-dependent fractal dimension of topographic surfaces: An empirical investigation with applications in geomorphology and computer mapping, Mathemat. Geol. 16, 671–683 (1984).

    Article  Google Scholar 

  • Mohr, P., Ethiopian flood basalt province, Nature 303, 577–583 (1983).

    Article  ADS  Google Scholar 

  • Musgrave, F. K., Kolb, C. E., and Mace, R. S., The synthesis and rendering of eroded fractal terrains, Computer Graphics 23, 41–50 (1989).

    Article  Google Scholar 

  • National Geophysical Data Center (NGDC), Relief of the surface of the Earth, Report MGG-2: Boulder, CO, World Data Center A for Marine Geology and Geophysics, NOAA (1985).

    Google Scholar 

  • Newman, W. I., and Turcotte, D. L., Cascade model for fluvial geomorphology, Geophys. J. Internat. 100, 433–439 (1990).

    Article  ADS  Google Scholar 

  • Ollier, C. D., Morphotectonics of passive continental margins: An introduction, Zeits. Geomorphol., Suppl. Bd. 54, 1–9 (1985).

    ADS  Google Scholar 

  • Ollier, C. D., and Marker, M. E., The Great Escarpment of southern Africa, Zeits. Geomorphol., Suppl. Bd. 54, 37–56 (1985).

    Google Scholar 

  • Ollier, C. D., and Powar, K. B., The Western Ghats and the morphotectonics of Peninsular India, Zeits. Geomorphol., Suppl. Bd. 54, 57–69 (1985).

    Google Scholar 

  • Pain, C. F., Morphotectonics of the continental margins of Australia, Zeits. Geomorphol., Suppl. Bd. 54, 23–35 (1985).

    Google Scholar 

  • Sayles, R. S., and Thomas, T. R., Surface topography as a non-stationary random process, Nature 271, 431–434 (1978).

    Article  ADS  Google Scholar 

  • Tarboton, D. G., Bras, R. L., and Rodriguez-Iturbe, I., The fractal nature of stream networks, Water Resources Res. 24, 1317–1322 (1988).

    Article  ADS  Google Scholar 

  • Voss, R. F., Fractals in nature: From characterization to simulation, in: The Science of Fractal Images (H. O. Peitgen and D. Saupe, eds.), Springer-Verlag, New York, pp. 21–70 (1988).

    Chapter  Google Scholar 

  • Weissel, J. K., Long-term erosional development of rifted continental margins: Toward a quantitative understanding, in: Pacific Rim Congress 90, Proceedings, vol. III, Australian Institute of Mining & Metallurgy, Parkville, Victoria, pp. 63–70 (1990).

    Google Scholar 

  • Weissel, J. K., and Karner, G. D., Flexural uplift of rift flanks due to mechanical unloading of the lithosphere during extension, J. Geophys. Res. 94(B10), 13919–13950 (1989).

    Article  ADS  Google Scholar 

  • Willgoose, G., Bras, R. L., and Rodriguez-Iturbe, I., A model of river basin evolution, EOS Trans. Amer. Geophys. Union 71, 1806–1807 (1990).

    Article  ADS  Google Scholar 

  • WoldeGabriel, G., Aronson, J. L., and Walter, R. C., Geology, geochronology, and rift basin development in the central sector of the main Ethiopia Rift, Geol. Soc. Amer. Bull. 102, 439–458 (1990).

    Article  Google Scholar 

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Weissel, J.K., Malinverno, A., Harding, D.J., Karner, G.D. (1995). Erosional Development of the Ethiopian Plateau of Northeast Africa from a Fractal Analysis of Topography. In: Barton, C.C., La Pointe, P.R. (eds) Fractals in Petroleum Geology and Earth Processes. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1815-0_8

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  • DOI: https://doi.org/10.1007/978-1-4615-1815-0_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5733-9

  • Online ISBN: 978-1-4615-1815-0

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