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Progress in Signal-Based Bayesian Monitoring

Introduc4on  

David  A.  Moore1,  Kevin  Mayeda1,  Stephen  C.  Myers2,  Min  Joon  Seo1,  Stuart  J.  Russell1  University  of  California,  Berkeley1  and  Lawrence  Livermore  Na.onal  Laboratory2  

Signal  Envelope  Model  •  Global seismic monitoring for the Comprehensive Nuclear-Test-Ban Treaty (CTBT) aims to recover the time, location, depth, and magnitude for all seismic events in the magnitude range of interest. •  Data from the International Monitoring System (IMS) are processed in real time at the International Data Centre (IDC) in Vienna. Our goal is to improve the sensitivity and accuracy of automated processing at IDC.

Signal-­‐Based  vs.  Detec4on-­‐Based  Monitoring  

Signal-­‐based  Bayesian  monitoring   CONCLUSIONS  •  Bayesian methods are a powerful and promising approach to monitoring problems. In particular, signal-based monitoring improves on traditional methods by making full use of the available data, with potential for significant performance improvements. •  The SIG-VISA prototype system includes an empirically-calibrated, physics-based model of observed waveform envelopes. •  Gaussian Process regression enables learning of flexible, data-driven probabilistic models of spatial parameters. •  Waveform matching / correlation effects can be recovered from Bayesian inference in a spatially conditioned model, enabling localization from a single detection in some cases.

REFERENCES  Arora, Nimar S., Stuart J. Russell, Paul Kidwell, and Erik Sudderth, “Global seismic monitoring as probabilistic inference,” In NPIS 23, MIT Press, 2011. Harris, D.B, “A wave-form correlation method for identifying quarry explosions,” Bull. Seism. Soc. Am., 81, 2395–2418, 1991. Harris, D. B. and D. A. Dodge, “An autonomous system for grouping events in a developing aftershock sequence,” Bull. Seismol. Soc. Amer ., vol. 101, no. 2, pp. 763–774, 2011. Mayeda, K., Hofstetter, A., O'Boyle, J.L., and Walter, W.R. (2003). Stable and transportable regional magnitudes based on coda-derived moment-rate spectra. Bulletin of the Seismological Society of America, 93(1), 224-229. Myers, S.C., G. Johannesson, and W. Hanley (2007). A Bayesian hierarchical method for multiple-event seismic location. Geophys. J. Int., 171, 1049-1063. Schaff, D. P., Bokelmann, G. H. R., Ellsworth, W. L., Zanzerkia, E., Waldhauser, F., & Beroza, G. C. (2004). Optimizing Correlation Techniques for Improved Earthquake Location. Bull. Seism. Soc. Amer, 94(2), 705-721. Slinkard, Megan E., Dorthe B. Carr, Stephen L. Heck, and Christopher J. Young (2011). Towards an automated waveform correlation detector system. In Monitoring Research Review, Tucson, Arizona. Thorbjarnardottir, B. S. and J. C. Pechmann (1987). Constraints on relative earthquake locations from cross-correlation of waveforms. Bull. Seismol. Soc. Am., 77, 1626–1634.

ACKNOWLEDGEMENTS  We gratefully acknowledge the support of DTRA for this work; also the support of CTBTO for the work on NET-VISA and the technical cooperation of CTBTO personnel including Ronan Le Bras and Jeff Given. We thank Sheila Vaidya of LLNL and Ola Dahlman, former Chair of CTBTO Working Group B, for their moral support and encouragement in this project. We also thank Megan Slinkard and Regina Eckert of Sandia National Labs for sharing with us their data on correlated arrival waveforms.

SIG-VISA is a probabilistic generative model of seismic event origins, propagation, and observed waveform envelopes, including event signals along with station background noise:

•  NET-VISA is a detection-based Bayesian monitoring system whose performance is limited by the classical, bottom-up, threshold-based detections algorithms used in station processing. It misses about 2-3 times fewer events than SEL3. •  SIG-VISA, a signal-based system, uses generative models that span the range from events to waveform traces. This approach has several qualitative advantages over NET-VISA, with the potential for significantly improved sensitivity and localization performance.

Blue dots and triangles are primary seismic stations.

events

detections

waveform signals

 SEL3  

sta.on  processing  

NET-­‐VISA  

 SIG-­‐VISA  

model  inference   model  inferenc

e  

Bayesian monitoring with a generative approach Pθ(world) describes prior probability for what is (events) Pφ(signal | world) describes forward model (propagation, measurement, etc.) Detection-based Bayesian monitoring: P(world | f (signal)) ∝ Pφ(f (signal) | world) Pθ(world) where f (signal) = set of all detections Signal-based Bayesian monitoring: P(world | signal) ∝ Pφ(signal | world) Pθ(world)

•  The signal model encodes a distribution over waveform envelopes at each station given parameters for all hypothesized events.

