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

Abstract

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.Plain Language Summary Measures of topographic roughness are important as they can be used to better understand the fundamental processes shaping planetary surfaces and map regional variations of texture or identify geomorphologic units. Here we use a new approach to characterize the roughness of the Moon, which involves the comparison of a theoretical wavelet to topographic measurements. From this comparison we can identify at which scales the topographic roughness changes in properties and quantify these properties. We find that the roughness has distinct characteristics in three scale ranges: 330-659 m, 1.3-21.1 km, and 42.2-168.8 km. For example, at scales lower than 659 m, mare basalt surfaces appear to become rougher with age as they contain more 330-to 659-m-diameter craters, whereas between 1.3 and 21.1 km, contiguous geological units exhibit different levels of roughness, which allows to delineate them. The new approach to characterize the surface roughness has successfully been applied and validated on the Moon and can thus be confidently used to better understand the processes shaping other less studied planetary surfaces and aid in their geologic mapping.

Hemispherical differences in the shape and topography of asteroid (101955) Bennu

“…Surface roughness can be used to infer differences in the geological processes that have acted on a surface. This approach has been used to analyze several planetary bodies [e.g., (21)(22)(23)(24)(25)]. As a measure of surface roughness, we divided the complete OLA point cloud-which was decimated to make the 20-cm GDTM, and therefore coregistered with it-into surface patches and assessed the standard deviation (SD) between the OLA returns within each patch.…”

Comparison of Topographic Roughness of Layered Deposits on Mars

“…The sizes of the calculation windows were restrained to 60 m (5 pixels; ~1/2 of 100 m), 132 m (11 pixels; ~1/8 of 1 km), and 252 m (21 pixels; ~1/4 of 1 km) as a trial to reduce the blocky appearance of roughness caused by large windows [36]. This scale selection accorded with the criteria that the scales for wavelet analysis must differ by factors of 2 [22,39].…”

Reunderstanding Geomorphological Features in Chang'e-5 Sampling Region Based on Multiscale Roughness Model

“…Image transform is a useful tool for two-dimensional image analysis [45]. Since DEM is a three-dimensional representation of terrain and can be considered as a two-dimensional image, the transform-based methods are developed and applied for terrain analysis of the solid planets [28,40]. Based on the theories of these studies, topographic signatures can be described by a series of frequency components.…”

“…Generally, the topographic signatures can be extracted by Fourier or wavelet roughness methods [30,40]. In these methods, terrain can be described by a series of frequency components.…”