Seismology based strong ground motion attenuation relationship for
national zoning map
TAO Zhengru
Institute of Engineering Mechanics, China Earthquake Administration
2011.11.25-11.30, HIT·Harbin
1
• Empirical method• For regions with enough data (e.g. western US and Japan)• For most countries or regions?
• More and more strong motion observationinstruments are installed…
• Space• Time
2
Background
3
National strong motion observation network system (Li et al., 2008)
How to establish relationships for regions with few or without strong
ground motion records?
Background• In China, strong ground motion records
are not enough now.• Mapping method (Hu, 1980s):
This method assumes that, for region A of enoughacceleration observation data and a region B of few suchdata, earthquake pairs (MA, RA; MB, RB) exist in theintensity attenuation curves IA(MA, RA) of region A andIB(MB, RB) of region B, so that they give the sameintensity I and ground motion Y.
Region A:
Region B:
]0461log[7231566.0297.1)log(5.0 AM
AAA eRMY
)10log(014.200659.0500.1514.0 AAAA RRMI
)24lg(136.44461019.5 BBB RMI
]700.1log[902.1548.0027.2)log(425.0 BM
BBB eRMY
China Earthquake Data Center
FrameworkTarget region
Data from digital seismic network
Data from strong motion networkEmpirical relations
∆σ, Q0 and η
µGA
Strong ground motion attenuation
relationship
Stochastic Method
Comparison
Methodology
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Assuming the accelerations, on the far-field and an elas ichalf space, are band-limited, finite-duration, white Gaussiannoise, and based on Brune ω2 model, he source Fourierspectra FA(M0, f, R) on a site can be described as
fIfPfAfRDRGfMSCRfMFA ,,,, 00
where, C is proportion factor; S(M0, f) is source spectrum for a specifiedseismic moment; G(R) is geometric spreading function; D(R, f) isanelastic attenuation function; A(f) is the amplification factor of nearsurface amplitude; P(f) is a high-cut filter that rapidly reduces amplitudesat high frequencies; I(f) is spectrum shape parameter, used to shape thespectrum to correspond to the particular ground-motion measure ofinterest.
130130
70
1
1307070
1
701
)(
RR
R
RR
RG
( , ) expfRD R f
Q
0Q Q f
1/28
max
( ) 1 fP ff
( ) (2 )zI f f
6 1/30 04 9 10 ( / )f M
9
2
0
00
1
),(
ff
MfMS
304 ssRFVR
C
Following Hanks (1979), we estimate the arms using Parseval’s theorem. The estimation is valid for a time window equal to the faulting duration Tdbeginning with the direct shear arrival; in Hanks (1979), Td =1/fo. In terms of spectral parameters, Ω0 and fo, the result is
1 2
0ms
d
maT
According to the relation between Fourier spectrum and power spectrum and the definition of spectral moment, the latter can be calculated by the following numerical integration,
22 ( )kkm f FA f df
0
dfefdffFAmf
f
Q
fRf
f
max
0
max
0
2
200
2
0 )2(2)(2
The peak factor γm, which describes the ratio of peak to rms motion, is calculated by the following numerical integration,
PGA= γm * arms
0
2exp112 dzz eNm
2140
2
mmm
NN
e
z TfN ezez ,, 2 21022
1 mmf z
21242
1 mmfe
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CASE OF SENDAI AREA
12
13
1996.1-2011.4
12 F-net stations632 earthquakes
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Distribution of hypocentral distance with Mw
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Distribution of focal depth with Mw
6
Δσ Qo η
40~100 bars 100~300 0.6~1
Δσ Qo η
45.17 bars 124.91 0.61
Inversion ranges
Inversion results
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PGA attenuation relations Strong motion data from K-NET
• 4256 strong motion data (Mw≥4.5 and focal depth≤30 km)
• 88 K-NET bedrock stations (TG<0.2s)
Empirical relations• Tatsuo Kanno, et al., (2006)
• Hongjun Si, et al., (2000)
• Yoshimitsu Fukushima, et al., (1990)
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370260)1000550log(00310560)log( 5.0 wMw XXMPGA
30.10034.0)10032.0(log41.0)log( 41.010 RRMPGA sM
s
eqeqw XXDMPGA 0030log28012000390580)log(
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N
i valuepredicted
valueobserved
Nresidual
110 )(log
1
PGA relations Mw=5 Mw=6 Mw=7
Fukushima (1990) -0 2970 -0.0613 0.0887
Kanno (2006) -0.4168 -0.3503 -0.3591
Si(2000), D=10 -0 2003 -0.1698 -0.2407
Si(2000), D=20 -0 2393 -0.2088 -0.2797
Si(2000), D=30 -0 2783 -0.2478 -0.3187
This study -0 5093 -0.3894 -0.2520
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Case of Southwestern China
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Yunnan Province
2001-2007
26 seismic stations162 earthquakes863 records
Sichuan Province
2001-2007
29 seismic stations48 earthquakes147 records
Distribution of hypocentral distance with Mw
24
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Distribution of focal depth with Mw
Inversion ranges (Ye, 2001; Su, 2009)
Δσ Qo η
40~200 bars 90~400 0.15~0.8
Inversion results
Δσ Qo η
105.14 bars 92.41 0.21
PGA attenuation relations
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Strong ground motion data
• 66 strong motion data (Mw≥4.5 and D≤30 km)• 36 strong motion station (bedrock)
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Empirical relations• Yanxiang YU and Suyun WANG (Western China, 2006)
• Jiancheng LEI, et al. (Sichuan basin, 2007)
• Jiancheng LEI, et al. (southwestern region, 2007)
• Jianwen CUI, et a . (Yunnan 2006)
• Jianguang XIANG and Dong GAO (Yunnan, 1992)
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)018.2(log954.1532.0206.2)(log 06.0
00sM
ss eRMMPGA
)5292.2(log1920.20665.0380713349.0)(log 333.0
02
10sM
ss eRMMPGA
)340.0(log441.1501.00101)(log521.0
010sM
ss eRMMPGA
)0617.1(log8499.10715.04539.15206.1)(log385.0
0
2
10sM
ss eRMMPGA
)8691.0(log639210845.05408.182441)(log38.0
0
2
10sM
ss eRMMPGA
)4022.0(log3846.10812.04860.11376.2)(log56.0
10
2
0sM
ss eRMMPGA
)13(log)0889.07317.2(2881.05549.3)(log 1010 RMMPGA ss
5785.15275.0)15(071291 RePGA sM
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N
i valuepredicted
valueobserved
Nresidual
110 )(log
1
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Relations Mw =5 Mw =6 Mw =7
Xiang, et al. (1992) -0.1524 -0 0895 0.1381
Cui, et al. (2006) 0 3242 0.1188 0 2376
Yu, et al. (2006)-0 0907 -0 2262 -0.1191
0.1957 0 0306 0 0524
Lei, et al. (2007)0 2543 -0 0437 0.1091 0.4792 0.1359 0 2108
Lei, et al. (2007)0 2997 0 0083 0.1130
0 3395 0 0646 0.1222
This study 0.2092 0.1053 -0.1217
The endThanks
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