Measuring bedload motion time at sub-second scale using Benford's law from long-term acoustic recordings

Bedload transport is a natural process that strongly affects the Earth’s surface system. An important component of quantifying bedload transport and establishing early warning systems is obtaining the parameters at the onset of bedload motion. Bedload transport can be monitored with passive acoustic methods, e.g., hydrophones. Yet, an efficient method for identifying the onset of bedload transport from long-term continuous acoustic data is still lacking. Benford’s Law defines the specific frequency distribution of the first digits of datasets that have been used to distinguish stochastic from chaotic processes in nature when this process causes higher energy events than baseline. Here, we apply Benford’s law to continuous acoustic recordings from Baiyang hydrometric station, a tributary of Liwu River, Taiwan at the frequency of 32 kHz from stationary hydrophones deployed for three years since 2019. We construct a workflow to parse sound combinations of bedload transportation and analyze them in the context of hydrometric sensing constraining the onset, and recession of bedload transportation. We identify two bedload transportation events that lasted 17 and 45 hours, respectively, covering about 0.35% of the time per year. Our workflow allows filtering 99% of background signal and focuses on two events including bedload motions. Given that fluvial seismology has successfully monitored fluvial processes, continuous monitoring in three directions (N-S, W-E, vertical) brings board discussion orientations, e.g., the direction of source or migration of mass movement. Therefore, we suggest that the application of Benford’s law on seismic data of Earth's surface processes has great potential.