The Fractal Surface of Mars

Image caption: (A) Hillshade map of the HiRISE digital elevation model of test site 6 (sublimated terrain). (B) Map of roughness defined by the local fractal dimension (Fractal D.). (C) Experimental variogram of (B) for distances up to 200 m. (D) Segmentation of (B) into four classes using the roughness quartiles. Credit: Pardo-Igúzquiza and Dowd, 2021.

An understanding of the roughness of the surface of a planetary body is useful in several applications, including characterizing wind speed near the ground, improving remote sensing by radar, and other geological studies. The fractal dimension of a surface is one way of characterizing its roughness. A smooth surface, like polished glass, will have a fractal dimension close to two, while a rough surface, like the surface of a sandy desert, will have a fractal dimension closer to three, representing how the surface of the sand, in a sense, fills space three-dimensionally.

In a recent paper, E. Pardo-Igúzquiza (Instituto Geológico y Minero de España) and P. A. Dowd (University of Adelaide) aim to estimate fractal dimension at a variety of geologically distinct locations on Mars by computing variograms for each location. A variogram, for purposes of this study, estimates how much the ground height varies from place to place as a function of distance between points on the ground. Pardo-Igúzquiza and Dowd calculated the fractal dimension using variograms in six locations on Mars, each of which is representative of a different type of terrain. The roughest of the six locations that they examined was sublimated terrain, where carbon dioxide can be deposited in the cold season and can sublimate in the warm season. This sublimation results in a large number of depressions in the ground, roughening the surface. The variogram indicates that geological features in the sublimated terrain, such as the depressions, preferentially have mean sizes of 5 meters and 30 meters. Maps of surface roughness, such as those produced in Pardo-Igúzquiza and Dowd’s work, may unveil structures not easily seen by other means and thus serve as an additional tool for planetary geologists to investigate our solar system. READ MORE