Earthquake Fingerprints: Extracting Waveform Features for Similarity-Based Earthquake Detection

Abstract

Seismologists are increasingly adopting data mining and machine learning techniques to detect weak earthquake signals in large seismic data sets. The detection performance of these new methods, especially their sensitivity and false detection rate, depends on the choice of feature representation for waveform data. We have previously introduced Fingerprint and Similarity Thresholding (FAST), a new method for waveform-similarity-based earthquake detection that uses a pattern mining approach to detect earthquake signals without template waveforms. FAST has two key steps: fingerprint extraction and efficient indexing for similarity search. In this work, we focus on FAST fingerprint extraction: the method used to map short-duration waveforms to a set of features, called waveform fingerprints, used for detection. We describe the FAST fingerprint extraction method, a data-adaptive variation on the Waveprint audio fingerprinting method tailored for use in continuous seismic data. We compare the performance of the FAST fingerprint extraction method with existing fingerprinting techniques designed for audio identification. To overcome the challenges associated with using limited or incomplete event catalogs to evaluate detection algorithms, we propose a framework for quantifying the performance of different fingerprint extraction methods in the context of blind similarity-based detection. Our framework uses computational experiments on benchmark data sets, constructed with known event waveforms, to compute a measure of fingerprint effectiveness. We use this framework to show that, among the audio fingerprinting schemes considered in this work, our proposed FAST fingerprint extraction method achieves the most consistent performance in distinguishing similar, low signal-to-noise earthquake waveforms from noise in waveform data sets from eight stations in the Northern California Seismic Network.

Appendix

1.1 Signal-to-Noise Ratio

In this work, the signal-to-noise ratio (SNR) is computed using a 15-s interval of waveform data following the P-wave arrival. For signal x and noise n, each of duration $M = 300$ samples (15 s of data sampled at 20 samples per second), the SNR is given by:

$$\begin{aligned} SNR = \frac{P_{{\text {signal}}}}{P_{{\text {noise}}}}, \quad {\text {where}} \quad P_{{\text {signal}}} = \frac{1}{M} \sum \limits _{i=0}^{M} | x[i] |^{2}, \; {\text { and }}\; P_{{\text {noise}}} = \frac{1}{M} \sum \limits _{i=0}^{M} | n[i] |^{2}. \end{aligned}$$

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1.2 Noise Segment Classification

Noise segments are assigned one of these three labels based on two criteria: (1) an STA/LTA threshold, and (2) a uniform energy criterion that quantifies how uniform the energy is across the 2-min interval. A noise segment is labeled as “clean” noise if the maximum STA/LTA ratio in the interval is below 3.0 and the uniform energy score is below 0.1. A noise segment is labeled as “non-noise” if the maximum STA/LTA ratio in the interval exceeds 6.0 or the uniform energy score exceeds 0.2. All other noise segments are labeled “lively” noise. The parameters for short and long windows used in the STA/LTA ratio are 3 and 45 s, respectively. The uniform energy score, $u^{(j)}$, associated with a noise segment $n^{(j)}$ of length M samples is defined as:

$$\begin{aligned} u^{(j)} = \frac{1}{M}\sum \limits _{k=1}^{M} \left| \, s^{(j)}[k] - \frac{k}{M} \, \right| , \quad \text {where} \quad s^{(j)}[k] = \sum _{i=1}^{k}\left( n^{(j)}[i] \right) ^{2}, \end{aligned}$$

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and $n^{(j)}$ is normalized such that $|| n^{(j)} ||^{2}_{2} = 1$. This value represents the difference between the cumulative signal energy over the interval and the cumulative energy for a signal with uniform energy, and u takes values between 0 and 0.5, with larger values associated with larger deviations from uniform signal energy.

1.3 Events in Benchmark Data Set, by Station

The list of events in the benchmark data set and the corresponding earthquake waveform and noise data matrices, by station, are available upon request (see Figs. 12, 13).

Fig. 12

Map plots show the epicenter locations for the events in the earthquake waveform benchmark data set for stations NC.CCOB, NC.MCB, NC.GDXB, and NC.CBR. The location of each station is marked with a blue triangle, and the event epicenters are shown in red. The set of earthquakes is selected independently for each station depending on whether a P-phase arrival was recorded in the NCSN phase-pick catalog for a given event

Fig. 13

Map plots show the epicenter locations for the events in the earthquake waveform benchmark data set for stations BK.CVS, BK.JRSC, BK.PKD, and BK.SAO. The location of each station is marked with a blue triangle, and the event epicenters are shown in red. The set of earthquakes is selected independently for each station depending on whether a P-phase arrival was recorded in the NCSN phase-pick catalog for a given event