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Ground‐Motion Prediction Equation( GMPE) for Taiwan
Po‐Shen Lin
Disaster Prevention Technology Research Center,
Sinotech Engineering Consultants, INC.

Disaster Prevention Technology Research Center ( DPTRC )中興社防災科技研究中心

Outline• Introduction of GMPE
– Important component of PSHA
– From attenuation equation to GMPE
– Steps for building GMPE

• Taiwan’s GMPE – Past、Present、Future• Conclusion• Future work

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Steps in Probabilistic Seismic Hazard Analysis

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What is GMPE
• “Was”– Attenuation relations– Attenuation relationships– Attenuation equations• It is an equation that can be used to predict thepossible ground‐motion value during a futureearthquake.
• Most of then are “empirical”, and wasdeveloped from a set of ground‐motion datawith proper physical meaning中興社防災科技研究中心

Why Call them “Ground‐Motion Prediction Equations”• “Attenuation Equations” is a poor term
– They describe the INCREASE of amplitudewith magnitude at a given distance– They describe the CHANGE of amplitude withdistance for a given magnitude (usually, but
not necessarily, a DECREASE of amplitudewith increasing distance).

Art McGarr, 2006

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Ground Motion Prediction Equations• Empirical regressions of recorded data
• Estimate ground shaking parameter (peak groundacceleration, peak velocity, spectral acceleration orvelocity response) as a function of(1) magnitude(2) distance(3) site• May consider fault type (strike‐slip, normal, reverse)
Art McGarr, 2006

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Steps for building GMPE
• Establish database• Select form of predictive equation• Perform regression analyses• Evaluate uncertainty

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Combination of horizontal measurements• Arithmetic mean (算數平均數)• Both• Geometric mean (幾何平均數)• Largest component• Random• Resultant (a=a1*cosθ+a2*sinθ)• Vectorial addition ( av  a1 (t )2  a2 (t )2 )• GMRotI50

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Characterisation of source• Earthquake magnitude, M– ML– MS– mb– MW• Source mechanism– Strike slip、normal faulting、reverse• Tectonic setting– Crustal、subduction

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Characterisation of path
• Definitions of source‐to‐site distance– Epicentral distance、hypocentral distance、
rupture centroid distance、centre‐of‐energy‐
release distance、surface projection distance (Rjb)、surface projection distance with focal depth、
rupture distance (Rrup) 、seismogenic distance、
average site to rupture end distance、equivalent
hypocentral distance (EHD)

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source‐to‐site distance(Abrahamson and Shedlock, 1997)

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Characterisation of site
• From data selection• Multiplicative factor• Shear‐wave velocity (Vs30)

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Form of the predictive equation

Y=f(M,R,Pi)
Y: Ground motion parameter of interest– M: The magnitude of the earthquake– R: Distance from the source to the particular site
– Pi: Other parameters (earthquake source, local
site conditions, wave propagation path…)

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Analysis techniques• The majority of ground motion estimation
studies use the ordinary least squares
method• Two‐stage method• Non‐linear regression• Maximum‐likelihood method (mixed effectsmethod)

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Author茅聲燾(1978)

Equation

ParameterRegion

台灣地區 CWB震度

5

台灣
東北部

SMART-1

6R為震央距離， 台灣地區M為芮氏規模(ML) (岩盤)

SMA-1

49

Y = 0.3725e0.876MD-1.836，D=(R2+400)1/2(g)R為震源距離Tsai & Bolt
PGA = 17.5e0.869M(R+0.0606e0700M)-1.09(1983)(gal)

R為震源距離，M為芮氏規模(ML)倪與邱(1991)ln(PGA) = 6.09 + 0.26M–0.87ln(R+6.9) (gal)Chiu and Niln(PGA) = 4.15 + 1.41ML-2.37ln(R+13.7) (gal)(1993)

Data

EventsRecords

R為震央距離，花蓮地區 SMART-2
M為芮氏規模(ML)R為測站至斷層破TSMIP(7個地震)

黃正耀(1995)

Y = 0.0253e1.5873M (R+0.3155e0.6165M)-2.3027

劉坤松(1996)

Y = 0.0308e1.20M (R+0.1413e0.6892M)-1.741(g)

R為震源距離， 台灣東北M為芮氏規模(ML) 部地區

TSMIP

羅俊雄
(1996)

Y = 0.0267e1.354M (R+0.2138e0.7499M)-1.0329(g)

R為震源距離， 台灣地區M為芮氏規模(ML) (岩盤)

SMA-1

羅俊雄
(1996)

Y = 0.0273e0.1058M (R+0.141e0.656M)-1.6472(g) 裂面之最短距離， 台灣地區辛在勤
(1998)PGA = 12.44e1.31ML r-1.487(gal)

r為震源距離，台灣地區
ML為芮氏規模(ML)

TSMIP

22

劉坤松(1999)ln(PHA)=-1.339ln(r+2.12)-0.0071r+1.167M+2.192+G(1.475ln(r)-6.792)ln(PVA)=-1.681ln(r+2.45)-0.0036r+1.250M+
2.210+G(1.009ln(r)-4.464)
ln(PHV)=-1.377ln(r+1.67)-0.0023r+1.581M3.070+G(1.066ln(r)-4.909)ln(PVV)=-1.415ln(r+1.58)-0.0012r+1.666M-r 為震源距，M 為台灣地區
地震矩規模TSMIP

35(g) 裂面之最短距離， 台灣地區M為芮氏規模(ML)7526

R為測站至斷層破TSMIP

M為芮氏規模(ML)2187

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Most used GMPE for the Engineer

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斷層線下盤

上盤

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李錫堤等(1999)
Loh et al.
Y = 0.02968e1.2 M (R+0.1464e0.698M)-1.7348(2000)

台灣地區
美濃水庫

TSMIP

(g) 裂面之最短距離， 台灣地區

TSMIP

R為測站至斷層破M為(MW)?

