An Empirical Approach to Subspace Detection

Sarah A. Barrett, & Gregory C. Beroza

Published 2014, SCEC Contribution #1800

Subspace detection uses the singular value decomposition of a design set of waveforms to find orthonormal representations (left singular vectors) that portray common characteristics of the seismograms. The first singular vector carries the dominant information common to the group of events, and as a result, closely resembles the stack of the design set. For a dense cluster of earthquakes, the second singular vector contains information representative of slight offsets in event location. This vector closely resembles the time derivative of the stack. Successive singular vectors contain information that is less important to representing the entire group. The singular vectors can be scanned through a continuous record, much like template matching, to identify earthquakes missing from the catalog. We use an empirical representation of the subspace by building a matrix comprised of two rows: the stack and the stack derivative, weighted by their respective singular values, to scan through the continuous catalog. We show an application to a Southern California sequence in which the use of an empirical subspace detects more uncataloged events with a lower false detection than using a stack alone. We suggest that template detection might be improved by using a matrix of the template and its time derivative with minor additional computational cost.

Barrett, S. A., & Beroza, G. C. (2014). An Empirical Approach to Subspace Detection. Seismological Research Letters, 85(3), 594-600.