Rigorous Predictive Noise Modeling Approach for Model-Based Onset Detection and Enhanced Picking of P-Waves in Seismic Signals

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.