Mapping landslides in lunar impact craters using Chebyshev polynomials and Dem's

Geological slope failure processes have been observed on the Moon surface for decades. However, a detailed and exhaustive lunar landslide inventory has not been produced yet. Since several space agencies are looking forward a new era of lunar exploration leading to the establishment of permanent manned stations and to the exploitation of lunar resources, the knowledge of landslide location is quite important. Despite the absence of water on the Moon and the different surface processes, the lunar slope failures can be classified in a similar way than the ones on the Earth’s surface. While, mechanisms can be compared, predisposing and triggering factors of landslides on the Moon are completely different. The major triggering factor could be considered the effect of impact cratering, process quite common on the Moon’s surface due to the lack of atmosphere. As a part of the “Moon Mapping” cooperative project between Italy and China, an approach for lunar landslide detection in impact craters has been proposed. The simple type of impact craters has been chosen as study case. For a preliminary survey, WAC (Wide Angle Camera) images and a 100 m x 100 m resolution digital elevation model (WACGDL100 DEM) both derived from LROC NASA mission have been exploited in combination with the criteria applied by Brunetti et al. (2015) to detect landslides on the Moon surface. These criteria are based on the visual analysis of optical images to recognize mass wasting features, which resulted in deviations from the initial crater shape. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sectional profiles in order to obtain a parametric characterization (Mahanti, et al., 2014) useful for classification into different morphological shapes. The Chebyshev polynomials have been used due their orthogonality properties and the low approximation error. Here a new implementation of Chebyshev polynomial approximation is proposed for estimating crater’s cross-sectional profiles, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analysing the contribution of odd coefficients of the estimated Chebyshev polynomials, since they are representing the asymmetric component of a transversal profile. Indeed, in the case a landslide had occurred inside a crater, the original shape of the crater should have been modified by adding an asymmetric component. After removing the effect of the terrain slopes and the crater bottom inclination, which may give a contribution to the general asymmetry of the crater shapes but they are not related to the presence of a landslide, the flatness of the profile obtained by using only the odd coefficients is analysed. As far as that such an unflatness is large, the probability that the crater hosts a landslide will be higher. As a measure of the profile unflatness the residuals with respect to a horizontal line are considered (see Figure 1). In this work two threshold methods were implemented to detect unflatness of the odd coefficient profile: an adaptive and a fixed threshold. Both of them presented very good results in the identification of landslides within a test conducted on a total number of 51 craters. After the analysis of four orthogonal profiles per crater, we correctly classified 87.7% of cross-sectional profiles really affected by slope failures by using the fixed thresholding. On the other side, we obtained a correct classification of 83.3% of cross-sectional profiles without slope failures, still using the same thresholding method. Even though a complete successful rate could not be achieved, these results are quite encouraging since the proposed automated procedure would allow to a first scrutiny of the presence of landslides in craters, to be refined afterwards with visual recognition and the analysis of other types of data, e.g., using multi-spectral images available from Chang’E-1 mission that are available through the “Moon Mapping” project.