Generalized fractal-based laws for scattering from planetary surfaces: A unifying scale-explicit paradigm

Fractal-based scattering laws, when used to fit radar observations, provide an estimate for surface root-mean-square (RMS) slope that is explicit in its scale dependence. Furthermore, fractal-based laws outperform, in a minimum residual sense, the widely used Hagfors' and Gaussian laws, which they subsume as special cases when their Hurst exponent parameter, H, takes the values 1/2 and 1, respectively. The use of a fixed, scale-independent value for H restricts the modeling capacity of the fractal-based laws. Allowing H to be a function of the horizontal scale R leads to a generalized scattering law that unifies the fractal-based laws with fixed H and the conventional Hagfors, Gaussian, and exponential laws. A new procedure employing the generalized fractal-based laws is applied to Magellan altimetry data for the surface of Venus at 12.6 cm -λ. Near-nadir Magellan backscatter data are modeled using a linear combination of two conventional scattering laws in order to obtain statistically significant fits. The Hankel transform is used to obtain a scale-explicit interpretation that gives the surface RMS slope as a function of horizontal scale. An analysis of the scattering integral gives insights into the range of scales which are effective in the scattering process and for which the RMS slope estimate can be considered reliable. Copyright 2006 by the American Geophysical Union.