Bayesian earthquake early warning: a dispatch from one of many frontiers of real-time seismology

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Bayesian earthquake early warning: a dispatch from one of many frontiers of real-time seismology Georgia Cua 1, Thomas Heaton 2, Stefan Wiemer 1, CISN Early

1 Bayesian earthquake early warning: a dispatch from one of many frontiers of real-time seismology Georgia Cua 1, Thomas Heaton 2, Stefan Wiemer 1, CISN Early Warning Group, SAFER WP2 1 Swiss Seismological Service, ETH Zürich 2 California Institute of Tecnhology 5th International Workshop on Statistical Seismology, Erice

2 Earthquake hazard information at different time scales Long term seismic hazard maps decades 10% probability of being exceeded in 50 yrs Euro-Med Seismic Hazard Map (Giardini et al, 2003)

3 Earthquake hazard information at different time scales decades Intermediate-term forecasts years

4 Earthquake hazard information at different time scales decades short-term forecasts years hours Gerstenberger et al, 2003

5 Earthquake hazard information at different time scales decades years hours seconds minutes Real-time seismology - goal: provide timely information to assist in post-earthquake mitigation, response, recovery efforts early warning (earthquakes, tsunamis) rapid source characterization ShakeMaps human impact, casualty estimates (PAGER) economic loss estimates aftershock forecasts

6 Information traveling at ~300,000 km/s Earthquake source region S-wave 3.5 km/s P- wave 6 km/s Target warning area t Origin time Early warning ShakeMaps 1st P detection damaging motions at target region

7 Chronology 1868: Cooper proposes setting up seismic detectors near Hayward fault, ring a bell in central San Francisco 1960s: Japan Railway starts developing early warning system to slow or stop high-speed trains (currently UrEDAS) 1985: Heaton proposes conceptual framework for modern computerized alert network for Southern California 1989: Loma Prieta aftershock sequence - temporary seismic deployment provides constructions workers ~20 seconds of warning (Bakun, 1994) 1991: Mexico Seismic Alert System provides up to 70 seconds of warning to Mexico City from earthquakes nucleating in the Guerrero region, about 300 km away 1991: Taiwan Central Weather Bureau begins widespread deployment of strong motion

In tens of seconds, you could (possibly) larger warning times, increasing complexity duck and cover save data, stop elevators protect emergency response facilities (hospitals, fire stations) slow

8 In tens of seconds, you could (possibly) larger warning times, increasing complexity duck and cover save data, stop elevators protect emergency response facilities (hospitals, fire stations) slow trains, abort airplane landings, direct traffic shut down gas valves, secure equipment, hazardous materials initiate shutdown procedures in manufacturing facilities active / semi-active structural control (Grasso, 2005) in general, reduce injuries, prevent secondary hazards, increase effectiveness of emergency response; larger warning times better most of the time, Light shaking in X seconds, just enjoy the ride messages over mobile phones Goltz, 2002

9 Different flavors of early warning Single station approach Tau-C approach (Wu and Kanamori, 2004) Front detection known source region (eg. Mexico City, Bucharest) Network-based approach Many possible source regions Elarms (Allen and Kanamori, 2003), Virtual Seismologist (Cua and Heaton, 2006), Nowcast (Japan) Same ingredients as non-real time seismic hazard analysis Sourc e x Path x Site effects Predicted ground motions, onset times, uncertainties

10 Virtual Seismologist (VS) method for seismic early warning Bayesian approach to seismic early warning designed for regions with distributed seismic hazard/risk Modeled on back of the envelope methods of human seismologists for examining waveform data Shape of observed envelopes, relative frequency content Capacity to assimilate different types of information Station locations, state of health of the seismic network Previously observed seismicity Known fault locations Gutenberg-Richter recurrence relationship

11 Bayes Theorem: a review Given available waveform observations Y obs, what are the most probable estimates of magnitude and location, M, R? posterior likelihood prior the answer Prior = beliefs regarding M, R before considering observations Y obs Likelihood = how observations Y obs modify beliefs about M, R Posterior = current state of belief, combination of prior and Y obs maxima of posterior = most probable estimates of M, R given Y obs spread of posterior = variances on estimates of M, R

12 Full acceleration time history 1-sec envelopes 9 channels (horizontal and vertical acceleration, velocity, and filtered displacement) 1 observed envelope => 11 envelope parameters

13 70 events, 2 < M < 7.3, R < 200 km Non-linear model estimation (inversion) to characterize waveform envelopes for these events ~30,000 time histories Data set for learning the envelope characteristics

