Are topographic data sets fractal?

Lewis E. Gilbert

    Research output: Contribution to journalArticlepeer-review

    72 Scopus citations


    The scale invariant properties of fractal sets make them attractive models for topographic profiles because those profiles are the end product of a complex system of physical processes operating over many spatial scales. If topographic data sets are fractal, their power spectra will be well represented by lines in log-log space with slopes s such that -3≤s<-1. The power spectra from a Digital Elevation Model (30 meter sample spacing) of the Sierra Nevada Batholith and from Seabeam center beam depths (425 meter sample spacing) along a flowline in the South Atlantic are curved. Straight sections in the spectra can be identified but the slopes of those sections are strongly dependent upon the particulars of the data analysis. Fractal geometry must be used with caution in the discussion of topographic data sets.

    Original languageEnglish (US)
    Pages (from-to)241-254
    Number of pages14
    JournalPure and Applied Geophysics PAGEOPH
    Issue number1-2
    StatePublished - Mar 1 1989


    • Topography
    • fractal


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