Testing Kalman Smoothing/PCA Transient Signal Detection Using Synthetic Data

Kang Hyeun Ji, & Thomas A. Herring

Published 2013, SCEC Contribution #1834

The Southern California Earthquake Center (SCEC), a community of researchers from over 60 institutions worldwide, has made efforts to understand earthquakes and mitigate earthquake risk in southern California and elsewhere. The broad objective of SCEC’s tectonic geodesy disciplinary activities is to make available a variety of geodetic data collected in southern California and use these data for addressing problems associated with deformation processes. One of the topics of interest for fulfilling this objective is to “develop a geodetic network‐processing system that will detect anomalous strain transients” (Murray‐Moraleda and Lohman, 2010).
Our detection method consists of smoothing based on Kalman filtering and principal component analysis (PCA) (Ji and Herring, 2013). Smoothing improves the signal‐to‐noise ratio (SNR) in the time domain by reducing the white noise with adjustments for steady motions and temporally correlated noise, whereas PCA improves the SNR in the space domain by accounting for the spatial coherence of transient signals. This method is based purely on data without any source‐specific model, in contrast to the Network Inversion Filter (Segall and Matthews, 1997; McGuire and Segall, 2003) that requires definition of fault geometry and typically assumes elastic deformation. Inaccurate fault geometry or inelastic deformation may lead to unreliable fault‐slip estimates and limit the detection capability of the filter. The Network Strain Filter (NSF) proposed by Ohtani et al. (2010) is similar to our method in that it avoids source‐specific models and uses Kalman filtering. However, for spatially coherent transient deformation the NSF uses predefined wavelets that are included in the Kalman filter, whereas our method uses data‐based eigenvectors from PCA after Kalman filtering.

SCEC has supported a project, the transient‐detection exercise, in which participants applied their detection methods to synthetic Global Positioning System (GPS) daily‐position time series and reported back on any transient signals they detected. Because the data characteristics are known ex post facto, participants have evaluated and improved their methods. Here we present our detection procedure and discuss strengths and weaknesses of the method learned from the SCEC test results. Analyses of the test results have led to improvements in the detection method and we discuss reprocessed results here.

Citation
Ji, K., & Herring, T. A. (2013). Testing Kalman Smoothing/PCA Transient Signal Detection Using Synthetic Data. Seismological Research Letters, 84(3), 433-443. doi: 10.1785/0220120155.