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Titel Influence of a discontinuity on the spectral and fractal analysis of one-dimensional data
VerfasserIn R. P. H. Berton
Medientyp Artikel
Sprache Englisch
ISSN 1023-5809
Digitales Dokument URL
Erschienen In: Nonlinear Processes in Geophysics ; 11, no. 5/6 ; Nr. 11, no. 5/6 (2004-12-15), S.659-682
Datensatznummer 250008995
Publikation (Nr.) Volltext-Dokument vorhandencopernicus.org/npg-11-659-2004.pdf
 
Zusammenfassung
The analysis of a data area or segment containing steep transitions between regions with different textures (for example a cloud and its background) leads to addressing the problem of discontinuities and their impact on texture analysis. In that purpose, an original one-dimensional analytical model of spectrum and roughness function has been worked out, with a discontinuity between two fractal regions, each one specified by its average µ, standard deviation σ, spectral index β and Hurst exponent H. This has the advantage of not needing the generation of a fractal structure with a particular algorithm or random functions and clearly puts into evidence the role played by the average in generating spectral poles and side lobes. After validation of the model calibration, a parametric study is carried out in order to understand the influence of this discontinuity on the estimation of the spectral index β and the Hurst parameter H. It shows that for a pure µ-gap, H is well estimated everywhere, though overestimated, and β is overestimated in the anti-correlation range and saturates in the correlation range. For a pure σ-gap the retrieval of H is excellent everywhere and the behaviour of β is better than for a µ-gap, leading to less overestimation in the anti-correlation range. For a pure β-gap, saturation degrades measurements in the case of raw data and the medium with smaller spectral index is predominant in the case of trend-corrected data. For a pure H-gap, there is also dominance of the medium with smaller fractal exponent.
 
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