Upload File

bayesian inference for signal-based seismic …russell/papers/agu15...agu_sigvisa_poster_2015_2.pptx...

  • Home
  • Documents
  • Bayesian Inference for Signal-Based Seismic …russell/papers/agu15...agu_sigvisa_poster_2015_2.pptx Created Date 12/17/2015 3:00:40 AM
1
• Traditional monitoring systems relying on station processing discard significant information present in the original recorded signal. • SIG-VISA (Signal-based Vertically Integrated Seismic Analysis) is a system for global seismic monitoring through Bayesian inference directly on observed signals, incorporating a rich representation of the physics underlying the signal generation process. • Bayesian inference correctly combines statistical evidence from travel times and signal correlations, providing a unified approach to that encompasses promising recent techniques such as waveform matching and double differencing. • We are making progress in scaling up the required computations to be tractable for large-scale global monitoring. Bayesian Inference for Signal-Based Seismic Monitoring David A. Moore 1 , Kevin Mayeda 1 , Stephen C. Myers 2 , Stuart J. Russell 1 University of California, Berkeley 1 and Lawrence Livermore National Laboratory 2 Detections of DPRK Events Overview Unifying Monitoring as Bayesian Inversion Signal-Based Monitoring Inference events detections waveform signals Traditional Monitoring (GA/SEL3) station processing NET-VISA SIG-VISA model inference model inference Bayesian monitoring with a generative model of seismic signals: P θ (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)) ∝ P φ ( f (signal) | world) P θ (world) where f (signal) = set of all detections Signal-based Bayesian monitoring: P(world | signal) ∝ P φ (signal | world) P θ (world) Generative Signal Model The SIG-VISA signal model defines a probability distribution over observed signals, incorporating the event bulletin and a parameterized envelope template as latent variables that act through physical and statistical processes to generate the observed signals. × + = Envelope template: depends on event location, depth, magnitude, phase. Repeatable modulation: related to Green’s function. Wavelet coefs depends on event location, depth, phase. Background noise: autoregressive process at each station. Observed envelope: sum of all arriving phases, plus background noise. Bayesian Cross-Correlation Existing monitoring and location techniques can be viewed as inverting individual aspects of the underlying physics. Physical phenomenon when inverted, yields Modeled in SIG-VISA Predictable travel times (1D) Traditional pick -based monitoring IASPEI 91 travel time model Spatial continuityof waveforms Waveform matching / cross-correlation methods for sub- threshold detections Gaussian process (kriging) model of wavelet coefficients describing signal modulation Spatial continuityof travel -time residuals Double-differencing Gaussian process model of travel -time residuals Other predictable regularities (attenuation, coda decay rates, spectral content, etc.) Not exploited by existing techniques GP models of envelope shape parameters, Brune and Mueller -Murphy source models By combining all of these phenomena into a single forward model, inverted using Bayesian inference, SIG-VISA unifies and extends existing techniques within a single system, exploiting waveform correlations and historical data where available while gracefully reverting to travel-time-based inference for de novo events. SIG-VISA uses the framework of Markov Chain Monte Carlo (MCMC) to sample from the posterior distribution over event hypotheses conditioned on observed signals. Move types include: • Template parameter moves modify the shape parameters describing a envelope template. • Event attribute moves modify the location, depth, time, and magnitude of an event hypothesis to better fit the templates associated with that event at stations across the network. • Template birth/death/split/merge moves create and destroy shape templates to explain fluctuations the observed signals. New templates are proposed with probability proportional to the height of the observed envelope, minus envelopes from all current templates. • Event birth/death moves propose new hypothesized events to explain unassociated templates. • Event locations are proposed by Hough transform, using a 3D (lon, lat, time) accumulator array. • Weights of accumulator bins are sums of “votes” from all current unassociated templates; each template votes for all bins in its backprojected space-time cone. • Additional proposal mechanism based on historical waveform data (see Bayesian cross-correlation, right) The generative signal model fully specifies the posterior distribution P(world | signal) from a mathematical standpoint. In practice, sampling from this distribution is computationally difficult. Designing tractable inference algorithms is an important and ongoing component of the project. Example of template birth moves finding an explanation for an observed signal. The final frame shows the result after several additional template parameter moves. LEB event 5335760 P arrival at MKAR array (MK31) len=250s, freq=2-3Hz mb=4.37, dist=7318km Template fit Wavelet modulation, scaled by template Background noise Observed envelope Signal Decomposition Visualizing the internal representation of the model allows us to decompose an observed signal into a base shape, repeatable waveform structure, and non-repeatable background noise. By explicitly modeling station background noise as an AR process, we derive a new, easily computed statistic that resembles cross-correlation but can be formally interpreted as a posterior probability. (for autoregressive noise process R) Locations from Waveform Correlation Correlated waveforms of doublet events Normalized cross-correlation Log odds of candidate offsets under Bayesian cross-correlation Bayesian alignment posterior We use this statistic to compute proposal probabilities for historical events (see next pane), but it may have applications more generally as a drop-in replacement wherever normalized cross-correlation is used. Combining travel-time information with waveform correlations provides more precise location estimates. Simplified SIGVISA model detects and locates all confirmed DPRK tests (2006, 2009, 2013), by automated processing on vertical channels at 15 three-componentstations. Locating held-out doublet (gold star) from aftershock sequence of Banda Sea event (mb 5.0, April 20 2009): Posterior from travel-time-based model (12 3-component stations) Log probabilitiesof MCMC proposal distribution,using Bayesian correlation at MKAR SIG-VISA posterior conditioned on waveform at MKAR SIG-VISA posterior conditioned on waveforms from MKAR, CMAR, ASAR, FITZ ILAR 0.8-4.5Hz vertical signal (2009 event) Location posterior ellipse contains LEB event 2009 P arrival We gratefully acknowledge the support of DTRA for this work under Basic Research Grant #HDTRA-11110026, as well as the support of the CTBTO through the provision of IMS data and the use of the vDEC experimental platform. In progress: Bayesian analysis of purported 2010 DPRK test using waveform correlations from IMS and regional stations. Acknowledgements

