Why Waveform Correlation Sometimes Fail

Abstract:

Waveform correlation detectors used in explosion monitoring scan noisy geophysical data to test two competing hypotheses: either (1) an amplitude-scaled version of a template waveform is present, or, (2) no signal is present at all. In reality, geophysical wavefields that are monitored for explosion signatures include waveforms produced by non-target sources that are partially correlated with the waveform template. Such signals can falsely trigger correlation detectors, particularly at low thresholds required to monitor for smaller target explosions. This challenge is particularly formidable when monitoring known test sites for seismic disturbances, since uncatalogued natural seismicity is (generally) more prevalent at lower magnitudes, and could be mistaken for small explosions. To address these challenges, we identify real examples in which correlation detectors targeting explosions falsely trigger on both site-proximal earthquakes (Figure 1, below) and microseismic "noise". Motivated by these examples, we quantify performance loss when applying these detectors, and re-evaluate the correlation-detector's hypothesis test. We thereby derive new detectors from more general hypotheses that admit unknown background seismicity, and apply these to real data. From our treatment, we derive "rules of thumb'' for proper template and threshold selection in heavily cluttered signal environments. Last, we answer the question "what is the probability of falsely detecting an earthquake collocated at a test site?", using correlation detectors that include explosion-triggered templates.

Figure Top: An eight-channel data stream (black) recorded from an earthquake near a mine. Red markers indicate a detection. Middle: The correlation statistic computed by scanning the template against the data stream at top. The red line indicates the threshold for event declaration, determined by a false-alarm on noise probability constraint, as computed from the signal-absent distribution using the Neyman Pearson criteria. Bottom: The histogram of the correlation statistic time series (gray) superimposed on the theoretical null distribution (black curve). The line shows the threshold, consistent with a right-tail probability, computed from the black curve.