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

Given available waveform observations Y obs, what are the most probable estimates of magnitude and location, M, R? “likelihood”“prior” “posterior”  prior = beliefs regarding M, R without considering waveform data, Y obs  likelihood = how waveform observations Y obs modify our beliefs  posterior = current state of belief, a combination of prior beliefs,Y obs  maxima of posterior = most probable estimates of M, R given Y obs  spread of posterior = variance on estimates Bayes’ Theorem: a review “the answer”

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

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

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

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

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

 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 on Magnitude as a function of Z: M low = Z = -0.3 log(Acc) log(Disp) Slope= Int = 7.88 Defining the likelihood (2): ground motion ratios M low(HEC) = -0.3 log(65 cm/s/s) log(6.89e-2 cm) = 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

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? Seismic Early Warning