Surface slope probabilities from the spectra of weak radar echoes: Application to Mars

Slope probability densities were derived from the power spectra of radar echoes from Mars using integral inversion. The inverse problem is ill-posed; that is, small changes in the data can lead to large changes in the solution. We describe a method of stabilizing the inversion, which was necessary for echoes with signal-to-noise power spectral densities on the order of unity, and for those with broad spectral distributions. The resulting slope probabilities usually consisted of a component due to quasi-specular reflection which decreased rapidly with tilt, plus a broad, slowly decreasing, “diffuse” component due to scattering from (1) surface scales small compared with a radar wavelength, or (2) larger features with high slopes. In the absence of more complete polarization measurements, we are unable to In the absence of more complete polarization measurements, we are unable to distinguish between these possibilities. Root mean square tilts have been determined separately for the two cases. For case (1), values of rms tilt associated with surface features responsible for the quasi-specular echo are normally less than 3°; for case (2), values greater than 8° are common. Knowledge of the depolarization of radar returns would help distinguish between these possibilities.