Upload: others

Post on 15-Jul-2020

5 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: Bayesian Inference for Signal-Based Seismic …russell/papers/agu15...agu_sigvisa_poster_2015_2.pptx Created Date 12/17/2015 3:00:40 AM

• Traditionalmonitoringsystemsrelyingonstationprocessingdiscardsignificantinformation presentintheoriginalrecordedsignal.

• SIG-VISA(Signal-basedVerticallyIntegratedSeismicAnalysis)isasystemforglobalseismicmonitoring throughBayesianinferencedirectlyonobservedsignals,incorporatingarichrepresentationofthephysicsunderlyingthesignalgenerationprocess.

• Bayesianinferencecorrectlycombinesstatisticalevidencefromtraveltimesandsignalcorrelations,providingaunifiedapproachtothatencompassespromisingrecenttechniquessuchaswaveformmatchinganddoubledifferencing.

• Wearemakingprogressinscalinguptherequiredcomputationstobetractableforlarge-scaleglobalmonitoring.

Bayesian Inference for Signal-Based Seismic MonitoringDavidA.Moore1,KevinMayeda1,StephenC.Myers2,StuartJ.Russell1

UniversityofCalifornia,Berkeley1 andLawrenceLivermoreNationalLaboratory2

Detections of DPRK Events

Overview Unifying Monitoring as Bayesian Inversion

Signal-Based Monitoring

Inference

events

detections

waveform signals

TraditionalMonitoring(GA/SEL3)

stationprocessing

NET-VISA

SIG-VISA

model

inference model

inference

Bayesianmonitoringwithagenerativemodelofseismicsignals:Pθ(world) describespriorprobabilityforwhatis (events)Pφ(signal|world) describesforwardmodel(propagation,measurement,etc.)

Detection-basedBayesianmonitoring:P(world|f(signal))∝ Pφ(f(signal)|world)Pθ(world)where f(signal)=setofalldetections

Signal-basedBayesianmonitoring:P(world|signal)∝ Pφ(signal|world)Pθ(world)

Generative Signal Model

TheSIG-VISAsignalmodeldefinesaprobabilitydistributionoverobservedsignals,incorporatingtheeventbulletinandaparameterizedenvelopetemplateaslatent variablesthatactthroughphysicalandstatisticalprocessestogeneratetheobservedsignals.

×

+

=

Envelopetemplate:dependsoneventlocation,depth,magnitude,phase.

Repeatablemodulation:relatedtoGreen’sfunction.Waveletcoefs dependsoneventlocation,depth,phase.

