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Vertically Integrated Seismic Analysis

Stuart RussellComputer Science Division, UC Berkeley

Nimar Arora, Erik Sudderth, Nick Hay

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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

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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

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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

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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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

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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!

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STA/LTA Threshold

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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

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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Overall Pick Error

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WRA Pick Error

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Overall IASPEI Error

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WRA - IASPEI Error

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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Overall Azimuth Error

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WRA - Azimuth Error

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Seismic event

Travel times

Seismic event

Travel times

Station 1picks

Station 2picks

Generative structure

Detected atStation 1?

Detected atStation 2?

Station 1noise

Station 2 noise

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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)

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Evaluation vs LEB (human experts)

F1 Precision/

Recall

Error/S.D.

(km)

Average Log-likelihood

SEL3 (IDC Automated)

55.6 46.2 / 69.7 98 / 119 _

VISA (Best Start) 80.4 70.9 / 92.9 100 / 117 -1784

VISA (SEL3 Start) 55.2 44.3 / 73.4 104 / 124 -1791

VISA (Back projection Start)

50.6 49.1 / 52.0 126 / 139 -1818

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INFERENCE EXAMPLE

model2_71_223.avi

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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

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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)