Scale-Invariance in the Spatial Development of Landslides in the Umbria Region (Italy)

摘要

Understanding the spatial distribution of mass movements is a major issue in the management and forecasting of landslide risk. In this context, the present study examines the most widespread types of landslide in the Umbria region (central Italy), that is, slides and flows, in order to establish if it is possible to identify a well-defined structure in their spatial pattern. By using the landslide inventory map available for the area and by resorting to the principles of fractal theory, the scaling properties of the landslide sample were investigated. The application of the box-counting algorithm to the maps of landslide triggering points and landslide areas allowed for the identification of a clear scale-invariant structure. Two distinct types of fractal behaviour were recognized, separated by a scale value of 1 km and characterized by capacity dimensions of 1.35 and 1.76, in the ranges of 25 m-1 km and 1-16 km, respectively. The comparison between the scaling exponents obtained from a map of points and one of areas, and the elaboration of the cumulative frequency distributions of landslide areas supported the interpretation of this result: the higher capacity dimension describes the spatial distribution of landslides in the Umbria region, while the lower contains additional information about their geometries, suggesting that the latter also possess scaling properties. Based on the finding of two different types of behaviour of landslides in space, the hypothesis is discussed that the contribution of each causal factor (i.e., predisposing and triggering factors) to the occurrence of landslide events and to their spatial development could be different in the two scale ranges identified, depending on its spatial variability at local and regional scale. According to this hypothesis, factors with high local variability (i.e., topographic attributes) would mainly affect the assortment of landslide geometries, while those with high regional variability (e.g., rainfalls and lithology) would mainly affect the pattern of the landslides.