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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 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 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 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 5 sec after P envelope acc(cm/s/s) 65 amplitudes vel (cm/s) 1.00E+00 at HEC, 5 seconds disp (cm) 6.89E-02 After P arrival Defining the likelihood (1): attenuation relationships x x x maximum velocity 5 sec. after P-wave arrival at HEC prob(Yvel=1.0cm/s | M, R) Estimating magnitude from ground motion ratios P-wave frequency content scales with magnitude (Allen & Kanamori, Nakamura) Slope=-1.114 Int = 7.88 linear discriminant analysis on acceleration and displacement M = -0.3 log(Acc) + 1.07 log(Disp) + 7.88 M 5 sec after HEC = 6.1 P-wave 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 Magnitude M 5 sec after HEC = 6.1 P-wave from P-wave acceleration, displacement Magnitude Examples of Prior Information 1) Gutenberg-Richter log(N)=a-bM 2) voronoi cells- nearest neighbor regions for all operating stations Pr ( R ) ~ R 3) 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 Voronoi & seismicity prior M, location estimate combining waveform data & prior M5 sec=6.1 M, R estimate from waveform data peak acc,vel,disp 5 sec after P arrival at HEC ~5 km 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 Conclusions Bayes’ Theorem is a powerful framework for realtime 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 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) Slope=-1.114 Int = 7.88 Lower bound on Magnitude as a function of Z: Mlow = -1.114 Z + 7.88 = -0.3 log(Acc) + 1.07 log(Disp) + 7.88 Mlow(HEC) = -0.3 log(65 cm/s/s) + 1.07 log(6.89e-2 cm) + 7.88 = 6.1 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 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?