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Multifractals and Wavelets : A potential tool in

The study of fractal quantities and structures exhibiting highly erratic features on all scales has proved to be of outstanding signiicance in various disciplines. While scaling phenomena are pervasive in natural and man-made constructs, such objects are less fractal than multifractal. In most simple terms this means that moments of diierent orders scale diierently with increasing resolution. This paper should be understood as a tutorial in multi-fractals and their analysis via wavelets, in view of possible applications in geophysics. It is elaborated how a description of the well log measurement through wavelets provides a new way of modeling reeection of waves in a material which is dependent on frequency. The wavelet analysis has the potential to provide an explanation for the inconstencies that are observed when comparing sub-surface models that have been constructed from measurements with diierent resolutions, such as surface seismic, vertical seismic prooles and well logs.