14 RMS S-wave horizontal acceleration (NEHRP sites C and below)

15 Acceleration amplification relative to average rock station

16 Average Rock and Soil envelopes as functions of M, R RMS horizontal acceleration

Estimating M from ratios of ground motion P-wave frequency content scales with M (Nakamura, 1988) Find the linear combination of log(acc) and log(disp) that minimizes the

17 Estimating M from ratios of ground motion P-wave frequency content scales with M (Nakamura, 1988) Find the linear combination of log(acc) and log(disp) that minimizes the variance within magnitude-based groups while maximizing separation between groups (eigenvalue problem) Z ad = 0.36log(acc) 0.93log(disp) 0.36 acc = log disp 0.93 Estimating M from Z ad

18 Distinguishing between P- and S-waves

19 Bayes Theorem (again) How are observed quantities (ground motion envelopes) related to magnitude and location? shape of envelopes as functions of M, R estimating M from ground motion ratio distinguishing between P- and S-wave station corrections L(M,lat,lon) = stations P,S i=1 j=1 L(M,lat,lon) ij L(M,lat,lon) ij = (ZAD Z ij j (M )) σ ZADj k=1 Y obs,ijk Y ijk (M,lat,lon) 2 2σ ijk

20 Bayes Theorem (again) What else do we know about earthquakes? About the network monitoring the region? fault locations Gutenberg-Richter relationship log N(M ) = a bm previously observed seismicity station locations not yet arrived data (Horiuchi, 2003, Rydelek and Pujol, 2003))

21 High station density CPP WLT MLS DLA LLS SRN STG PLS Polygons are voronoi cells (nearest neighbor regions) 1st arrival at SRN implies EQ location within SRN voronoi cell Green circles seismicity in preceding 24 hrs

22 CISN M=4.75

23 Low station density 28 September 2004 M6.0 Parkfield, California EQ

24 3 sec after initial P detection at PKD 2 nd P arrival at PHL log(prob(lat,lon data)) prob(lat,lon data)

25 Cost-benefit analysis for early warning users a = actual peak ground motion level at user site (we don t know this) a thresh = ground motion level above which damage occurs a pred = predicted ground motion level from EWS σ pred = uncertainty on predicted ground motion level Assume for now that user initiates actions when a pred > a thresh when a pred < a thresh P ex =probability of missed alarm when a pred > a thresh 1-P ex =probability of false alarm a pred a thresh a thresh a pred

26 $C damage = cost of damage if no action was taken and a > a thresh $C act = cost of initiating action; also the cost of false alarm $C ratio = $C damage / $C act state of prob. of state of nature cost of cost of nature given apred "Do nothing" "Act" a > a thresh P ex $Cdamage $Cact a < a thresh 1-P ex free! $Cact It is cost-effective to act when P ex =P crit =1/C ratio =C act /C damage user threshold predicted ground motion level at which user should act uncertainty on predicted ground motion error function

27 C ratio =1.1 C ratio =2 C ratio =5 C ratio =5 0 Applications with C ratio < 1 should not use early warning information C ratio ~ 1 means false alarms relatively expensive C ratio >> 1 means missed warnings are relatively expensive; initiate actions even when a pred <a thresh, need to accept false alarms Simple applications with C ratio >> 1 stopping elevators at closest floor, ensuring fire station doors open, saving data

28 Conclusions Bayesian framework allows integration of many types of information to produce most probable solution and uncertainty estimates Robustness of source estimates is proportional to station density. Prior information is useful in regions with low station density, but increases complexity of information Need to carry out Bayesian approach from source estimation through user response. Gutenberg-Richter relationship can reduce false alarms at cost of increasing vulnerability to missed alarms We need realistic values of Cratio (cost of missed alarms/ cost of false alarms) to do cost-benefit analysis for operational early warning => more dialogue between seismologists and potential user community Certain level of false alarms must be tolerated if user wants to ensure proper actions are taken during the infrequent, damaging event

29 Future activities Training VS using datasets from test sites Design and development of real-time codes / deployment in Switzerland / California Initial development and testing in Switzerland / California Portability + regional customization Installation / testing at other test sites Iceland, Italy (SAFER) Regional customization with cooperation from local networks

30 Ground motion prediction equations collaborating with T. Heaton, Caltech

31 Ground motion prediction equations

32 Early Warning Implementation VirtualSeismologist v1.0 (~late 2007) Real-time data 1-sec PGA, PGV, PGD envelopes Prior information earthquake weather network topology Software development philosophy emphasizes portability and regional customization. Some of the portable modules included in the distribution: Distinguish between P and S arrivals Estimate M from ratios of available peak ground motions Find M, location that maximize a likelihood functions determined from observations Find M, location that maximize the Bayes posterior (prior x likelihood) Warning info peak ground motions, uncertainties at subscriber sites Regional customization PGA, PGV, PGD attenuation relationships relationship between magnitude and ground motion ratios site amplification / station-specific correction

