Surface roughness is a statistical measure of change in surface height over a given spatial horizontal scale after the effect of broad‐scale slope has been removed and can be used to understand how geologic processes produce and modify a planet's topographic character at different scales. The statistical measure of surface roughness employed in this study of Mercury was the root‐mean‐square deviation and was calculated from 45 to 90°N at horizontal baselines of 0.5–250 km with detrended topographic data from individual Mercury Laser Altimeter tracks. As seen in previous studies, the surface roughness of Mercury has a bimodal spatial distribution, with the cratered terrain (dominated by the intercrater plains) possessing higher‐surface roughness than the smooth plains. The measured surface roughness for both geologic units is controlled by a trade‐off between impact craters generating higher‐surface roughness values and flood‐mode volcanism decreasing surface roughness. The topography of the two terrain types has self‐affine‐like behavior at baselines from 0.5 to 1.5 km; the smooth plains collectively have a Hurst exponent of 0.88 ± 0.01, whereas the cratered terrains have a Hurst exponent of 0.95 ± 0.01. Subtle variations in the surface roughness of the smooth plains can be attributed to differences in regional differences in the spatial density of tectonic landforms. The northern rise, a 1000 km wide region of elevated topography centered at 65°N, 40°E, is not distinguishable in surface roughness measurements over baselines of 0.5–250 km.
- surface roughness
- impact craters