Investigating the Surface Roughness of Mercury

The Mercury Laser Altimeter (MLA) on the MErcury, Surface, Space ENviorment, GEochemistry, and Ranging (MESSENGER) spacecraft has acquired high-resolution topographic measurements of Mercury’s northern hemisphere. These measurements permit the quantification of surface roughness on Mercury over baselines between 500 m and 200 km. In contrast to previous studies of Mercury’s surface roughness, which have employed median differential surface slope, we calculate surface roughness as the root mean square (RMS) deviation of the difference in height. If the topography is self-affine or fractal, a power law can be fit to the RMS deviation as a function of baseline length. The exponent of this fit is called the Hurst exponent. This Hurst exponent describes whether or not a surface is self-affine, which occurs when processes produce a surface roughness that is inherently random.

The surface roughness of Mercury’s northern hemisphere reflects the observed bimodal nature of Mercury: the northern smooth plains have lower roughness values than the rougher heavily cratered terrain and intercrater plains. The relationship between RMS height and baseline length on Mercury shows two fractal sections, one between lengths of 500 m and 1 km, and another between lengths of 1 km and 20 km. We also find that the northern rise is indistinguishable from the surrounding smooth plains across all measured baselines, implying that the rise did not alter its surface topography at the baselines used in this study. Craters that host radar-bright deposits have similar roughness values to craters that do not host such deposits. Finally, fresh crater ejecta within the smooth plains have similar roughness values (particularly at the 1 km baseline) to the intercrater plains, supporting the interpretation that the intercrater plains may result from the modification of volcanic plains via cratering.