Factors controlling landslide frequency-area distributions

A power‐law relation for the frequency–area distribution (FAD) of medium and large landslides (e.g. tens to millions of square meters) has been observed by numerous authors. But the FAD of small landslides diverges from the power‐law distribution, with a rollover point below which frequencies decrease for smaller landslides. Some studies conclude that this divergence is an artifact of unmapped small landslides due to lack of spatial or temporal resolution; others posit that it is caused by the change in the underlying failure process. An explanation for this dilemma is essential both to evaluate the factors controlling FADs of landslides and power‐law scaling, which is a crucial factor regarding both landscape evolution and landslide hazard assessment. This study examines the FADs of 45 earthquake‐induced landslide inventories from around the world in the context of the proposed explanations. We show that each inventory probably involves some combination of the proposed explanations, though not all explanations contribute to each case. We propose an alternative explanation to understand the reason for the divergence from a power‐law. We suggest that the geometry of a landslide at the time of mapping reflects not just one single movement but many, including the propagation of numerous smaller landslides before and after the main failure. Because only the resulting combination of these landslides can be observed due to a lack of temporal resolution, many smaller landslides are not taken into account in the inventory. This reveals that the divergence from the power‐law is not necessarily attributed to the incompleteness of an inventory. This conceptual model will need to be validated by ongoing observation and analysis. Also, we show that because of the subjectivity of mapping procedures, the total number of landslides and total landslide areas in inventories differ significantly, and therefore the shapes of FADs also differ considerably.