Creating the Virtual Seismologist:Developments in

Ground Motion Characterization and Seismic Early Warning

Georgia B Cua

Advisor: Thomas Heaton

Advisory/Defense Committee:

James Beck, Egill Hauksson, Hiroo Kanamori

Civil Engineering / Seismolab Seminar

3 January 2005

Given the data available at a given time, what is the optimal decision?

What are the best (most probable) estimates of magnitude and location given the available data? What is the optimal decision (wait, act, don’t act) given the current source estimates and their uncertainties?

Goal in seismic early warning:To provide timely information to guide damage-mitigatingactions that can be taken in the few seconds between thedetection of an earthquake and the onset of large groundmotions at a given site.

In tens of seconds, you could …

duck and cover save data, shut down gas, stop elevators secure equipment, hazardous materials stop trains, abort airplane landings, direct traffic initiate shutdown procedures protect emergency response facilities such as

hospitals, fire stations in general, reduce injuries, prevent secondary

hazards, increase effectiveness of emergency response; larger warning times better

Source: Goltz. 2002

Outline Bayes’ theorem and the Virtual Seismologist (VS) method in seismic

early warning

Using envelope attenuation relationships to study average properties of Southern California ground motions

Estimating magnitude from ratios of P-wave ground motions; prior information relevant to early warning

Applying the VS method to So. California events

How to use seismic early warning information

Conclusions

Virtual Seismologist (VS) 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 Known fault locations Gutenberg-Richter recurrence relationship

Bayes’ Theorem: a review

Given available waveform observations Yobs, what are the mostprobable estimates of magnitude and location, M, R?

“posterior” “likelihood” “prior”

“the answer”

Prior = beliefs regarding M, R before considering observations Yobs

Likelihood = how observations Yobs modify beliefs about M, R

Posterior = current state of belief, combination of prior and Yobs

maxima of posterior = most probable estimates of M, R given Yobs

spread of posterior = variances on estimates of M, R

Some central ideas Bayes’ theorem is a useful framework for applications in real-time

seismology, which typically have contrasting requirements for speed and reliability of estimates; Bayes prior mimics how humans make judgments with a sparse set of observations

Need to carry out Bayesian approach from source estimation through user response. In particular, the Gutenberg-Richter recurrence relationship should be included in either the source estimation or user response.

Robustness of source estimates is proportional to station density in epicentral region; sparsely instrumented regions need prior information, which introduces complexity

Use of earthquake occurrence models (particularly short-term seismicity-based forecasts) as prior information

If a user wants ensure that proper actions are taken during the “Big One”, false alarms must be tolerated.

Part 1:

Characterizing Southern California ground motion envelopes as functions of magnitude, distance, frequency, and site

“likelihood”

Parameterization of envelopes; attenuation relationshipsSaturation of rock vs soil sitesAttenuation characteristics of P and S wave amplitudesStation corrections

Full acceleration time history

envelope definition– max.absolute value over 1-second window

Ground motion envelope: our definition

P,S-wave envelopes – rise time, duration, constant amplitude, 2 decay parameters

Noise – constant

Modeling ground motion envelopes

70 events, 2 < M < 7.3, R < 200 km9 channels (Z, NS, EW, acc., vel., disp.)

~900 rock records, ~2400 soil records~30,000 time histories

Functional form for M, R-dependence of P- and S-wave amplitudes

C(M

) (k

m)

the “effective epicentral distance”increases asC(M) becomes large

1, … , 36 (P- and S-wave amplitudes for 18 channels)

ROCKS-wave

SOILS-wave

Scaling for small magnitudes-

Magnitude-dependent saturation of rock and soil sites (S-waves)

horizontal S-wave acceleration horizontal S-wave velocity

horizontal S-wave displacement

Saturation important for M>5, when source dimensions become comparable to station distance, large amplitudes may induce yielding in soilsMagnitude-dependent saturation appears to be primarily a source effect, since rock and soil are equally affectedThe exception is horizontal acceleration at close distances to large events. Slight over-saturation of soil ground motions, possibly due to non-linear site effects.

Magnitude-dependent saturation of rock and soil sites (P-waves)

vertical P-wave acceleration vertical P-wave velocity

vertical P-wave displacement

For horizontal S-wave amplitudes,soil site exhibit stronger saturation than rock sites.It seems the opposite holds for vertical P-wave amplitudes – rock sites appear to exhibit more saturation

Comparison of P- and S-wave saturationfor horizontal and vertical ground motions

P- and S-wave horizontal acceleration (soil) P- and S-wave vertical acceleration (soil)

It appears that horizontal P-waves exhibit stronger saturation than horizontal S-waves Difference between P- and S-waves is less pronounced on the vertical channelUniquely decomposing P- and S-waves is troublesome, particularly in the horizontal direction

Station Corrections

Average residual at a given station relative to expected ground motion amplitude given by attenuation relationship

Defined for stations with 2 or more available records

Consistent with generally known station behavior

PAS, PFO are typically used as hard rock reference sites SVD anomalous due to proximity to San Andreas

