Statistics
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufm.p11b1034s&link_type=abstract
American Geophysical Union, Fall Meeting 2003, abstract #P11B-1034
Statistics
3250 Fractals And Multifractals, 5464 Remote Sensing, 5470 Surface Materials And Properties, 6225 Mars
Scientific paper
We present global maps of two-dimensional fractal statistics for Mars topography calculated by applying the two-dimensional Fourier spectral approach to MOLA altimetry measurements over spatial scales extending from approximately 450 meters to 15 kilometers. Three global maps were generated: 1) surface (two-dimensional) fractal dimension, 2) roughness amplitude at a scale of one kilometer, and 3) linear model fit error in the log-log relation of mean power spectral density to radial wavenumber. The linear model fit error is a convenient way to judge the appropriateness of the fractal model. Examination of the fractal dimension and model error maps reveals that a majority of the surface is well modeled by fractal geometry. This is evidenced by minimal systematic spatial variation in fractal dimension and low model fit errors, with the northern plains exhibiting slightly higher overall error than the cratered highlands. There are also several spatially coherent regions in the fractal dimension map that have enhanced values. These regions include Amazonis Planitia and southeast Elysium Planitia. On the other hand, Isidis Planitia and portions of the Olympus Mons aureole exhibit high model fit errors which imply a lower applicability of fractal geometry to these terrains. The one kilometer roughness amplitude map exhibits a tremendous amount of spatial detail and clearly delineates differing roughness terrains. The portions of Amazonis Planitia and southeast Elysium Planitia with enhanced fractal dimension have roughness amplitudes significantly below the global mean, while the Valles Marineris system, the circum-Argyre region, and the chaotic and heavily eroded terrains located along the crustal dichotomy boundary exhibit elevated roughness values. The Tharsis region is particularly rich in detail, displaying a wide range of spatially contiguous roughness provinces that are traceable to known surface units. Comparison of the roughness amplitude map to the MOLA pulse width-derived roughness data (75 meter baseline) reveals a strong correlation with a few notable exceptions. The circum-polar debris mantle located 30 to 45 degrees bilaterally from the equator and a small yet distinct terrain located northwest of Olympus Mons are both evident in the 75 m pulse width data but are not expressed in the longer wavelength roughness amplitude map. This implies that the surface processes responsible for producing these terrains are dominant only at shorter length scales.
Arvidson Ray E.
Deal Kim S.
Neumann Gregory A.
Seelos Frank P.
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