Haar wavelets, fluctuations and structure functions: Convenient choices for geophysics
Résumé
Geophysical processes are typically variable over huge ranges of space-time scales. This has lead to the development of many techniques for decomposing series and fields into fluctuations Δν at well-defined scales. Classically, one defines fluctuations as differences: (Δν) diff = ν(x +Δx)-ν(x) and this is adequate for many applications (Δx is the "lag"). However, if over a range one has scaling Δν ∝ Δx H, these difference fluctuations are only adequate when 0