Some “average” rock stations are: DGR, JCS, HEC, MWC, AGA, EDW

rock only= 0.308

rock w/ station corr= 0.243

~21% reduction in

How much do station corrections improve standard deviation?

rock + soil= 0.315

horizontal acceleration ampl rel. to ave. rock site

horizontal velocity ampl rel. to ave. rock site vertical P-wave velocity ampl rel. to ave. rock site

Vertical P-wave acceleration ampl rel. to ave. rock site

Average Rock and Soil envelopes as functions of M, R rms horizontal acceleration

Ground motion models summary:defining prob(Yobs|M,R)

Saturation of rock and soil sites Soil sites saturate ground motions more than rock Stronger saturation at higher frequencies Difference between rock and soil sites decreases with

increasing ground motion amplitude P-waves appear to have higher degree of saturation

than S-waves ? Station-specific data contributes to ~20% variance

reduction Attenuation relationships for P and S waves Predictive relationships for envelopes of different

channels of ground motion as functions of M,R Could also use a Bayesian approach in model class

selection (Beck and Yuen, 2003)

Part 2:

The Virtual Seismologist (VS) method for seismic early warning

Estimating magnitude from ratios of ground motionDefining the Bayes likelihood function using ground motion ratios and envelope attenuation relationshipsDefining the Bayes priorInclusion of not-yet-arrived data (Rydelek and Pujol (2004), Horiuchi (2004))Examples: Yorba Linda, Hector Mine, (Parkfield) How subscribers might use early warning information

P-wave frequency content scales with M (Allen and Kanamori, 2003,

Nakamura, 1988) Find the linear combination of

log(acc) and log(disp) that minimizes the variance within magnitude-based groups while maximizing separation between groups (eigenvalue problem)

Estimating M from Zad

Estimating M from ratios of ground motion

Distinguishing between P- and S-waves

(**)

Defining the Bayes prior, prob(M,R)

Locations of mapped faults Previously observed seismicity (24 hr preceding

mainshock) Gutenberg-Richter magnitude-frequency relationship

State of health of the seismic network (Voronoi cells) Not-yet-arrived data (Rydelek and Pujol (2004), Horiuchi et

al (2004)) More important for regions with low station density;

complicates the source estimate

“prior”

ideally provided by short-term seismicity-based EQ forecasts, such as STEP (Gerstenberger, Wiemer, Jones, 2003) or

ETAS (Helmstetter, 2003)

Applying VS method to So. Cal. events

Station density in epicentral region VS single station estimates (M,R) – 3 sec amplitudes at 1st

triggered station Effects of different priors, in particular, the G-R relationship Prior information particularly important for regions with low station

density VS multiple station estimates (M,lat,lon) Evolution of VS estimates with time Amplitude-based location (strong-motion centroid) Examples

2002 M=4.75 Yorba Linda -high station density 1999 M=7.1 Hector Mine – low station density 2004 M=6.0 Parkfield

SRN

STGLLS

DLA

PLS

MLS

CPP

WLT

Voronoi cells are nearest neighbor regions If the first arrival is at SRN, the event must be within SRN’s Voronoi cell prev. obs. seismicity related to mainshock

Station Voronoi Area Epi. Dist P arrival

(km^2) (km) (sec)

SRN 436 9.9 2.2

CPP 556 17.1 3.1

WLT 269 19.1 3.65

PLS 710 20.5 3.95

MLS 612 22.1 4.05

STG 1591 28.1 4.9

LLS 1027 30.1 5.9

DLA 284 30.6 6.05

3 sec after initial P detection at SRN

M, R estimates using 3 sec observations at SRN

Epi dist est=33 km

M=

5.5

Note: star marks actual M, RSRN

Prior information:-Voronoi cells-Gutenberg-Richter

Prior information:-Voronoi cells-No Gutenberg-Richter

8 kmM=4.4

9 kmM=4.8

Single station estimate:

No prior information

Rydelek and Pujol (2004) hyperbola

Constraints implied by arrivals

(a) 1st P at SRN (b) at CPP 1 sec

(c) at WLT 1.5 sec (d) 3 arrivals

Contours shown are magnitudeestimates w/o G-R.

1iR R

CISN M=4.75

For regions with high station density, how long it takes until there is enough data (arrivals and amplitudes) to uniquely determine the source estimates is relatively short

The error in using the 1st triggered station’s location as the estimate for the epicenter is small (~15 km for Yorba Linda)

Estimating magnitude using VS method, and estimating epicenter as location of 1st triggered station is acceptable.

