Adaptive Waveform Correlation Detectors for Arrays: Algorithms for Autonomous Calibration

Waveform correlation detectors compare a signal template with successive windows of a continuous data stream and report a detection when the correlation coefficient, or some comparable detection statistic, exceeds a specified threshold. Since correlation detectors exploit the fine structure of the full waveform, they are exquisitely sensitive when compared to power (STA/LTA) detectors. The drawback of correlation detectors is that they require complete knowledge of the signal to be detected, which limits such methods to instances of seismicity in which a very similar signal has already been observed by every station used. Such instances include earthquake swarms, aftershock sequences, repeating industrial seismicity, and many other forms of controlled explosions. The reduction in the detection threshold is even greater when the techniques are applied to arrays since stacking can be performed on the individual channel correlation traces to achieve significant array gain. In previous years we have characterized the decrease in detection threshold afforded by correlation detection across an array or network when observations of a previous event provide an adequate template for signals from subsequent events located near the calibration event. Last year we examined two related issues: (1) the size of the source region calibration footprint afforded by amore » master event, and (2) the use of temporally incoherent detectors designed to detect the gross envelope structure of the signal to extend the footprint. In Case 1, results from the PETROBAR-1 marine refraction profile indicated that array correlation gain was usable at inter-source separations out to one or two wavelengths. In Case 2, we found that incoherent detectors developed from a magnitude 6 event near Svalbard were successful at detecting aftershocks where correlation detectors derived from individual aftershocks were not. Incoherent detectors might provide 'seed' events for correlation detectors that then could extend detection to lower magnitudes. This year we addressed a problem long known to limit the acceptance of correlation detectors in practice: the labor intensive development of templates. For example, existing design methods cannot keep pace with rapidly unfolding aftershock sequences. We successfully built and tested an object-oriented framework (as described in our 2005 proposal) for autonomous calibration of waveform correlation detectors for an array. The framework contains a dynamic list of detectors of several types operating on a continuous array data stream. The list has permanent detectors: beam forming power (STA/LTA) detectors which serve the purpose of detecting signals not yet characterized with a waveform template. The framework also contains an arbitrary number of subspace detectors which are launched automatically using the waveforms from validated power detections as templates. The implementation is very efficient such that the computational cost of adding subspace detectors was low. The framework contains a supervisor that oversees the validation of power detections, and periodically halts the processing to revise the portfolio of detectors. The process of revision consists of collecting the waveforms from all detections, performing cross-correlations pairwise among all waveforms, clustering the detections using correlations as a distance measure, then creating a new subspace detector from each cluster. The collection of new subspace detectors replaces the existing portfolio and processing of the data stream resumes. This elaborate scheme was implemented to prevent proliferation of closely-related subspace detectors. The method performed very well on several simple sequences: 2005 'drumbeat' events observed locally at Mt. St. Helens, and the 2003 Orinda, CA aftershock sequence. Our principal test entailed detection of the aftershocks of the San Simeon earthquake using the NVAR array; in this case, the system automatically detected and categorized approximately 2/3 of the events above magnitude 2.8.« less