Multifractals and Wavelets: A potential tool in Geophysics
Riedi, Rudolf H.
The study of fractal quantities and structures exhibiting highly erratic features on all scales has proved to be of outstanding significance 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 different orders scale differently with increasing resolution. This paper should be understood as a tutorial in multifractals 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 reflection of waves in a material which is dependent on frequency. The wavelet analysis has the potential to provide an explanation for the inconsistencies that are observed when comparing subsurface models that have been constructed from measurements with different resolutions, such as surface seismic, vertical seismic profiles and well logs.