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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.

Detecting and picking the onset of P-waves in seismic signals has a fairly rich literature, among which model-based (predictive) approaches hold immense promise. A majority of these models are usually built on certain critical assumptions, namely, stationarity, linearity, and Gaussianity. Despite their criticality, very little reported literature exists on validating these assumptions on real seismic data. Furthermore, the predictive capabilities of these models are not utilized to their best potential in detection. Therefore, there exists a strong need for a rigorous approach to model seismic noise and develop a method that builds on the statistical properties of residuals resulting from the noise models. The objectives of this work are (i) to critically study certain long-held assumptions in seismic noise modeling, (ii) to develop rigorous time-series models for background noise that are commensurate with the noise properties, so as to (iii) devise a residual-based method for detection and enhanced picking of P-waves. An important finding of this work, arising from our study on 185 historical data sets, is that these standard assumptions do not hold for most of the data sets under study; rather, they exhibit additional special features such as heteroskedasticity and integrating effects. Consequent to these novel discoveries, we develop auto-regressive integrated moving average-generalized auto-regressive conditionally heteroskedastic (ARIMA-GARCH) models for seismic noise. The proposed residual-based detector and picker is found to be highly effective with a 90% detection rate while picking 91% of the events with an accuracy of ≤ 0.625 seconds based on tests with 100 historical data sets. Further, when the noise model is used in combination with the existing AIC-based pickers, the number of events picked with an accuracy of ≤ 0.625 seconds is 50% more than the existing AR-AIC picker. Therefore, the proposed method can be considered highly competitive and effective in P-wave detection and picking.