Transcript Envelope-based Seismic Early Warning: further developments

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
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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
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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?