ANALYSIS OF THE TOPOGRAPHIC ROUGHNESS OF THE MOON USING THE WAVELET LEADERS METHOD AND THE LUNAR DIGITAL ELEVATION MODEL FROM THE LUNAR ORBITER LASER ALTIMETER AND SELENE TERRAIN CAMERA (Invited Presentation)

Measures of topographic roughness are important in planetary applications as they can be used to map regional variations of texture or identify geomorphologic units. They can also be used to better understand the fundamental processes shaping planetary surfaces. Here we use a new approach, the Wavelet Leaders Method (WLM), and the SLDEM2015 digital elevation model to provide a new global and local isotropic characterization of the lunar roughness. The WLM is a wavelet-based multifractal formalism that allows the identification of scale breaks (and scaling regimes), the definition of scaling properties (mono versus multi fractality) and the calculation of the Hölder exponent that characterizes each pixel. The SLDEM2015 was derived by co-registering high vertical precision Lunar Orbiter Laser Altimeter range measurements to high spatial resolution Terrain Camera stereo images. For our global analysis, we studied the roughness of baselines ranging between 330 m and 1,350 km. We identify scale breaks at 1.3, 42.2 and 337.6 km. We thus calculated the scaling properties and Hölder exponent values for three scaling regimes: 330–659 m, 1.3–21.1 km, and 42.2–168.8 km, which are representative of different major geological events. We find that the dichotomy between the highlands and the maria is present at all scales and that most of the surface has a monofractal behavior. Between 330–659 m, the Hölder exponent map shows the unique signature of Orientale basin, rilles and a correlation with the age of mare units. Between 1.3–21.1 km, it shows the unique signature of the Orientale basin and a relationship with the density of 5-20 km diameter craters. We also conducted a local analysis of complex craters, basins, rilles and light plains at baselines between 165–659 m and 1.3–21.1 km. For the former, we find that sloped terrains have the lowest Hölder exponent values and that the Hölder exponent values of complex crater ejecta is related to the density of <500 m diameter craters. In the case of basins, we clearly see the distinction between the different geologic units. A change in roughness properties of light plains and Orientale ejecta in the local (165-659 m) compared to the global (330-659 m) analysis suggests the presence of an additional scale break near 165 m which will need to be investigated further.