Rudolf H. Riedi.
Multifractals and wavelets: a potential tool for geophysics.
Proceedings of the 68th SEG Meeting, New Orleans, Louisiana, USA, 1998.

Abstract: 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.