•  Each observed envelope is modeled with a shaped template combined with a stochastic modulation signal for each arriving phase, and a background noise process at each station:

•  SIG-VISA uses a paired-exponential envelope template whose arrival time, amplitude, and decay rate depend on event magnitude and the event->station path. Template fits to historical signals are used to train predictive models for new observations.

LeJ:  An  observed  envelope  showing  the  P  and  S  arrivals  and  subsequent  coda  decays.  The  red  line  indicates  the  template  fit.  

•  Waveform shape is known to be highly repeatable across events with the same location and source mechanism (Thorbjarnardottir and Pechmann, 1987; Harris, 1991).

•  SIG-VISA captures this effect by replacing the independently sampled modulation signal with a signal conditioned on the event location, causing nearby events to generate correlated waveforms:

observedEnvelope  =  template  x  exp(modula.on)  +  sta.onNoise  

•  This causes a statistical “waveform matching” effect to emerge from inference in the probabilistic model.

•  Signals are represented parametrically as a sum of basis functions (e.g. Fourier basis), with coefficients modeled by a spatial Gaussian process.

•  The current automated system (SEL3) detects 69% of real events and creates twice as many spurious events. •  16 human analysts find more events, correct existing ones, throw out spurious events, and generate LEB (“ground truth”). •  Unreliable below magnitude 4 (about 1 kiloton).

Seismic  Event  

Travel  4mes  

Sta4on  1  noise  

Path-­‐specific  signal  characteris4cs  

Seismic  Event  

Travel  4mes  

Sta4on  2    signal  envelope  

Sta4on  2  noise  

Path-­‐specific  signal  characteris4cs  

Sta4on  1    signal  envelope  

0  

0.5  

1  

1.5  

AFI   CTA   DAV   FITZ   GNI  

Med

ian  Ab

solute  Residual  

Amplitude  Predic4on  (ver4cal  component,  2-­‐3Hz)  

Baseline   Linear   GP  

0  

0.01  

0.02  

AFI   CTA   DAV   FITZ   LPAZ   GNI  

Med

ian  Ab

solute  Residual  

Coda  Decay  Predic4on  (ver4cal  component,  2-­‐3Hz)  

Baseline   Linear   GP  

Waveform  Matching  Path-­‐Specific  Characteris4cs  

Observed envelope amplitudes and decay rates vary with the event source location, with effects from distance and depth as well as local variation in seismic structure.

We model these effects empirically using a nonparametric spatial Gaussian Process regression (kriging) model, which learns for each seismic station a probability distribution over template parameters for events at every point on the Earth:  

Coda  decay  ra

te  

The nonparametric model captures local variation, yielding improved predictions relative to a distance-dependent linear model:

Spatial model of coda decay rates observed by Charter Towers station. (red = sharper decay).

The spatial model enables inference from signal characteristics to possible event locations:

Prior location density

Synthe.c  reference  envelope  (red)  and  a  sampled  envelope  (blue)  from  a  Gaussian-­‐process  genera.ve  model  for  a  nearby  event  loca.on.    

The  same  reference  envelope  (red)  and  a  sampled  envelope  (blue)  from  a  distant  event  loca.on.    

Fourier  features  for  two  nearby  and  correlated  events  (red,  blue)  vs.  a  distant  event  (green).  

Posterior  loca.on  density  of  IMS  event  4689462  from  a  single  sta.on  observa.on  (MKAR)  using  a  waveform  matching  model  trained  on  data  from  99  other  events,  shown  in  red.  The  posterior  peak  is  8.4km  from  the  true  event  loca.on,  marked  by  a  green  star.  

•  Station noise is modeled by an autoregressive process, retrained hourly at each station to capture regional and temporal variation in noise properties.

•  Observed signals are modeled independently across a range of narrow frequency bands, automatically learning spectral characteristics and frequency-specific decay rates.

•  Amplitude for each phase within each frequency band is predicted from event magnitude using a physics-based source model (Brune, 1971; Mueller and Murphy, 1971) and a path-specific learned transfer function (next column).

FUTURE  WORK  •  Computationally efficient algorithms for training and probabilistic inference at global scale. •  Model refinement based on geophysical expertise. •  Dependent modeling of array station elements. •  Putting it all together: a practical, effective global monitoring system.

Correlated  event  waveforms  (IMS  events  4686108,  4689462,  correla.on  .60).  

Par.al  posterior  densi.es  condi.oned  on  one  (leb)  and  five  (right)  Fourier  coefficients.    

Posterior location density given coda decay rate

Coda decay rate likelihood

Right:  A  synthe.c  envelope  generated  from  the  template  with  an  autoregressive  modula.on  process.