羅俊雄與
Spectral Acceleration at 80 periods (0.029~10台灣地區
溫國樑，sec)
2000
ln A = 2.8096 + 0.8993M–0.4381 ln Dp –De、Dh、Dp分別為震Chang et(1.0954–0.0079 Dp ) ln De央距、震源距與震 台灣地區al. (2001) ln A=4.7151 + 0.8468M–0.1745 ln Dp –1.2972
源深度(km)ln DhTSMIP

TSMIP

4519台灣地區

TSMIP

93104

M為地震矩規模
MW，rrup為距斷層破 台灣地區log10(PGV)=-2.49+0.810M-log10(rrup+0.00871× 裂面距離(km)TSMIP

601941

趙曉玲(2001)
log10(PGA)=0.00215+0.581M-log10(rrup+0.008
Wu et al.
(2001)

71×100.5M)-0.00414rrup100.5M)-0.00268rrup

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20

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Seismotectonic framework of Taiwan

Data source:
1.Central Weather Bureau(CWB)
2.Institute of Earth Sciences, Academia Sinica

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Strong‐motion data for GMPE – Crustal

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Strong‐motion data for GMPE – Subduction

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Ground‐motion prediction equation
For Crustal Earthquake

For Subduction zone earthquakeln y  C1  F1  C3 (8.5  MW )2  (C4  C5 (MW  6.3))ln( (R2  exp(H )2 )) C6FNM + C7FRV  C8 ln(VS30 /1130)
Where F1  C 2 ( M W  6.3)
 F1  (  H  C 5 )( M W  6.3) WhereM W  6 .3
M W  6 .3



ln y  C1  C 2 M  C 3 ln R  C 4 e C5 M  C 6 H  C 7 Z t  C8 ln(Vs30 / 1130)

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Variation of the standard deviation in the SA
equation with periods from 0.01‐5.0 sec

Total sigma

Intra-event
sigma (σ)

Inter-event
sigma (τ)

StationEarthquake
epicenter`

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StationEarthquakeepicenter

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The notations••••

i → eventk → sta onl → region
Residuals– Intra‐event, ik inter‐eventi– Inter‐station, sk intra‐station rik– Inter‐path, pkl intra‐path 0ik– Inter‐region, SRl intra‐region 0i• Standard deviations– Intra‐event,  inter‐event– Inter‐station,  s intra‐station  r– Inter‐path,  p intra‐path  0– Inter‐region,  SR intra‐region  0

Following the notationof Walling (2009)

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Decomposition of the variability of empirical groundmotion prediction equation ‐ conclusion2 T   SR
  02   s2   p2  20

T   2  2Inter-event2 2   SR  02

small source region
unexplained inter-event
variability

Single-path sigma  sp Intra-event 2   s2   r2Inter-site(site-term)

record-to-record   2r

 2   s2   p2   02

 02   02

2p20

unexplained intra-event
variability

path-to-path

Single-site sigma

 ss   2   r2

(single-station sigma)

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Reduction of the inter‐event, intra‐event, and total
standard deviation from the TSMIP data, if the ergodic
assumption is removed
Single Site

Single PathTotal

Intraevent

Total

InterEvent

IntraEvent

SS

r

SP

00PGA

0.91T0.86

0.54T0.69

0.43

T=0.10.88T

0.81

0.53T0.69

0.42

T=0.30.90T0.86

0.60T

0.69

0.55

T=0.50.89T

0.83

0.61T0.69

0.57

T=1.00.86T0.75

0.59T0.69

0.51

T=3.00.86T0.69

0.60T0.69

0.51

Correlation of notation differences for中興社防災科技研究中心
components ofvariability from previous studies with the currentstudy2  2Standard Deviation

This Study

Chen & Tsai(2002)

Atkinson(2006)

Morikawa et al(2008)

Total

TregInter-eventIntra-eventInter-site

SSSingle site,
record-to-recordrrInter-path

P

Intra-event,Single Path0Inter-source region

SRInter-event,Single Region

0Single Site (total)

SS

i

Single Path(total)

SP

ie

(no correction)

E(no correction)

(appliedcorrection)
(appliedcorrection)(appliedcorrection)

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Comparison of single‐path standard deviations (σSP) asa fraction of σTPGAThis Study

Atkinson (2006)

Morikawa et al.
(2008)

0.54T0.67T

0.46T

T=0.1
0.38T0.53T
T=0.3

0.60T

0.68T

0.44T

T=0.5
0.61T
T=1.00.59T

0.45T
0.67T0.47T

T=3.00.60T

0.47T中興社防災科技研究中心

Conclusion• More and more strong‐motion data
• Strong ground motion parameters– PGA, PGV, PGD, Ia and Sa• Including crustal earthquake and subduction zoneearthquake• Source‐to‐site distance– From epicenter distance to the closest distance to fault
rupture plane• Site parameters– From rock/soil to Vs30

• Hanging‐wall and footwall

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Future work
• For GMPE
– More predictor variables for source, path and site
– Directivity– Nonlinear site effect– Strong‐motion difference due to various stress drop

• For Ground‐motion prediction– Empirical approach– Seismological approach• Empirical Green’s functions (EGFs)• Stochastic Green's functions (SGFs)• Hybrid Green’s functions (HGFs)

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Thank you for your attention.

Disaster Prevention Technology Research Center ( DPTRC )