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Unsupervised Approaches for Post-Processing in Computationally EfficientWaveform-Similarity-Based Earthquake Detection

Karianne Bergen1, Clara Yoon2, Ossian O’Reilly2, Gregory Beroza2

1Institute for Computational and Mathematical Engineering, Stanford University, 2Department of Geophysics, Stanford University email: kbergen@stanford.edu

Introduction

Fingerprint and Similarity Thresholding (FAST) promises to allow large-scaleblind search for similar waveforms in long-duration continuous seismic data [1].n Waveform similarity search applied to datasets of months to years of data will

identify significantly more low-magnitude events than traditional methods forearthquake detection.

n New approaches for processing the output from similarity-based detection arerequired - manual inspection is infeasible for large data volumes.

n We explore data mining techniques for improved detection post-processing.

FAST: Method Overview

FAST is inspired by the Waveprint [2] algorithm for identifying audio clips, adaptedto continuous seismic waveform data.

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Detec1onResults

Post-Processing

§  Iden6fyingevents§  Combiningovernetwork§  Removingfalseposi6ves§  Clusteringwaveforms

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DatabaseGenera1on&Search

Fastapproximatesimilaritysearchusing§ MinHashand§  LocalitySensi6veHashing

FASTAlgorithmicPipeline

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FeatureExtrac1on

SpectralImage

Topcoefficients(mostdiscrimina-ve)

BinaryFingerprint

HaarTransform

n Database search returns list of “candidate pairs” - post-processing is necessaryto eliminate non-earthquakes (false positives, correlated noise)

Event Identification and Network Detection

How do we identify earthquakes from waveform pairs returned by FAST?

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n Output of FAST(single channel): sparse matrix - (candidate) pairs of similar waveformsn Single event pairs often result in multiple detections: time-adjacent windows overlapn Multiple (sequential) detections of a single event pair appear along a diagonal line (fixed

inter-event time ∆t) in similarity matrixn Link all detections for each event pair for improved thresholding

How do we combine single-station detection results from FAST over a network of seismic stations?

n Network detection can improve detection sensitivityn Limited move-out (multiple channels at single sta-

tion or nearby stations): sum single-channel similar-ity matrices → network similarity matrix

n Challenge: move-out varies between stations and isunknown a priori in blind search

n Inter-event time is uniform across network for agiven event pair

n Pseudo-association: group detections by inter-event time (diagonal) across multiple stations

Data set: Iquique foreshocks, 2014-03-21 Time (s), from 831580 20 40 60

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Waveforms of event pair recordedacross multiple stations

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Similarity matrix: event pair detected across multiple stationsappears along same diagonal, but with minimal temporal overlap

Clustering Waveforms

Clustering is a set of techniques for identifying groups of similar waveforms within the full set of detections returned by FAST, which can be used to:n Organize detection results for easier interpretation (i.e. find interesting structure/patterns in the data),n Identify new template waveforms for template matching or subspace detection, andn Remove additional false alarms (e.g. outliers, non-earthquake clusters)

Application: Guy-Greenbrier Fault, central Arkansas

n FAST detects 746 new earthquakes that were not identified by templatematching in one month of data (July 2010) at station WHAR [3]

n Similarity matrix for new detections has a block-like structure - apply spectralclustering to identify 8 broad waveform clusters

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n Reclustering within large clusters can identify repre-sentative waveforms or small clusters, e.g. cluster 8

n e.g. Hierarchical clustering (complete-linkage)identifies representative waveforms within clusters

(Right) Clustering can aid in visualization and interpretation of alarge number of new detections: cluster membership of new FASTdetections plotted over time. Injection began at well #1, closest tothe Guy-Greenbrier Fault, on 7 July 2010 (at 518400s in figure).

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Feature Extraction

“Good” feature extraction can reduce false detectionsn Binary fingerprints act as proxies for waveforms in efficient similarity searchn Fingerprints must be discriminative: (dis)similar waveforms should have

(dis)similar fingerprintsn False detections preferred to missed detections, but too many hurt performance

How are “most discriminative” Haar coefficients selected?

n Top magnitude coefficients (often used for efficient compression)n Most atypical coefficients, as measured by:

n Z-score (mean, standard deviation), orn Median Absolute Deviation (MAD) across data set

n MAD-based Haar coefficient selection demonstrates the best performancein low SNR settings and is most efficient.

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Comparison of the performance of Haar coefficient-selection methods on synthetictest. The MAD-based coefficient selection best separates the repeated waveformsfrom the noise.

(Right) Test data (a): 12 pairs of repeatedwaveforms (SNR 1.25-5) planted at knowntimes in 3hrs of noise (bandpass 1-10Hz).Detection results from FAST shown for (b)top magnitude, (c) top Z-score, and (d) topMAD Haar coefficients. Location of truerepeated events indicated by orange verti-cal lines, and the detection statistic (simi-larity value) is plotted in blue. Top 400 co-efficients selected in results pictured, butresults hold for top 100-800 coefficients.

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(Left) Efficiency of binary representations (orderedfrom least to most efficient): top magnitude (blue),top Z-score (orange) and top MAD (purple), withGini index of 0.73, 0.28, and 0.11, respectively.

Alternate Feature Extraction Approaches (on-going work)

n Time-domain features: bag-of-waveforms, wavelets, random projections,n Data-driven features: spectral hashing, shift-invariant sparse coding,

nonnegative matrix factorization (NMF)-based features

References

[1] Yoon, C., et al. (2015). “Earthquake detection through computationallyefficient similarity search.” Science Advances, 1(11).

[2] Baluja, S., and Covell, M. (2008). “Waveprint: Efficient wavelet-basedaudio fingerprinting.” Pattern Recognition, 41(11).

[3] Yoon, C. et al., (2015) AGU Fall Meeting Abstract S13B-2850.ReadmoreaboutFAST(doi:10.1126/sciadv.1501057)