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Influence of a discontinuity on the spectral and fractal analysis of one-dimensional data

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Academic year: 2021

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Figure 1.  Model of one-dimensional discontinuity between two homogeneous fractal media
Fig. 2. Optimisation of the regression interval [k a , k b ]. Plot of the difference β est –β between the true and the estimated spectral indices as a function of the bounds (k a , k b ).
Fig. 3. Comparison of Power-Spectral Density (PSD) profiles for a single medium (N = 1000) as given by the analytical formula (16) (solid smooth or upper curve) and as calculated from a realisation of the numerical FBM, App
Fig. 4. Examples of Power-Spectral Density (PSD) profiles for monofractal (left) and bifractal (right) discontinuities (N 1 = N 2 = 500) as given by the analytical formula (15) (solid smooth or upper curve) and as calculated from a realisation of the numer
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