Backgroundnoise:autoregressiveprocessateachstation.

Observedenvelope:sumofallarrivingphases,plusbackgroundnoise.

Bayesian Cross-Correlation

Existingmonitoringandlocationtechniquescanbeviewedasinvertingindividualaspectsoftheunderlyingphysics.

Physical phenomenon wheninverted,yields ModeledinSIG-VISAPredictabletraveltimes(1D)

Traditionalpick-basedmonitoring

IASPEI91traveltimemodel

Spatialcontinuityofwaveforms

Waveform matching/cross-correlationmethodsforsub-thresholddetections

Gaussianprocess(kriging)modelofwaveletcoefficients describingsignalmodulation

Spatial continuityoftravel-timeresiduals

Double-differencing Gaussianprocessmodeloftravel-timeresiduals

Otherpredictableregularities(attenuation,codadecayrates,spectralcontent,etc.)

Notexploitedbyexistingtechniques

GP modelsofenvelopeshapeparameters,BruneandMueller-Murphysourcemodels

Bycombiningallofthesephenomenaintoasingleforwardmodel,invertedusingBayesianinference,SIG-VISAunifiesandextendsexistingtechniqueswithinasinglesystem,exploitingwaveformcorrelationsandhistoricaldatawhereavailablewhilegracefullyrevertingtotravel-time-basedinferencefordenovoevents.

SIG-VISA uses the framework of Markov Chain Monte Carlo (MCMC) tosample from the posterior distribution over event hypotheses conditionedon observed signals. Move types include:

• Templateparametermovesmodifytheshapeparametersdescribingaenvelopetemplate.

• Eventattributemovesmodifythelocation,depth,time,andmagnitudeofaneventhypothesistobetterfitthetemplatesassociatedwiththateventatstationsacrossthenetwork.

• Templatebirth/death/split/mergemoves createanddestroyshapetemplatestoexplainfluctuationstheobservedsignals.Newtemplatesareproposedwithprobabilityproportionaltotheheightoftheobservedenvelope,minusenvelopesfromallcurrenttemplates.

• Eventbirth/deathmoves proposenewhypothesizedeventstoexplainunassociatedtemplates.• EventlocationsareproposedbyHoughtransform,usinga3D(lon,lat,time)accumulatorarray.

•Weightsofaccumulatorbinsaresumsof“votes”fromallcurrentunassociatedtemplates;eachtemplatevotesforallbinsinitsbackprojectedspace-timecone.

• Additionalproposalmechanismbasedonhistoricalwaveformdata(seeBayesiancross-correlation,right)

ThegenerativesignalmodelfullyspecifiestheposteriordistributionP(world|signal)fromamathematicalstandpoint.Inpractice,samplingfromthisdistributioniscomputationallydifficult.Designingtractableinferencealgorithmsisanimportantandongoingcomponentoftheproject.

Exampleoftemplatebirthmovesfindinganexplanationforanobservedsignal.Thefinalframeshowstheresultafterseveraladditionaltemplateparametermoves.

LEBevent5335760ParrivalatMKARarray(MK31)len=250s,freq=2-3Hzmb=4.37,dist=7318km

Templatefit

Waveletmodulation,scaledbytemplate

Backgroundnoise

Observedenvelope

Signal Decomposition

Visualizingtheinternalrepresentationofthemodelallowsustodecomposeanobservedsignalintoabaseshape,repeatablewaveformstructure,andnon-repeatablebackgroundnoise.

ByexplicitlymodelingstationbackgroundnoiseasanARprocess,wederiveanew,easilycomputedstatisticthatresemblescross-correlationbutcanbeformallyinterpretedasaposteriorprobability.

(forautoregressivenoiseprocessR)

Locations from Waveform Correlation

Correlatedwaveformsofdoubletevents

Normalizedcross-correlation

LogoddsofcandidateoffsetsunderBayesiancross-correlation

Bayesianalignmentposterior

Weusethisstatistictocomputeproposalprobabilitiesforhistoricalevents(seenextpane),butitmayhaveapplicationsmoregenerallyasadrop-inreplacementwherevernormalizedcross-correlationisused.

Combiningtravel-timeinformationwithwaveformcorrelationsprovidesmorepreciselocationestimates.