33 Time-scales of earthquake hazard years before hours before sec after min after Long term hazard (faults, tectonics) Short term hazard (recent seismicity) Earthquake Early warning (ground motions) Magnitude, location (arrival times, ampl) ShakeMaps

34 Low station density 28 September 2004 M6.0 Parkfield, California EQ

35 3 sec after initial P detection at PKD 2 nd P arrival at PHL log(prob(lat,lon data)) prob(lat,lon data)

36 Virtual Seismologist (VS) method for seismic early warning Modeled on back of the envelope methods of human seismologists for examining waveform data Shape of envelopes, relative frequency content Bayes theorem to continually update estimates as data becomes available, and assimilate different types of information Previously observed seismicity State of health of seismic network Known fault locations Gutenberg-Richter recurrence relationship years before hours before sec after min after Long term hazard (faults, tectonics) Short term hazard (recent seismicity) Earthquake Early warning (ground motions) Magnitude, location (arrival times, ampl) ShakeMaps

37 Virtual Seismologist (VS) method for seismic early warning Modeled on back of the envelope methods of human seismologists for examining waveform data Shape of envelopes, relative frequency content Bayes theorem to continually update estimates as data becomes available, and assimilate different types of information Previously observed seismicity State of health of seismic network Known fault locations Gutenberg-Richter recurrence relationship years before hours before sec after min after Long term hazard (faults, tectonics) Short term hazard (recent seismicity) Earthquake Early warning (ground motions) Magnitude, location (arrival times, ampl) ShakeMaps

38 larger warning times for regions further from the source region warning most useful for large earthquakes at distance blind zone (21 km) with no warning Wu, 2002

39 Are large earthquake ruptures deterministic or not? Olsen and Allen, 2005 Rydelek and Horiuchi, 2006

40 from J. D. Cooper, 1898 courtesy of H. Negishi, NIED

41 Earthquake hazard information at different time scales decades Early warning years hours seconds

42 Earthquake hazard information at different time scales decades years Rapid earthquake source characterization ShakeMaps human impact, casualty, loss estimates (PAGER) hours seconds minutes

44 Probabilistic warning times

45 3 sec after initial P detection at SRN No prior information Epi dist est=33 km M=5.5 L(M,lat,lon) = stations P,S i=1 j=1 L(M,lat,lon) ij L(M,lat,lon) ij = (ZAD Z ij j (M )) σ ZADj k=1 Y obs,ijk Y ijk (M,lat,lon) 2 2σ ijk

46 3 sec after initial P detection at SRN Prior information: -Voronoi cells 9 km M=4.8 log N(M ) = a bm Prior information: -Voronoi cells -Gutenberg-Richter 8 km M=4.4

47 Modeling ground motion envelopes P,S-wave envelopes rise time, duration, constant amplitude, 2 decay parameters Noise constant

48 How do peak P- and S-wave amplitudes depend on magnitude, distance, frequency, site? log 10 A = am + b(r 1 + C(M )) + d log 10 (R 1 + C(M )) + e R 1 = R + 9

49 P-wave frequency content scales with size Nakamura, 1988, Kanamori, 2004

50 16 October 1999 M=7.1 Hector Mine, Califoria, Earthquake Voronoi cells from Hector Voronoi cells from Yorba Linda Previously observed seismicity within HEC s voronoi cell are related to mainshock

51 (a) P arrival at HEC (b) No arrival at BKR Constraints on location from arrivals and non-arrivals 3 sec after initial P detection at HEC (c) No arrival at DEV (d) No arrival at DAN (e) No arrival at FLS (f) No arrival at GSC

52 Evolution of single station (HEC) estimates prob(lat,lon data)

53 CISN M=7.1

54 Marginal pdfs for Hector Mine, 3 sec after initial P detection Prior information is important for regions with relatively low station density Magnitude estimate can be described by by Gaussian pdfs; location estimates cannot Possibly large errors (~60 km) in assuming the epicenter is at the 1 st triggered station

55 From the user s perspective, it is optimal to wait whenever possible (the real reason we procrastinate) later estimate (high density) initial estimate (low density)

Earthquake early warning for informationbased

Earthquake early warning for informationbased societies Georgia Cua Swiss Seismological Service ETH Zürich, Switzerland EOST-IPGS Universite Louis Pasteur 22 November 2007 Outline What is early warning