The electromagnetic measurement of range to a topographic surface from a satellite platform, such as that performed by the Earth Resources Satellite-1 (ERS-1) synthetic aperture radar (SAR), results in a geometrically distorted image which displays characteristics not readily identifiable with natural terrain features. This paper hypothesizes that SAR signals may be examined as a set of singularities which arise from a scale independent topography where the radar returns originate with variations in local terrain slope. The hypothesis is explored through the use of fractal geometry, SAR image simulations, ERS-1 SAR data, and analysis using the continuous wavelet transform. By using the language of fractal geometry, the topographic descriptors of slope and elevation are transformed into singularity strengths through numerical simulations modeling range foreshortening. Input data are from (1) a digital elevation model (DEM) and (2) fractally interpolated DEMs. Continuous wavelet transforms (CWT) are employed in a scale-space analysis of the SAR simulations to analyze and explain the relationships between singularity strength and the various models of topography. By comparing the results to an identical analysis of actual SAR data (ERS-1 SAR SGC), the CWT modulus maxima show that the overall singularity behavior of SAR image simulations derived from fractally interpolated DEMs more closely resembles actual SAR data than do simulations from the original DEM. At detail scales, measurements from the modulus maxima of SAR image simulations better approximate actual SAR data as the complexity of the DEM increases. At coarser scales, the generalizations depicted by the modulus maxima from the simulations correspond closely to the actual data.