Wavelet analyses of Mars polar topography

We have analyzed topography tracks over the Mars northern polar cap (compos ed of H2O ice, CO2 ice, and sediments) and the Antarctic ice sheet on Earth using a Mexican hat wavelet transform. The great utility of the wavelet tr ansform is that it gives both spatial and spectral resolution. We have used the variance of the wavelet output in order to quantify the spectral conte nt of the topography tracks. At short wavelengths, for both the Mars northe rn polar cap and the Antarctic ice sheet, we find a power law dependence of the wavelet transform variance on wavelength, with a power law exponent of beta approximate to 3.5-3.7. This compares with a power law exponent of si milar to2.0 (Brownian motion), typical of topography on both Mars and Earth . There is a power law smoothing of the ice topography at short wavelengths on both planetary bodies. At long wavelengths we infer a similar power law dependence with beta approximate to 1.5-2.0, typical of planetary topograp hy. A transition is observed between the smooth short-wavelength behavior ( high beta) to rougher long-wavelength behavior (low beta). This fairly shar p transition occurs at a wavelength of similar to 24 kin for Mars and simil ar to 11 kin for Antarctica. The transitions appear to scale with ice thick nesses and suggest a relaxation of short-wavelength topography by ice flows or surface processes.