1 Vertically Integrated Seismic Analysis Stuart Russell Computer Science Division, UC Berkeley Nimar Arora, Erik Sudderth, Nick Hay

2 Outline  Seismic event monitoring as probabilistic inference  Vertically integrated probability models …  Connect events to sensor data and everything in between  Associate events and detections optimally  Automatically take nondetections into account  May improve low-amplitude detection and noise rejection  Inference using MCMC (poster)  Empirical estimation of model components  Preliminary experimental results

3 Bayesian model-based learning  Generative approach  P  (world) describes prior over what is (source), also over model parameters, structure  P  (signal | world) describes sensor model (channel)  Given new signal, compute P(world | signal) ~ P  (signal | world) P  (world)  Learning  Adapt model parameters or structure to improve fit  Operates continuously as data are acquired and analyzed  Substantial recent advances in modeling capabilities, general-purpose inference algorithms

4 Generative model for IDC arrival data  Events occur in time and space with magnitude  Natural spatial distribution a mixture of Fisher-Binghams  Man-made spatial distribution uniform  Time distribution Poisson with given spatial intensity  Magnitude distribution Gutenberg-Richter  Aftershock distribution (not yet implemented)  Travel time according to IASPEI91 model+corrections  Detection depends on magnitude, distance, station*  Detected azimuth, slowness w/ empirical residuals  False detections with station-dependent distribution

5 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

6 Inference  MCMC (Markov chain Monte Carlo) (see poster S31B for details)  Efficient sampling of hypothetical worlds (events, travel times, detections, noise, etc.)  Converges to true posterior given evidence  Key point: computing posterior probabilities takes the algorithm off the table; to get better answers, either  Improve the model, or  Add more sensors

7 Vertical integration: Detection  Basic idea: analyzing each signal separately throws away information.  Multiple weak signals are mutually reinforcing via a higher- level hypothesis  Multiple missing signals indicate that other “detections” may be coincidental noise  Simple example: K sensors record either  Independent noise drawn from N[0,1]  Common signal drawn from N[0,1-  ] + independent N[0,  ] noise  Separate detectors fail completely!  Joint detection succeeds w.p. 1 as   0 or K    Travel time accuracy affects detection capability!

8 STA/LTA Threshold

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12 Outline  Seismic event monitoring as probabilistic inference  Vertically integrated probability models …  Connect events to sensor data and everything in between  Associate events and detections optimally  Automatically take nondetections into account  May improve low-amplitude detection and noise rejection  Inference using MCMC (poster)  Empirical estimation of model components  Preliminary experimental results

13 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

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16 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

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19 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

20 Overall Pick Error

21 WRA Pick Error

22 Overall IASPEI Error

23 WRA - IASPEI Error

24 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

25 Overall Azimuth Error

26 WRA - Azimuth Error

27 Seismic event Travel times Seismic event Travel times Station 1 picks Station 2 picks Generative structure Detected at Station 1? Detected at Station 2? Station 1 noise Station 2 noise

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29 Analyzing Performance  Min-cost max-cardinality matching where edges exist between prediction and ground truth events within 50 seconds and 5 degrees.  Precision – percentage of predictions that match.  Recall – percentage of ground truths that match.  F1 – harmonic mean of precision and recall.  Error – average distance between matching events. (Cost of matching / size of matching)

30 Evaluation vs LEB (human experts) F1Precision/ Recall Error/S.D. (km) Average Log- likelihood SEL3 (IDC Automated) / / 119_ VISA (Best Start) / / VISA (SEL3 Start) / / VISA (Back projection Start) / /

31 INFERENCE EXAMPLE

32 Summary  Vertically integrated probability models  Connect events, transmission, detection, association  Information flows in all directions, reinforcing or rejecting local hypotheses to form a global solution  Better travel time model => better signal detection  Nondetections automatically play a role  Local sensor models calibrated continuously with no need for ground truth  May give more reliable detection and localization of lower-magnitude events

33 Ongoing Work  More sophisticated MCMC design  Add more phases and phase relabeling  Extend model all the way down to waveforms  Evaluation using data from high-density networks (Japan Meteorological Agency, some regions within ISC data)