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 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

Q1: Given available data, what ismost probable magnitude andlocation estimate?

Q2: Given a magnitude and location estimate, what are the expected ground motions?

Seismic Early Warning