Semiempirical statistics of correlation-detector performance

Statistical analyses were conducted on the capability of correlation detectors for similar events. Semiempirical synthetic runs took a 50-sec window on an Lg wave recorded at 750-km distance filtered from 1 to 3 Hz and embedded it 300,000 times in real continuous background seismic noise. The noise was selected for 36 days spread throughout the year to capture diurnal and seasonal variations. No screening for random, unknown signals in the noise was performed. A correlation detector has a 50% probability of detection with 1.5 false alarms per day for a signal-to-noise ratio (SNR) of 0.32, which corresponds to a full magnitude unit reduction in detection threshold over a standard short-term average/long-term average (STA/LTA) technique. A scaled cross-correlation coefficient performs slightly better with one false alarm per day and has fewer false triggers on unknown, random signals. Summing the cross-correlation traces together for all three components enhances the detection signal similar to beamforming. A correlation detector summing the correlation traces for the three components together has a 96% probability of detection with zero false alarms in 36 days for an SNR of 0.32. The significant result of this study is that a correlation detector has more than an order of magnitude improvement in detection threshold for similar events with acceptably low false alarm rates to be used in practice.