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Fig. 21

image

Plots of the log-correlations vs. log (Δx) for two 1D signals extracted from the Musca 250 μm map according to the scheme shown in Fig. 20. The analyzing wavelet is given by Eq. (27) with σ = 3.2. We use 500 scales from r = 1 to r = 500 and 400 values for Δx between 1 and 400. The chosen values for the scales are enough to highlight more than two nodes in a cascade, if such a cascade exists. Each image shows the graphs of the log-correlations for a few scales (curves from green to purple, corresponding to increasing scales) as well as the line y = − c2 log(Δx) with the slope c2 computed through linear regression, according to Eq. (C.3). The linear regression used to compute c2 is performed for scales between 10 and 200. The left panel shows the log-correlations corresponding to Col. 970 in the Musca observational map. The graphs of for different scales follow the slope given by the line y = −c2log(Δx). The right panel, corresponding to Col. 947, displays a different behavior: long-range correlations are observed, but the behavior seen in a log-normal multiplicative cascade is not present.

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