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. Plain Language Summary Natural hazards, such as debris flows and landslides, pose a significant threat to the exposed communities. Seismic instruments are seen as effective tools for detecting these hazardous processes and may be used in early warning systems. However, the difficulty lies in identifying the events of interest concisely and objectively. Our study explores Benford's law, describing the relative occurrence of the first non‐zero digit. We collected seismic data generated by various hazard events and compared the observed first‐digit distribution with their agreement with Benford's law. We found seismic signals of debris flows follow Benford's law during the run‐out phase, while ambient noise do not. Our detector, based on Benford's law and designed for debris flow, which is a computationally cheap and novel model, performs similarly to a machine learning algorithm previously used in the study site. Our work illustrates a new approach to detecting events and designing warning systems. Key Points The first‐digit distribution of seismic signal