Quantitative roughness characterization of geological surfaces and implications for radar signature analysis

Stochastic surface models are useful for analyzing in situ roughness profiles and synthetic aperture radar (SAR) images of geological terrain. In this paper, two different surface models are discussed: surfaces with a stationary random roughness (conventional model) and surfaces with a power-law roughness spectrum (fractal model). In the former case, it must be considered that for short profiles (L<200l₀), the measured values of rms-height s and correlation length l may be significantly smaller than the intrinsic values s₀ and l₀. In the latter case, rms-height and correlation length depend on the profile length L, and the surface is better characterized by slope and offset of the roughness spectrum (which are independent of L), The sensitivity of the SAR signature to variations in surface roughness parameters is evaluated by means of theoretical scattering models. For smoother geological surfaces such as most arid terrain types, single scattering is dominant, which means that the roughness parameters can be determined from SAR data using comparatively simple algorithms. Multiple scattering processes on rough surfaces such as a´a lava and variations of the local incidence angle due to large-scale terrain undulations make the retrieval of roughness parameters by means of inverse modeling much more complex. Field data of surface roughness indicate that rougher geological surfaces may be in the diffractal regime at higher radar frequencies, in which the scattering characteristics deviate significantly from the patterns observed for stationary surfaces. On the basis of surface and scattering models, recently published observations of roughness data and radar signatures from volcanic, alluvial, and arid surfaces are examined