An Empirical Approach to Subspace Detection

Abstract

Waveform cross‐correlation detection methods, or match filter techniques (Van Trees, 1968), exploit waveform similarity for proximal events, and have proven to be a powerful approach for detecting and characterizing seismic events. Among the advantages over more traditional techniques is the ability to detect in adverse observational conditions either when events are closely spaced in time, such that waveforms overlap, or when the signal‐to‐noise ratio (SNR) is much less than unity because signal strength is low. Correlation methods can also be used for precise measurements of relative arrival time (e.g., Schaff et al. , 2004) and relative amplitude (Rubinstein and Ellsworth, 2010) in support of precise relative location and relative size measurements. A complete and precise measurement of seismic events is critical for understanding earthquake processes, and as a result, the use of correlation‐based detection methods is growing rapidly. They have been used on mining‐induced seismicity (Gibbons and Ringdal, 2006), in nuclear test ban treaty verification research (Rowe et al. , 2012), to understand tectonic tremor as a swarm of low‐frequency earthquakes (Shelly et al. , 2006, 2007), and to increase the number of detected early aftershocks by more than an order of magnitude (Peng and Zhao, 2009). They have also been applied to detect previously unobserved earthquakes in situations of suspected induced seismicity (van der Elst et al. , 2013). Waveform matching is not always applicable because it requires prior identification of template events that are highly similar to the event(s) of interest. The subspace detection method is a generalization of template detection that exploits features common to a design set of earthquakes (Harris, 2006; Harris and Paik, 2006). Subspace detection uses the singular value decomposition (SVD) of the design set of waveforms to find an orthonormal representation (left singular vectors) that efficiently captures the important common characteristics of the waveforms. …