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Fractal reconstruction of sea-floor topography

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Abstract

Sea-floor bathymetric profiles exhibit features at many different scales of length; this suggests that they could be described as fractals. An algorithm interpolating a fractal line between points has been used to reconstruct bathymetric profiles from a few data points. In general, this fractal line has the same Fourier amplitude spectrum as real bathymetry, and, if the parameters of the interpolation are suitably chosen, it has a very similar appearance. The success of this fractal reconstruction algorithm for the sea-floor raises the possibility that it could be used to extrapolate, from data collected at one scale, the properties of the sea-floor at finer scales, and that similar techniques could be used to interpolate a surface between bathymetric profiles. The fractal character is a sign that the processes that shape the sea-floor are scale invariant and suggests that the renormalization group technique could be used to model these processes.

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Mareschal, J. Fractal reconstruction of sea-floor topography. PAGEOPH 131, 197–210 (1989). https://doi.org/10.1007/BF00874487

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Key words

  • Fractal
  • bathymetry
  • interpolation
  • fracture zone
  • ridge
  • tectonics