Georgia B Cua Advisor: Thomas Heaton Advisory/Defense Committee:

1. Creating the Virtual Seismologist:Developments in Ground Motion Characterization and Seismic Early Warning Georgia B Cua Advisor: Thomas Heaton Advisory/Defense Committee: James Beck, Egill Hauksson, Hiroo Kanamori Civil Engineering / Seismolab Seminar 3 January 2005

2. Goal in seismic early warning: To provide timely information to guide damage-mitigating actions that can be taken in the few seconds between the detection of an earthquake and the onset of large ground motions at a given site. Given the data available at a given time, what is the optimal decision? • What are the best (most probable) estimates of • magnitude and location given the available data? • What is the optimal decision (wait, act, don’t act) • given the current source estimates and their • uncertainties?

3. In tens of seconds, you could … • duck and cover • save data, shut down gas, stop elevators • secure equipment, hazardous materials • stop trains, abort airplane landings, direct traffic • initiate shutdown procedures • protect emergency response facilities such as hospitals, fire stations • in general, reduce injuries, prevent secondary hazards, increase effectiveness of emergency response; larger warning times better Source: Goltz. 2002

4. Outline • Bayes’ theorem and the Virtual Seismologist (VS) method in seismic early warning • Using envelope attenuation relationships to study average properties of Southern California ground motions • Estimating magnitude from ratios of P-wave ground motions; prior information relevant to early warning • Applying the VS method to So. California events • How to use seismic early warning information • Conclusions

5. 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 envelopes, relative frequency content • Capacity to assimilate different types of information • Previously observed seismicity • State of health of seismic network • Known fault locations • Gutenberg-Richter recurrence relationship

6. Bayes’ Theorem: a review Given available waveform observations Yobs, 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 Yobs • Likelihood = how observations Yobs modify beliefs about M, R • Posterior = current state of belief, combination of prior and Yobs • maxima of posterior = most probable estimates of M, R given Yobs • spread of posterior = variances on estimates of M, R

7. Some central ideas • Bayes’ theorem is a useful framework for applications in real-time seismology, which typically have contrasting requirements for speed and reliability of estimates; Bayes prior mimics how humans make judgments with a sparse set of observations • Need to carry out Bayesian approach from source estimation through user response. In particular, the Gutenberg-Richter recurrence relationship should be included in either the source estimation or user response. • Robustness of source estimates is proportional to station density in epicentral region; sparsely instrumented regions need prior information, which introduces complexity • Use of earthquake occurrence models (particularly short-term seismicity-based forecasts) as prior information • If a user wants ensure that proper actions are taken during the “Big One”, false alarms must be tolerated.

8. Part 1: Characterizing Southern California ground motion envelopes as functions of magnitude, distance, frequency, and site “likelihood” • Parameterization of envelopes; attenuation relationships • Saturation of rock vs soil sites • Attenuation characteristics of P and S wave amplitudes • Station corrections

9. Ground motion envelope: our definition Full acceleration time history envelope definition– max.absolute value over 1-second window

10. Modeling ground motion envelopes • P,S-wave envelopes – rise time, duration, constant amplitude, 2 decay parameters • Noise – constant

11. 70 events, 2 < M < 7.3, R < 200 km • 9 channels (Z, NS, EW, acc., vel., disp.) • ~900 rock records, ~2400 soil records • ~30,000 time histories

12. Functional form for M, R-dependence of P- and S-wave amplitudes 1, … , 36 (P- and S-wave amplitudes for 18 channels) the “effective epicentral distance”increases as C(M) becomes large C(M) (km)

13. SOIL S-wave ROCK S-wave • Scaling for small magnitudes-

14. Magnitude-dependent saturation of rock and soil sites (S-waves) horizontal S-wave acceleration horizontal S-wave velocity • Saturation important for M>5, when source dimensions become comparable to station distance, large amplitudes may induce yielding in soils • Magnitude-dependent saturation appears to be primarily a source effect, since rock and soil are equally affected • The exception is horizontal acceleration at close distances to large events. Slight over-saturation of soil ground motions, possibly due to non-linear site effects. horizontal S-wave displacement

