LANDSLIDES ARE SCALE SPECIFIC

Efforts towards estimation of landslide erosion rates and hazard prediction require a firm understanding of the statistical distribution of landslides. It has been suggested that the distribution of slope failures follows a negative power function of the failure size (in terms of area). This implies that landslides are a scale invariant process, meaning that the frequency of landslides is entirely dependent on their size, with no particular size being preferentially observed. However it has also been noted that this power law scaling description is only appropriate for the largest ~25% of landslides. In contrast, we show here that a log-normal distribution comprehensively and accurately describes the full range of landslides sizes for the Northridge and Gorkha coseismal landslide inventories. Furthermore, we present general statistical evidence which strongly suggests that previous inventories are best characterized by log-normal distributions. The implication of the log-normal description of landslides goes beyond a purely statistical improvement. While the commonly accepted power law distribution implies that slope failures are self-similar and scale invariant, a log normal distribution underscores the importance of scale. There is a range of magnitudes centered on a specific scale (the “mean” of the log normal distribution), for which landslides are preferentially observed. To either side of this scale, landslides become increasingly less frequent in a predictable way (given by the standard deviation of the distribution). We interpret this symmetrical decay as a trade-off between the physical parameters which control slope stability. While large slope failures are infrequent due to the scarcity of large, high angle hillslopes, the smallest landslides are equally uncommon due to a disparity between the cohesive strength of hillslope material and the weak driving forces on small slopes.