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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 Yobs , what are the most probable estimates of magnitude and location, M, R?
“likelihood” “prior”“posterior”
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
Bayes’ Theorem: a review
“the answer”
( , | ) ( | , ) ( , )obs obsprob M R Y prob Y M R prob M R
HEC 36.7 km
DAN 81.8 km
PLC 88.2 km
VTV 97.2 km
Example: 16 Oct 1999 Mw7.1 Hector Mine
5 sec after Pacc(cm/s/s) 65vel (cm/s) 1.00E+00disp (cm) 6.89E-02
Maximum envelope
amplitudesat HEC, 5 seconds
After P arrival
Defining the likelihood (1): attenuation relationships
maximum velocity5 sec. after P-wavearrival at HEC
prob(Yvel=1.0cm/s | M, R)
x xx
Estimating magnitude from ground motion ratios
Slope=-1.114Int = 7.88
P-wave frequency content scales with magnitude (Allen & Kanamori, Nakamura)
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
2Acceleration X X
Displacement X X
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-wavearrival using acceleration, velocity,displacement
M 5 sec after HEC = 6.1
P-wavefrom P-wave acceleration, displacement
Magnitude
Dis
tanc
e
MagnitudeD
ista
nc
e
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 estimatefrom waveformdata peak acc,vel,disp 5 sec after P arrivalat HEC
M5
sec=6.1
M, location estimate combiningwaveform 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: Mlow = -1.114 Z + 7.88 = -0.3 log(Acc) + 1.07 log(Disp) + 7.88
Slope=-1.114Int = 7.88
Defining the likelihood (2): ground motion ratios
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
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