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

Stochastic surface models are useful for analyzing in situ roughness profil es and synthetic aperture radar (SAR) images of geological terrain. In this paper, two different surface models are discussed: surfaces with a station ary random roughness (conventional model) and surfaces with a power-law rou ghness spectrum (fractal model). In the former case, it must be considered that for short profiles (L < 200l(0)), the measured values of rms-height s and correlation length l may be significantly smaller than the intrinsic va lues so and lo. In the latter case, rms-height and correlation length depen d 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 sen sitivity of the SAR signature to variations in surface roughness parameters is evaluated by means of theoretical scattering models. For smoother geolo gical surfaces such as most arid terrain types, single scattering is domina nt, which means that the roughness parameters can be determined from SAR da ta using comparatively simple algorithms. Multiple scattering processes on rough surfaces such as a'a lava and variations of the Ideal incidence angle due to large-scale terrain undulations make the retrieval of roughness par ameters by means of inverse modeling much more complex. Field data of surfa ce roughness indicate that rougher geological surfaces may be in the diffra ctal regime at higher radar frequencies, in which the scattering characteri stics deviate significantly from the patterns observed for stationary surfa ces. On the basis of surface and scattering models, recently published obse rvations of roughness data and radar signatures from volcanic, alluvial, an d arid surfaces are examined.