A prediction framework with time-frequency localization feature for detecting the onset of seismic events

Onset detection of P-wave in seismic signals is of vital importance to seismologists because it is not only crucial to the development of early warning systems but it also aids in estimating the seismic source parameters. All the existing P-wave onset detection methods are based on a combination of statistical signal processing and time-series modeling ideas. However, these methods do not adequately accommodate some advanced ideas that exist in fault detection literature, especially those based on predictive analytics. When combined with a time-frequency (t-f) / temporal-spectral localization method, the effectiveness of such methods is enhanced significantly. This work proposes a novel real-time automatic P-wave detector and picker in the prediction framework with a time-frequency localization feature. The proposed approach brings a diverse set of capabilities in accurately detecting the P-wave onset, especially in low signal-to-noise ratio (SNR) conditions that all the existing methods fail to attain. The core idea is to monitor the difference in squared magnitudes of one-step-ahead predictions and measurements in the time-frequency bands with a statistically determined threshold. The proposed framework essentially accommodates any suitable prediction methodology and time-frequency transformation. We demonstrate the proposed framework by deploying auto-regressive integrated moving average (ARIMA) models for predictions and the well-known maximal overlap discrete wavelet packet transform (MODWPT) for the t-f projection of measurements. The ability and efficacy of the proposed method, especially in detecting P-waves embedded in low SNR measurements, is illustrated on a synthetic data set and 200 real-time data sets spanning four different geographical regions. A comparison with three prominently used detectors, namely, STA/LTA, AIC, and DWT-AIC, shows improved detection rate for low SNR events, better accuracy of detection and picking, decreased false alarm rate, and robustness to outliers in data. Specifically, the proposed method yields a detection rate of 89% and a false alarm rate of 11.11%, which are significantly better than those of existing methods.