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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

The Wavelet Leaders Method (WLM) is a wavelet‐based multifractal formalism that allows the identification of scale breaks (thus scaling regimes), the definition of scaling properties (mono versus multi fractality of the surface), and the calculation of the Hölder exponent that characterizes each pixel, based on the comparison between a theoretical wavelet and topographic values. Here we use the WLM and the SLDEM2015 digital elevation model to provide a near‐global and a local isotropic characterization of the lunar roughness. The near‐global study of baselines between 330 m and 1,350 km reveals scale breaks at ~1.3, 42.2, and 337.6 km. Scaling properties and Hölder exponent values were calculated for the three corresponding scaling regimes: 330–659 m, 1.3–21.1 km, and 42.2–168.8 km. We find that the dichotomy between the highlands and the maria is present at all scales. Between 330 and 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 and 21.1 km, it shows the unique signature of the Orientale basin and a relationship with the density of 5‐ to 20‐km‐diameter craters. Scaling properties and Hölder exponent values were also calculated locally for complex craters, basins, rilles and light plains, for two scaling regimes: 165–659 m and 1.3–21.1 km. Relationships between the Hölder exponent values at 165–659 m, the density of <500‐m‐diameter craters and different geologic units were found and a potential scale break near 165 m was identified.