Benford's law in detecting rapid mass movements with seismic signals

Rapid mass movements are a major threat in populated landscapes, as they can cause significant loss of life and damage civil infrastructure. Previous work has shown that using environmental seismology methods to monitor such mass movements and establish monitoring systems offers advantages over existing approaches. The first important step in developing an early warning system for rapid mass movements based on seismic signals is automatically detecting events of interest. Though the approach, such as short-term average to long-term average ratio (STA/LTA) and machine learning model, was introduced to detect events (e.g., debris flow and rockfall), it is still challenging to calibrate input parameters and migrate existing methods to other catchments. Detection of debris flows, for instance, is similar to anomaly detection if we consider the seismic stations recording background signals as an overwhelming majority condition. 
Benford's law describes the probability distribution of the first non-zero digits in numerical datasets, which provides a functional, computationally cheap approach to anomaly detection, such as fraud detection in financial data or earthquake detection in seismic signals. In this study, seismic signals generated by rapid mass movements were collected to check the agreement of the distribution of the first digit with Benford's law. Subsequently, we develop a computationally efficient and non-site-specific model to detect events based on Benford's law using debris flows from the Illgraben, a Swiss torrent, as an example. Our results show that seismic signals generated by high-energy mass movements, such as debris flows, landslides, and lahars, follow Benford's law, while those generated by rockfall and background signals do not. Furthermore, our detector performance in picking debris-flow events is comparable to a published random forest and seismic network-based approach. Our method can be applied at other sites to detect debris-flow events without additional calibration and offers the potential for real-time warnings.