15. Magnitude-dependent saturation of rock and soil sites (P-waves) vertical P-wave velocity vertical P-wave acceleration • For horizontal S-wave amplitudes,soil • site exhibit stronger saturation than rock sites. • It seems the opposite holds for vertical P-wave • amplitudes – rock sites appear to exhibit • more saturation vertical P-wave displacement

16. Comparison of P- and S-wave saturation for horizontal and vertical ground motions P- and S-wave horizontal acceleration (soil) P- and S-wave vertical acceleration (soil) • It appears that horizontal P-waves exhibit stronger saturation • than horizontal S-waves • Difference between P- and S-waves is less pronounced on the • vertical channel • Uniquely decomposing P- and S-waves is troublesome, • particularly in the horizontal direction

17. Station Corrections • Average residual at a given station • relative to expected ground motion • amplitude given by attenuation • relationship • Defined for stations with 2 or more • available records • Consistent with generally known • station behavior • PAS, PFO are typically used as • hard rock reference sites • SVD anomalous due to proximity • to San Andreas • Some “average” rock stations are: • DGR, JCS, HEC, MWC, AGA, EDW

18. How much do station corrections improve standard deviation? rock + soil=0.315 rock only=0.308 rock w/ station corr=0.243 ~21% reduction in 

19. horizontal acceleration ampl rel. to ave. rock site Vertical P-wave acceleration ampl rel. to ave. rock site horizontal velocity ampl rel. to ave. rock site vertical P-wave velocity ampl rel. to ave. rock site

20. Average Rock and Soil envelopes as functions of M, R rms horizontal acceleration

21. Ground motion models summary:defining prob(Yobs|M,R) • Saturation of rock and soil sites • Soil sites saturate ground motions more than rock • Stronger saturation at higher frequencies • Difference between rock and soil sites decreases with increasing ground motion amplitude • P-waves appear to have higher degree of saturation than S-waves ? • Station-specific data contributes to ~20% variance reduction • Attenuation relationships for P and S waves • Predictive relationships for envelopes of different channels of ground motion as functions of M,R • Could also use a Bayesian approach in model class selection (Beck and Yuen, 2003)

22. Part 2: The Virtual Seismologist (VS) method for seismic early warning • Estimating magnitude from ratios of ground motion • Defining the Bayes likelihood function using ground motion • ratios and envelope attenuation relationships • Defining the Bayes prior • Inclusion of not-yet-arrived data (Rydelek and Pujol (2004), Horiuchi (2004)) • Examples: Yorba Linda, Hector Mine, (Parkfield) • How subscribers might use early warning information

23. Estimating M from ratios of ground motion • P-wave frequency content scales with M (Allen and Kanamori, 2003, 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) • Estimating M from Zad

24. Distinguishing between P- and S-waves

25. (**)

26. Defining the Bayes prior, prob(M,R) “prior” • Locations of mapped faults • Previously observed seismicity (24 hr preceding mainshock) • Gutenberg-Richter magnitude-frequency relationship • State of health of the seismic network (Voronoi cells) • Not-yet-arrived data (Rydelek and Pujol (2004), Horiuchi et al (2004)) • More important for regions with low station density; complicates the source estimate ideally provided by short-term seismicity-based EQ forecasts, such as STEP (Gerstenberger, Wiemer, Jones, 2003) or ETAS (Helmstetter, 2003)

27. Applying VS method to So. Cal. events • Station density in epicentral region • VS single station estimates (M,R) – 3 sec amplitudes at 1st triggered station • Effects of different priors, in particular, the G-R relationship • Prior information particularly important for regions with low station density • VS multiple station estimates (M,lat,lon) • Evolution of VS estimates with time • Amplitude-based location (strong-motion centroid) • Examples • 2002 M=4.75 Yorba Linda -high station density • 1999 M=7.1 Hector Mine – low station density • 2004 M=6.0 Parkfield

28. CPP MLS WLT DLA SRN PLS LLS STG • Voronoi cells are nearest neighbor regions • If the first arrival is at SRN, the event must be within SRN’s Voronoi cell • prev. obs. seismicity related to mainshock