SimplifiedSIGVISAmodeldetectsandlocatesallconfirmedDPRKtests(2006,2009,2013),byautomatedprocessingonverticalchannelsat15three-componentstations.

Locatingheld-outdoublet(goldstar)fromaftershocksequenceofBandaSeaevent(mb 5.0,April202009):

Posteriorfromtravel-time-basedmodel(123-componentstations)

LogprobabilitiesofMCMCproposaldistribution,usingBayesiancorrelationatMKAR

SIG-VISAposteriorconditionedonwaveformatMKAR

SIG-VISAposteriorconditionedonwaveformsfromMKAR,CMAR,ASAR,FITZ

ILAR0.8-4.5Hzverticalsignal(2009event)

LocationposteriorellipsecontainsLEBevent

2009Parrival

WegratefullyacknowledgethesupportofDTRAforthisworkunderBasicResearchGrant#HDTRA-11110026,aswellasthesupportoftheCTBTOthroughtheprovisionofIMSdataandtheuseofthevDECexperimentalplatform.

Inprogress:Bayesiananalysisofpurported2010DPRKtestusingwaveformcorrelationsfromIMSandregionalstations.

Acknowledgements

BAYESIAN INFERENCE Sampling techniques

Bayesian Inference & Neural Networks

Bayesian inference. - UFRGS

Bayesian Inference for Categorical Data Analysis: A Surveypeople.stat.sc.edu/Hitchcock/bayesfinal.pdf · Bayesian Inference for Categorical Data Analysis: ... Bayesian Inference for

Qualitative Robustness in Bayesian Inference - arXiv · Qualitative Robustness in Bayesian Inference ... Abstract The practical implementation of Bayesian inference requires numerical

VARIATIONAL BAYESIAN PHYLOGENETIC INFERENCE

DCM Bayesian Inference

Bayesian inference method

Bayesian Inference Ekaterina Lomakina TNU seminar: Bayesian inference 1 March 2013

Full Bayesian inference (Learning)...Learning paradigms Learning as inference Bayesian learning, full Bayesian inference, Bayesian model averaging Model identification, maximum likelihood

Robust Bayesian clustering - UCL Computer Science - · PDF fileRobust Bayesian clustering ... Bayesian learning, graphical models, approximate inference, variational inference,

Bayesian network inference

Bayesian Inference (II)

Bayesian estimation and § inference

Bayesian Inference (II) - University of California, Santa Cruzabrsvn/intro_bayes_2.pdf · Bayesian Inference in a Nutshell (Again) In Bayesian inference, uncertainty or degree of

Bayesian inference

Likelihood and Bayesian Inference · Likelihood and Bayesian Inference Joe Felsenstein Department of Genome Sciences and Department of Biology Likelihood and Bayesian Inference –

Inference in Bayesian Networks

Aspects of Bayesian Inference

Bayesian inference and generative models - TNU should I know about Bayesian inference? Because Bayesian principles are fundamental for • statistical inference in general • system

Approximate Bayesian Inference I:

Bayesian Inference, Basics - Stony Brookzhu/ams570/Bayesian_Basics.pdf · Bayesian Inference In Bayesian inference there is a fundamental distinction between • Observable quantities

Bayesian Inference!!!

Introduction to Bayesian Inference

Bayesian Inference (I)

Bayesian Inference, Review 4/25/12 Frequentist inference Bayesian inference Review The Bayesian Heresy (pdf)pdf Professor Kari Lock Morgan Duke University

Statistical Physics of Inference and Bayesian Estimation · Statistical Physics of Inference and Bayesian Estimation Florent ... Bayesian versus frequentistThe Bayesian approach assumes

Bayesian and frequentist inference for ecological ... · Key Words and Phrases: ecological inference, Bayesian inference, frequentist inference, voting patterns. 1 Introduction to

Bayesian inference on mixtures

Inference in Bayesian Nets

Bayesian LSS Inference - mpe.mpg.de

Quantum Bayesian Inference - informatyka.agh.edu.pl · QuantumBayesianInference Quantum Bayesian Inference MichałGrabowski MarcinPrzewięźlikowski InstituteofComputerScience,AGH,al

Analysis of the Regression Model Parameters · Coherent Bayesian Inference Analysis of parameters Model generation Example Practice Coherent Bayesian Inference Coherent Bayesian Inference

Bayesian Inference - Michael Clark

Bayesian Inference , Priors - Indico