Waveform correlation principles
The signals from a seismic event are normally detected by measuring an increase in the amplitudes recorded on a seismic trace. This is typically achieved by calculating a running signal-to-noise ratio (SNR). If the exact shape of a waveform were to be known in advance – ripple for ripple – we would be able to detect much weaker signals, buried deep in the background noise, by cross-correlating the incoming data with a waveform template. This is known as a matched signal detector. These have not been employed very frequently in the field of detection seismology because there are very few occasions in which the shape of a signal is known a priori. There are however many situations where almost identical signals have been observed from subsequent closely spaced events; this is to say that the seismic signal at a given sensor is like a geophysical fingerprint for earthquakes or explosions at a given site. In the same way that a human fingerprint at the scene of a crime, which matches a fingerprint record, can identify a likely suspect, a seismic signal which closely matches a previous observation can be used as evidence that the newly observed event must have occurred very close to the event which generated the first observation.
The principle is demonstrated in the plot below. The signal from a magnitude 3.5 earthquake in northern Norway in June 2005, recorded at a station in southern Norway, was extracted and used as a template. The template is then cross-correlated with continuous data from the same sensor, and any new occurrences of a similar signal will result in a relatively high value of the correlation coefficient. Two peaks within a minute of each other were detected in December of the same year, and data from a much closer station was able to confirm that there were in fact two separate events at the times indicated by these peaks, very close to the June 2005 event. Full details of this study are given by Gibbons et al. (2007).
Signal from a magnitude 3.5 earthquake cross-correlated
with continuous data from the same sensor.
There may be many situations where waveform correlation can be used to characterize aftershock sequences or to detect very small explosions (see Stevens et al., 2006). Most of the stations operated by NORSAR are arrays with many closely spaced seismometers. Stacking the cross-correlation traces from all the sites in an array, or even over many arrays or large networks, can lead to a very large improvement to the detectability of small events (see Gibbons and Ringdal, 2006). The reason for this is that when two seismic events are co-located, the times separating the corresponding patterns in the resulting wave trains are identical for all stations and this property can also be exploited to expose and sometimes measure timing errors on individual sensors (Gibbons, 2006).
References
Gibbons, S. J. (2006) “On the Identification and Documentation of Timing Errors: An Example at the KBS Station, Spitsbergen”, Seism. Res. Lett., 77, 559-571.
Gibbons, S. J. and Ringdal, F. (2006) “The detection of low magnitude seismic events using array-based waveform correlation”, Geophys. J. Int., 165, 149-166.
Stevens, J. L., Gibbons, S., Rimer, N., Xu, H., Lindholm, C., Ringdal, F., Kværna, T., and Murphy, J. R. (2006) “Analysis and simulation of chemical explosions in non-spherical cavities in granite” J. Geophys. Res., 111, B04306, doi:10.1029/2005JB003768.
Gibbons, S. J., Bøttger Sørensen, M., Harris, D. B., and Ringdal, F. (2007) “The detection and location of low magnitude earthquakes in northern Norway using multi-channel waveform correlation at regional distances”, Phys. Earth Planet. Inter., 160, 285-309.
Reprints of all publications can be obtained by sending an email to info@norsar.no.
Acknowledgements
This material is based upon work supported by the United States Department of Energy (National Nuclear Security Administration) under Award Number DE-FC52-05NA26604.
The data from the local station at Stokkvågen, Norway, displayed in the above plot are courtesy of the Norwegian National Seismic Network, operated by the Department of Earth Science at the University of Bergen.
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