Radar Scattering from a Self-Affine Fractal Surface: Near-Nadir Regime

Abstract

Planetary surfaces are better described by nonstationary fractal statistics than those more commonly assumed in current radar scattering models. Therefore, we have developed a radar scattering model applicable to self-affine fractal surfaces when observed near-nadir. The model predicts a family of angular scattering functions that smoothly transition between forms similar to the commonly utilized Hagfors, Gaussian, and exponential surface models. The model predicts that the near-nadir scattering behavior is determined by the wavelength-scaled roughness, i.e., the roughness that would be measured by a field worker using a ruler one wavelength in size, and the surface scaling behavior described by the fractal dimension or Hurst exponent. Additionally, this model predicts that the scattering behavior should scale with wavelength in a self-affine manner, i.e., the scattering behavior at long wavelengths should look “smoother” than that at short wavelengths. The scattering behavior predicted by the model is consistent with that observed for Venus by the Magellan altimeter experiment.