Envelope-based Seismic Early Warning: Virtual Seismologist method

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Envelope-based Seismic Early Warning Virtual
Seismologist method

• G. Cua and T. Heaton
• Caltech

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Outline

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

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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

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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

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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
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Defining the likelihood (1) attenuation
relationships
maximum velocity 5 sec. after P-wave arrival at
HEC
x
x
x
prob(Yvel1.0cm/s M, R)
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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
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Estimating M, R from waveform data5 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
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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

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M, location estimate combining waveform data
prior
Voronoi seismicity prior
M5 sec6.1
M, R estimate from waveform data peak
acc,vel,disp 5 sec after P arrival at HEC
5 km
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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
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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

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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 on Magnitude 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
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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

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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?