Benford's Law as Debris Flow Detector in Seismic Signals

Seismic instruments placed outside of spatially extensive hazard zones can be used to rapidly sense a range of mass movements. However, it remains challenging to automatically detect specific events of interest. Benford's law, which states that the first non-zero digit of given data sets follows a specific probability distribution, can provide a computationally cheap approach to identifying anomalies in large data sets and potentially be used for event detection. Here, we select vertical component seismograms to derive the first digit distribution. The seismic signals generated by debris flows follow Benford's law, while those generated by ambient noise do not. We propose the physical and mathematical explanations for the occurrence of Benford's law in debris flows. Our finding of limited seismic data from landslides, lahars, bedload transports, and glacial lake outburst floods indicates that these events may follow Benford's Law, whereas rockfalls do not. Focusing on debris flows in the Illgraben, Switzerland, our Benford's law-based detector is comparable to an existing random forest model that was trained on 70 features and six seismic stations. Achieving a similar result based on Benford's law requires only 12 features and single station data. We suggest that Benford's law is a computationally cheap, novel technique that offers an alternative for event recognition and potentially for real-time warnings.