ASSESSING LANDSLIDE INVENTORY COMPLETENESS UTILIZING BENFORD’S LAW

Landslide inventories provide insight into the frequency and location of their occurrence and can help validate landslide hazard models or susceptibility maps. However, most regional landslide inventories, such as those that occur during a storm event, are incomplete. By contrast, earthquake-triggered landslide inventories are typically more complete, especially those that utilize high resolution pre- and post-event digital elevation models. Earthquake-triggered landslide inventories allow us to explore alternative approaches to evaluate completeness of storm-triggered landslide inventories, which occur far more frequently across broader regions of the globe. Landslide inventories have typically been evaluated using frequency area distribution, where the large and medium landslides follow a power law distribution with a divergence for smaller landslides (decreased frequency). This divergence has been controversial and has been attributed to mapping errors, low spatial and temporal resolution, or physical failure processes. Here we propose a simpler method for assessing inventory completeness that is both scale- and base-invariant. Benford’s law predicts the frequency of first digits in empirical data sets (e.g., 1 occurs 30.1% of the time, 2 occurs 17.6%, etc.,), deviation from which indicates incomplete data sets due to either the population not being represented by the sample, or data or rounding errors. Of the globally distributed earthquake-induced landslide inventories we considered, 80% largely conformed to Benford’s Law. In the U.S., state-wide inventories are known to be incomplete, but sub-sets of these inventories in smaller, targeted areas (e.g., at county level) mapped with established protocols seem to conform well to Benford’s law. These results suggest that Benford’s law is a promising approach for evaluating landslide inventory completeness.