Voronoi cells from Hector

Voronoi cells from Yorba Linda

Station Voronoi Area Epi. Dist P arrival

(km^2) (km) (sec)

SRN 436 9.9 2.2

CPP 556 17.1 3.1

WLT 269 19.1 3.65

PLS 710 20.5 3.95

MLS 612 22.1 4.05

STG 1591 28.1 4.9

LLS 1027 30.1 5.9

DLA 284 30.6 6.05

Station Voronoi Area Epi. dist Fault dist. P arrival

(km^2) (km) (km) (sec)

HEC 5804 26.7 10.7 6

BKR 8021 77.1 68.6 13.7

DEV 3322 78.8 62 13.9

DAN 9299 81.8 77.6 14.5

FLS 2933 81.8 67.9 14.5

GSC 4523 92.5 77.6 16.2

SVD 1513 93.4 88.2 16.3

VTV 2198 97.2 89.2 16.9

SBPX 880 97.3 93.8 16.9

Previously observed seismicity within HEC’s voronoi cell are related to mainshock

Constraints on locationfrom arrivals andnon-arrivals 3 sec afterinitial P detection at HEC

(a) P arrival at HEC (b) No arrival at BKR

(c) No arrival at DEV

(e) No arrival at FLS

(d) No arrival at DAN

(f) No arrival at GSC

Evolution of singlestation (HEC) estimates

prob

(lat,l

on| d

ata)

Est. time M (no GR) M (GR)3 6.2 (0.5) 5.7 (0.52)

5.5 7.2 (0.42) 6.6 (0.55)7 7.1 (0.33) 6.9 (0.41)

CISN M=7.1

Prior information is important for regions with relatively low station densityMagnitude estimate can be described by by Gaussian pdfs; location estimates cannotPossibly large errors (~60 km) in assuming the epicenter is at the 1st triggered station

28 September 2004 M6.0 Parkfield, California earthquake Station Voronoi Area Epi. dist Fault dist. P arrival

(km^2) (km) (km) (sec)

PKD 13,371 20.81 1.73 3

PHL 39,775 48.43 45.4 7.5

SMM 4,610 65.57 59.7 10.2

RCT 11,887 114.9 111.4 18

VES 3,757 116.2 112.1 18.1

SAO 39,930 142.6 112.3 22.3

CIS

N e

pi, R

=21

km

seismicity in Voronoi cell unrelated to mainshock

3 sec after initial P detection at PKD

log(

prob

(lat,l

on|d

ata)

)

prob

(lat,l

on|d

ata)

2nd P arrival at PHL

Cost-benefit analysis for early warning users

User A would like to initiate a set of damage-mitigating actions if the ground motions at user site exceed athresh. Given source estimates (and uncertainties) from a seismic early warning system, User A can calculate the expected ground motion levels apred at her site. Assuming that the predicted ground motions are (log)normally distributed, the probability of exceeding athresh given apred

apred athresh

when apred < athresh

Pex=probability ofmissed warning

athresh apred

when apred > athresh

1-Pex=probability of false alarm

h i p i=Pr(h i|apred) "Do nothing" "Act"

a > a thresh Pex Cratio 1

a < a thresh 1-Pex 0 1

Let Cdamage be cost of damage if no action was taken and

a > athresh. Let Cact be the cost of initiating action; also the cost

of false alarm. Let Cratio= Cdamage / Cact

The critical exceedance level above which it is optimal to act is

(equate the expected costs of “do nothing” and “act”, and solve for Pex)

Pcrit can be related to the predicted ground motion level above which it is

optimal to act, apred,crit

Cratio=1.1

Cratio=2

Cratio=5

Cratio=50

Applications with Cratio < 1 should not use early warning informationCratio ~ 1 means false alarms relatively expensiveCratio >> 1 means missed warnings are relatively expensive; initiate

actions even when apred<athresh , need to accept false alarms

Simple applications with Cratio >> 1 stopping elevators at closest floor, ensuring fire station doors open, saving data

M4.75 Yorba Linda

M6.0 Parkfield

M6.5 San Simeon

M7.1 Hector Mine

The choice of prior (with or without Gutenberg-Richter) is irrelevant once there are enough observations to constrain the source estimates; the different estimates eventually converge

VS M estimates w/o Gutenberg-Richter almost always have a smaller error compared to actual M than estimates with Gutenberg-Richter

VS M estimates w Gutenberg-Richter in 4 cases are smaller than actual M. (In general, perhaps this is almost always the case.)

Users basing actions on estimates with G-R lower their probability of false alarms, but increase their vulnerability to missed warnings

Need to generate statistics about how VS estimates evolve with time, ie, how much larger are the initial estimates likely to grow

Some central ideas / Conclusions Bayes Theorem is a useful framework for applications in real-time

seismology, which typically have contrasting requirements for speed and reliability of estimates; Bayes prior mimics how humans make judgments with a sparse set of observations

Need to carry out Bayesian approach from source estimation through user response. In particular, the Gutenberg-Richter recurrence relationship should be included in either the source estimation or user response.

Robustness of source estimates is proportional to station density in epicentral region; sparsely instrumented regions need prior information, which introduces complexity

Use of earthquake occurrence models (particularly short-term seismicity-based forecasts) as prior information

If a user wants ensure that proper actions are taken during the “Big One”, false alarms must be tolerated.

Thank you