Abstract:
Rock-strewn surfaces are apparently common on Mars, and radar backscatter data offer the most direct means for remotely estimating their statistical properties. This paper examines the height statistics of power-law and exponential rock size-frequency distributions, and demonstrates the dependence of root-mean-square (rms) height on horizontal scale as a function of the distribution parameters. In general, strewn surfaces have an inherent variation in roughness for horizontal length scales below the maximum rock diameter. This leads to variations in radar echo power with wavelength, even when the differential diameter function has an inverse-cubed power-law form. Size-frequency data for a rock-strewn test site in Hawaii are consistent, over a specific range of horizontal scales, with a power-law distribution. An exponential form, while better describing the rapid decline in rock abundance above a certain size threshold, underestimates the population at the smaller scales most relevant to radar scattering. Rock sphericity statistics, often cited in descriptions of rocky areas, appear to be consistent with a Rayleigh distribution of major and minor axis diameters about any chosen mean value. Depolarized backscatter data for the test site at 5.7-68 cm are proportional to the rms height at the wavelength scale, mirroring a similar trend for continuous rough rocky surfaces. An empirical model relating rms height to depolarized backscatter coefficient appears to well describe the behavior of strewn surfaces. The polarized echoes are consistent with Mie scattering from surface rocks for a reasonable choice of dielectric properties, but the number of free parameters and the interaction of the scatterer and surface yields weak remote-sensing roughness or dielectric constraints. While depolarized backscatter data provide robust estimates of the rms height for continuous and discrete roughness populations, their use in Mars landing site planning is model-dependent. For single-wavelength data, we cannot uniquely determine the size-frequency distribution and the maximum rock diameter. Dual-wavelength observations, in the S- to P-band range, may better constrain the surface properties.
