Lois d’échelles et propriétés statistiques multifractales de la topographie des planètes

Abstract : Over the past 20 years, the development of remote sensing methods and the success of space missions have considerably enriched our knowledge of planetary surfaces revealing an immense diversity of morphologies. Being the reflection of the interaction and the competition between geological processes whose modalities are variable from one body to the other, they are widely studied to trace the geological history of the telluric planets. In particular, precise information on the nature of processes and general laws controlling the formation and evolution of landscapes is recorded in the topographic field which can be analyzed as a statistical field. We report in this thesis the results of a comparative study of the statistical properties of the topography of the main bodies of the solar system based on the increasing volume of altimetric and photogrammetric data. Our approach focuses on the notion of scaling law which aims to characterize the symmetries of the field by translating the self-similar nature of natural surfaces: the details of a surface generally look like reduced versions of the whole. We use several methods of analyzing so-called "multifractal" to derive the best statistical model capable of describing the topography in different contexts and propose new indicators of roughness at the global, regional and local scale. We show that in spite of their diversity, the surface of the solar system respects similar statistical laws. In particular, we show that the overall distribution of the slopes of a body generally respects multifractal laws for scales greater than 10-20 km and presents a different statistical structure for the lower scales. Finally, we propose a method for generating spherical synthetic topographies whose statistical properties are similar to the topographies in the solar system.
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Submitted on : Friday, February 2, 2018 - 5:38:08 PM
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François Landais. Lois d’échelles et propriétés statistiques multifractales de la topographie des planètes. Planétologie et astrophysique de la terre [astro-ph.EP]. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLS453⟩. ⟨tel-01699851⟩



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