Application of a statistical surface model to planetary radar astronomy

A statistical model of the distribution of slopes and elevations on a cratered planetary surface is applied to scattering of radio waves by the moon and Venus. It is found that the quasi-specular component of backscattered power can be fit by any symmetric stable distribution for elevation differences whose characteristic exponent is between 1 and 2 (crater diameter population index between 2 and 3). The lack of dependence on wavelength of the roughness parameter for decimeter and meter wavelengths, however, suggests that surface elevation differences have nearly a Cauchy distribution, not a Gaussian distribution. The increase of the roughness parameter with wavelength at millimeter and centimeter wavelengths suggests that pebbles and blocks are the major component of small-scale surface roughness.