29. 3 sec after initial P detection at SRN Epi dist est=33 km M=5.5 Single station estimate: • Prior information: • Voronoi cells • Gutenberg-Richter M, R estimates using 3 sec observations at SRN No prior information 8 km M=4.4 • Prior information: • Voronoi cells • No Gutenberg-Richter 9 km M=4.8 Note: star marks actual M, RSRN

30. Constraints implied by arrivals (a) 1st P at SRN (b) at CPP 1 sec (c) at WLT 1.5 sec (d) 3 arrivals Contours shown are magnitude estimates w/o G-R. Rydelek and Pujol (2004) hyperbola

31. CISN M=4.75

32. For regions with high station density, how long it takes until there is enough data (arrivals and amplitudes) to uniquely determine the source estimates is relatively short • The error in using the 1st triggered station’s location as the estimate for the epicenter is small (~15 km for Yorba Linda) • Estimating magnitude using VS method, and estimating epicenter as location of 1st triggered station is acceptable.

33. Voronoi cells from Hector Voronoi cells from Yorba Linda • Previously observed seismicity within • HEC’s voronoi cell are related to mainshock

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

35. Evolution of single station (HEC) estimates prob(lat,lon| data)

36. CISN M=7.1

37. 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 • 1st triggered station

38. 28 September 2004 M6.0 Parkfield, California earthquake CISN epi, R=21 km • seismicity in Voronoi cell • unrelated to mainshock

39. 3 sec after initial P detection at PKD 2nd P arrival at PHL prob(lat,lon|data) log(prob(lat,lon|data))

41. Cost-benefit analysis for early warning users User A would like to initiate a set of damage-mitigating actions if the ground motions at user site exceed athresh. Given source estimates (and uncertainties) from a seismic early warning system, User A can calculate the expected ground motion levels apred at her site. Assuming that the predicted ground motions are (log)normally distributed, the probability of exceeding athresh given apred when apred < athresh Pex=probability of missed warning when apred > athresh 1-Pex=probability of false alarm apred athresh athresh apred

42. Let Cdamage be cost of damage if no action was taken and a >athresh. Let Cact be the cost of initiating action; also the cost of false alarm. Let Cratio=Cdamage / Cact The critical exceedance level above which it is optimal to act is (equate the expected costs of “do nothing” and “act”, and solve for Pex) Pcrit can be related to the predicted ground motion level above which it is optimal to act, apred,crit

43. Cratio=1.1 Cratio=2 Cratio=5 Cratio=50 • Applications with Cratio < 1 should • not use early warning information • Cratio ~ 1 means false alarms • relatively expensive • Cratio >> 1 means missed warnings • are relatively expensive; initiate • actions even when apred<athresh , • need to accept false alarms • Simple applications with Cratio >> 1 • stopping elevators at closest floor, • ensuring fire station doors open, • saving data

44. M4.75 Yorba Linda • The choice of prior (with or without Gutenberg-Richter) is irrelevant once there are enough observations to constrain the source estimates; the different estimates eventually converge • VS M estimates w/o Gutenberg-Richter almost always have a smaller error compared to actual M than estimates with Gutenberg-Richter • VS M estimates w Gutenberg-Richter in 4 cases are smaller than actual M. (In general, perhaps this is almost always the case.) • Users basing actions on estimates with G-R lower their probability of false alarms, but increase their vulnerability to missed warnings • Need to generate statistics about how VS estimates evolve with time, ie, how much larger are the initial estimates likely to grow M6.0 Parkfield M6.5 San Simeon M7.1 Hector Mine

45. Some central ideas / Conclusions • Bayes Theorem is a useful framework for applications in real-time seismology, which typically have contrasting requirements for speed and reliability of estimates; Bayes prior mimics how humans make judgments with a sparse set of observations • Need to carry out Bayesian approach from source estimation through user response. In particular, the Gutenberg-Richter recurrence relationship should be included in either the source estimation or user response. • Robustness of source estimates is proportional to station density in epicentral region; sparsely instrumented regions need prior information, which introduces complexity • Use of earthquake occurrence models (particularly short-term seismicity-based forecasts) as prior information • If a user wants ensure that proper actions are taken during the “Big One”, false alarms must be tolerated.

46. Thank you