Nonlinear Processes in Geophysics (Mar 2009)
Probability distributions of landslide volumes
Abstract
We examine 19 datasets with measurements of landslide volume, <I>V<sub>L</sub></I>, for sub-aerial, submarine, and extraterrestrial mass movements. Individual datasets include from 17 to 1019 landslides of different types, including rock fall, rock slide, rock avalanche, soil slide, slide, and debris flow, with individual landslide volumes ranging over 10<sup>−4</sup> m<sup>3</sup>≤<I>V<sub>L</sub></I>≤10<sup>13</sup> m<sup>3</sup>. We determine the probability density of landslide volumes, <I>p(V<sub>L</sub></I>), using kernel density estimation. Each landslide dataset exhibits heavy tailed (self-similar) behaviour for their frequency-size distributions, <I>p(V<sub>L</sub></I>) as a function of <I>V<sub>L</sub></I>, for failures exceeding different threshold volumes, <I>V<sub>L</sub></I>*, for each dataset. These non-cumulative heavy-tailed distributions for each dataset are negative power-laws, with exponents 1.0≤β≤1.9, and averaging β≈1.3. The scaling behaviour of <I>V<sub>L</sub></I> for the ensemble of the 19 datasets is over 17 orders of magnitude, and is independent of lithological characteristics, morphological settings, triggering mechanisms, length of period and extent of the area covered by the datasets, presence or lack of water in the failed materials, and magnitude of gravitational fields. We argue that the statistics of landslide volume is conditioned primarily on the geometrical properties of the slope or rock mass where failures occur. Differences in the values of the scaling exponents reflect the primary landslide types, with rock falls exhibiting a smaller scaling exponent (1.1≤β≤1.4) than slides and soil slides (1.5≤β≤1.9). We argue that the difference is a consequence of the disparity in the mechanics of rock falls and slides.
