Surface Slope Probabilities from the Spectra of Weak Radar Echoes: Application to Mars
Abstract
Slope probability densities were derived from the power spectra of radar echoes from Mars using integral inversion. The inverse problem is illposed; 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 signaltonoise 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 quasispecular 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 quasispecular 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.
 Publication:

Icarus
 Pub Date:
 June 1976
 DOI:
 10.1016/00191035(76)900403
 Bibcode:
 1976Icar...28..301L
 Keywords:

 Mars Surface;
 Power Spectra;
 Probability Density Functions;
 Radar Echoes;
 Signal Reflection;
 Diffuse Radiation;
 Radar Scattering;
 Signal Stabilization;
 Signal To Noise Ratios;
 Specular Reflection