Vertically Integrated Seismic Analysis

1. Vertically Integrated Seismic Analysis

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

6. Inference • MCMC (Markov chain Monte Carlo) (see poster S31B-1713 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

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

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

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

25. Overall Azimuth Error

26. WRA - Azimuth Error

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

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)

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)