PageRank for Earthquakes

Ana C. Aguiar, & Gregory C. Beroza

In Preparation 2013, SCEC Contribution #1803

We have analyzed Hi-Net seismic waveform data during the April 2006 tremor episode in the Nankai Trough in SW Japan using the autocorrelation approach of Brown et al. (2008), which detects low frequency earthquakes (LFEs) based on pair-wise waveform matching. We have generalized this to exploit the fact that waveforms may repeat multiple times, on more than just a pair-wise basis. We are working towards developing a sound statistical basis for event detection, but that is complicated by two factors. First, the statistical behavior of the autocorrelations varies between stations. Analyzing one station at a time assures that the detection threshold will only depend on the station being analyzed. Second, the positive detections do not satisfy "closure." That is, if window A correlates with window B, and window B correlates with window C, then window A and window C do not necessarily correlate with one another. We want to evaluate whether or not a linked set of windows are correlated due to chance. To do this, we map our problem on to one that has previously been solved for web search, and apply Google’s PageRank algorithm. PageRank is the probability of a “random surfer” to visit a particular web page; it assigns a ranking for a webpage based on the amount of links associated with that page. For windows of seismic data instead of webpages, the windows with high probabilities suggest likely LFE signals. Once identified, we stack the matched windows to improve the SNR and use these stacks as template signals to find other LFEs within continuous data. We compare the results among stations and declare a detection if they are found in a statistically significant number of stations, based on multinomial statistics. We compare our detections using the single-station method to detections found by Shelly et al. (2007) for the April 2006 tremor sequence in Shikoku, Japan. We find strong similarity between the results, as well as many new detections that were not found using templates from known LFEs. This approach should improve our ability to detect LFEs within weak tremor signals where they are not already identified, and should be broadly applicable to earthquake swarms and sequences.

Citation
Aguiar, A. C., & Beroza, G. C. (2013). PageRank for Earthquakes. Seismological Research Letters, (in preparation).