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Envelope-based Seismic Early Warning: Virtual Seismologist method

Envelope-based Seismic Early Warning: Virtual Seismologist method. G. Cua and T. Heaton Caltech. Outline. Virtual Seismologist method Bayes’ Theorem Ratios of ground motion as magnitude indicators Examples of useful prior information.

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Envelope-based Seismic Early Warning: Virtual Seismologist method

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  1. Envelope-based Seismic Early Warning: Virtual Seismologist method G. Cua and T. Heaton Caltech

  2. Outline • Virtual Seismologist method • Bayes’ Theorem • Ratios of ground motion as magnitude indicators • Examples of useful prior information

  3. Virtual Seismologist 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 • site amplification

  4. 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 without considering waveform data, Yobs • likelihood = how waveform observations Yobs modify our beliefs • posterior= current state of belief, a combination of prior beliefs,Yobs • maxima of posterior = most probable estimates of M, R given Yobs • spread of posterior = variance on estimates

  5. Example: 16 Oct 1999 Mw7.1 Hector Mine HEC 36.7 km DAN 81.8 km PLC 88.2 km VTV 97.2 km Maximum envelope amplitudes at HEC, 5 seconds After P arrival

  6. Defining the likelihood (1): attenuation relationships maximum velocity 5 sec. after P-wave arrival at HEC x x x prob(Yvel=1.0cm/s | M, R)

  7. Estimating magnitude from ground motion ratios • P-wave frequency content scales with magnitude (Allen & Kanamori, • Nakamura) • linear discriminant analysis on acceleration and displacement Slope=-1.114 Int = 7.88 M= -0.3 log(Acc) + 1.07 log(Disp) + 7.88 M 5 sec after HEC = 6.1 P-wave

  8. Estimating M, R from waveform data:5 sec after P-wave arrival at HEC from P-wave velocity “best” estimate of M, R 5 seconds after P-wave arrival using acceleration, velocity, displacement Distance Distance Magnitude Magnitude M 5 sec after HEC = 6.1 P-wave from P-wave acceleration, displacement

  9. Examples of Prior Information • Gutenberg-Richter log(N)=a-bM • voronoi cells- nearest neighbor regions for all operating stations • Pr ( R ) ~ R • previously observed seismicity • STEP (Gerstenberger et al, 2003), • ETAS (Helmstetter, 2003) • foreshock/aftershock statistics (Jones, 1985) • “poor man” version – increase probability of location by small % relative to background

  10. M, location estimate combining waveform data & prior Voronoi & seismicity prior M5 sec=6.1 M, R estimate from waveform data peak acc,vel,disp 5 sec after P arrival at HEC ~5 km

  11. A Bayesian framework for real-time seismology • Predicting ground motions at particular sites in real-time • Cost-effective decisions using data available at a given time Acceleration Amplification Relative to Average Rock Station

  12. Conclusions • Bayes’ Theorem is a powerful framework for real-time seismology • Source estimation in seismic early warning • Predicting ground motions • Automating decisions based on real-time source estimates • formalizing common sense • Ratios of ground motion can be used as indicators of magntiude • Short-term earthquake forecasts, such as ETAS (Helmsetter) and STEP (Gerstenberger et al) are good candidate priors for seismic early warning

  13. Defining the likelihood (2): ground motion ratios • Linear discriminant analysis • groups by magnitude • Ratio of among group to within group covariance is maximized by: Z= 0.27 log(Acc) – 0.96 log(Disp) • Lower bound onMagnitude as a function of Z: Mlow = -1.114 Z + 7.88 = -0.3 log(Acc) + 1.07 log(Disp) + 7.88 Slope=-1.114 Int = 7.88 Mlow(HEC) = -0.3 log(65 cm/s/s) + 1.07 log(6.89e-2 cm) + 7.88 = 6.1

  14. Other groups working on this problem • Kanamori, Allen and Kanamori – Southern California • Espinoza-Aranda et al – Mexico City • Wenzel et al – Bucharest, Istanbul • Nakamura – UREDAS (Japan Railway) • Japan Meteorological Agency – NOWCAST • Leach and Dowla – nuclear plants • Central Weather Bureau, Taiwan

  15. Seismic Early Warning Q1: Given available data, what is most probable magnitude and location estimate? Q2: Given a magnitude and location estimate, what are the expected ground motions?

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