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A wavelet-like model for distributions of objects in natural and man-madeterrestrial environments is developed. The model is constructed in aself-similar fashion, with the sizes, amplitudes, and numbers of objectsoccurring at a constant ratios between parent and offspring objects. Theobjects are randomly distributed in space according to a Poisson process.Fractal supports and a cascade model are used to organize objectsintermittently in space. In its basic form, the model is for continuouslyvarying random fields, although a level-cut is introduced to model two-phaserandom media. The report begins with a description of relevant concepts fromfractal theory, and then progresses through static (time-invariant),steady-state, and non-steady models. The results can be applied to such diversephenomena as turbulence, geologic distributions, urban buildings, vegetation,and arctic ice floes. The model can be used as a basis for synthesizingrealistic terrestrial scenes, and for predicting the performance of sensing andcommunication systems in operating environments with complex, intermittentdistributions of scattering objects.

Wavelet-based cascade model for intermittent structure in terrestrial environments