Earthquake Detection Using Benford's Law

Reliable detection of local earthquakes and accurate identification of P-wave onsets are fundamental tasks in seismology, yet many existing methods to accomplish them require extensive parameter tuning or large training datasets. In this study, we investigate the applicability of Benford's Law - a logarithmic distribution governing the occurrence of leading digits in naturally occurring data - as a statistical framework for local earthquake detection. We analyze continuous seismic waveform data from two contrasting tectonic environments in the Indian subcontinent: the intraplate Deccan Volcanic Province and the actively deforming Himalayan region. Using a sliding-window approach, we quantify the temporal conformity of first-digit distributions of seismic amplitudes to Benford's Law and apply an adaptive normalization scheme to account for station-specific noise. Our results show that local earthquake waveforms consistently conform to Benford's Law during the onset of seismic energy, while pre-event noise does not. Benford-derived statistical anomalies align closely with theoretical P-wave arrival times, with detection performance primarily controlled by window length. These results establish Benford's Law as a computationally inexpensive, parameter-light, and training-free tool for local earthquake detection.