Scale Space, Fractals and a Touch of Chaos

This paper deals with the fundamental issue of scale. The thesis which is presented is that scale is a concept which unifies some of the most current and interesting ideas in geology and geophysics. The introduction of this ooncept in a. formal wa.y into the literature is due to Witkin (1983) who coined the name scale space and applied it in a fascinating manner to the representation and decomposition of signals. Leaney and Ulrych (1988) extended this approach to event tracking and matching of well data. Scale, of course, is what fractals are all about and the paper goes on to deal with some recent results which describe the fractal nature of the reflectivity series and consequently of the underlying sedimentation process. Since fractal structure is a new geometric property which is exhibited by chaotic motions, the paper concludes with a brief look at a canonical chaotic .example and examines the possibility of wavelet estimation using a particular measure in phase space.