Limits on inference of Mars small-scale topography from MOLA data

Abstract

The surface roughness of Mars at scales from ∼1-200 m is of interest for lander hazard and radar-sounder clutter analysis, but MOLA data are the only current source of global topographic information. We use synthetic fractal profiles to determine the uncertainties associated with deriving self-affine statistics from detrended segments of MOLA tracks. The mean Hurst exponent derived from such segments is an underestimate of the true value, H, for H > 0.5, and an overestimate for H < 0.5. Values of H from independent samples along a profile are distributed about this biased mean value. The magnitudes of the bias and variance in H increase for shorter segments. Terrestrial topography data show that extrapolation of roughness statistics to smaller scales based on self-affine relationships is uncertain. Roughness at the 1-15 m scales may be poorly correlated with topography at >100-m scales. We suggest that any extrapolation be regarded as a lower bound on the true terrain statistics.