Many natural structures possess self-similar multiscales which can be characterized by power law spectra. Under appropriate conditions, knowledge of the strength of these scale sizes provides information on the physical processes which form these objects. In this paper, we investigate wave interactions with continuous fractal layers which model geological and variegated structures. Since fractal characteristics of the layers are embedded in the scattered field, they can be retrieved under appropriate conditions. This inversion can be performed in either the frequency or the time domain as desired.