Mars topography: bulk statistics and spectral scaling.

In this paper we present a systematic study of the Mars topography focusing on the statistical distributions and maps of the 5degrees x 5degrees cell-averaged mean elevations, standard deviations, skewness and kurtosis coefficients, and power spectra. Altogether, the obtained data suggest that at a 5degrees x 5degrees cell scale a large portion of the Martian surface may be reasonably considered as a Gaussian random field with a three-range spectrum consisting: (1) a high-energy low-wave-number range (approximate to 0.003 < k < approximate to 0.03 km(-1)) where the spectrum may deviate from a power law and attain a maximum; (2) scaling range 1 (approximate to 0.03 < k < approximate to (0.2-0.3) km(-1)) where the spectrum may be well approximated as S(k) proportional to k(-beta1); and (3) scaling range 2 ( approximate to (0.2-0.3) < k < approximate to 1.67 km(-1)) where the spectrum may be also approximated as a power function but with a different exponent, i.e., S(k) proportional to k(-beta2). The most probable values for the exponents are beta(1) = (2.2-2.4) and beta(2) = 3.8. The data show that the separation of these two scaling ranges most frequently occurs at L-c approximate to 3.3 km. At a scale larger than the 5degrees x 5degrees cell scale the topography is highly intermittent with patchy spatial distributions of the key statistical moments. This patchiness is superimposed with systematic north-to-south trends in statistical properties, reflecting the crustal dichotomy of the planet and large-scale differences in the surface-forming processes. (C) 2003 Elsevier Ltd. All rights reserved.