Analyse des données accélérométriques de K-net et
Kik-net : implications pour la prédiction du mouvement
sismique - accélérogrammes et spectres de réponse - et
la prise en compte des effets de site non-linéaire.
Guillaume Pousse
To cite this version:
Guillaume Pousse. Analyse des données accélérométriques de K-net et Kik-net : implications
pour la prédiction du mouvement sismique - accélérogrammes et spectres de réponse - et la prise
en compte des effets de site non-linéaire.. Géophysique [physics.geo-ph]. Université JosephFourier - Grenoble I, 2005. Français. <tel-00068748>
HAL Id: tel-00068748
https://tel.archives-ouvertes.fr/tel-00068748
Submitted on 13 May 2006
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Accélération (
.
-2
)
Vitesse (
-1
)
Déplacement (
0.017
0.002
0.00
0.000
0.000
PGA = 0.451
-0.50
0.0
-2
.
20.0
Temps ( )
-0.017
0.0
40.0
Intensité d’Arias
)
-2
95% maximum
5% maximum
Amplitude (
Amplitude (
.
)
-3
.
phase forte
2
Durée de
0.00
0.0
20.0
Temps ( )
Spectre de Fourier (
.
20.0
Temps ( )
-1
40.0
-0.002
0.0
40.0
.
-1
40.0
10-2
PSA(10 - 2 ) = 0.450
10-2
)
.
-2
10-1
100
Période ( )
Spectre de Fourier (
10 1
)
Spectre de Fourier (
10-3
Déplacement
Vitesse
10-2
10-4
10-5
10-6
100
Fréquence (
20.0
Temps ( )
10-1
10-3
10 -1
PGD = 0.0014
100
10-3
10-1
10-4
PGV = 0.01453
)
Accélération Spectrale
0.13
Accélération
.
0.50
101
)
10-7
10-1
100
Fréquence (
10 1
)
. )
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-1
10 0
Fréquence (
101
)
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60.0
40.0
20.0
0.0
4.0
5.0
6.0
7.0
5.0
6.0
7.0
% of K-net records
80.0
60.0
40.0
20.0
0.0
4.0
% of Kik-net records
80.0
60.0
50 km
100 km
150 km
200 km
250 km
300 km
350 km
40.0
20.0
0.0
4.0
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6.0
Magnitude
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soil A
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soil B
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soil C
depth (m)
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soil D
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0.0
1000.0
(
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prediction K-net
101
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101
100
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102
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102
10-2
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100
100
10-1
10-1
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101
10-2
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102
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102
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102
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1
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2
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1
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1
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8
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6
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4
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0
0
0
0
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2
10
2
0
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2
2
1
10
−2
2
10
2
1
10
−2
2
10
2
2
1
−2
2
10
2
0
−2
1
10
2
10
1
10
2
10
1
−2
2
10
1
10
2
10
−2
2
−2
2
2
10
−2
2
1
2
10
distance
−2
−2
2
1
10
2
10
0
1
10
2
10
−2
2
1
10
2
10
0
1
10
2
10
−2
2
1
10
2
10
0
1
10
2
10
0
10
distance
1
10
0
0
10
2
0
0
10
−2
0
0
0
−2
2
10
0
0
−2
1
10
soil C
1
10
soil D
2
soil A
σ(Fbc)=0.1321
2
soil B
σ(SMD)=0.2866
2
−2
residual
σ(AI)=0.5473
2
−2
2
1
10
2
10
soil E
σ(PGA)=0.2962
2
0
1
10
2
10
distance
−2
1
10
2
10
distance
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[OTp[di d!DbWXFU ) WvPVWX`cR3Ugp[di3`` QtNQPWx[O+\ l`cNQR3i_\bi~[d`V`[dT;U QtNQPY WNd]`cWbPVkQWbU{`VYZPVNQfT Ob[sNdYcRGNQR
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H
62i
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! ) ) ) ) ; K ) T!
P
P
P
0
4
6
−2
8
4
6
8
−2
4
6
8
−2
2
2
2
2
0
0
0
0
4
6
−2
8
4
6
8
−2
4
6
8
−2
2
2
2
2
0
0
0
0
−2
4
6
−2
8
4
6
8
−2
4
6
8
−2
2
2
2
2
0
0
0
0
−2
4
6
−2
8
4
6
8
−2
4
6
8
−2
2
2
2
2
0
0
0
0
−2
4
6
−2
8
Mw
4
6
Mw
8
−2
4
6
8
−2
4
6
8
4
6
8
4
6
8
4
6
8
6
8
soil B
0
soil C
0
soil D
0
soil A
σ(Fbc)=0.1321
2
−2
R
σ(SMD)=0.2866
2
−2
residual
σ(AI)=0.5473
2
soil E
σ(PGA)=0.2962
2
4
Mw
Mw
Q * **S *\[6" K O(' * r L3'* #N;.$PO/(a [<\O'
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8:8:9,9,;; <><>='= ?V? sDUXEYW @@
8:9,8:9,;;<>='<>='? )?V[ Z ac/ @ @
8:9,; <>= ? pX\ J'@
(BIKCC P>DSD1TEG) M1F1HHI&IJBBFF
B(B(C CMQTEGS1MEF1HHNOIJB(BP B
B(B(C CDTFB(DPRM1QHHNOIJB(BP B
KI B(C LC MLGTMD1M1* LHHNOI&B1BL B
B(IKIKCC CLGLGT(DS1P>B1QGT1LT1EHHHNONI&B(B(BP PB
IKC LGDD1EHI&B1L
B(B(CC PRP>M1QEGL-,D1PR+ HHNONOB(B(PP B(B(CC P>P>DM1SEG-D1M1 HHNNB(B(PP B(B(CC P>P>D1M1L-EG/F1PR. HHNONOB(B(PP
B(IKCC F(PRP>LF1LGEM1HHNONOBB(B P B(IKCC LPREGLGD(MPRT1HHNONBB(B P B(IKCC LGPRFQ-S1PREEHHNONOBB(B P
B(IKCC SM(BP>T1F1EQHHNONOBBBB B(IKCC QGM1DL-SP>B1T1HHNONBBBB B(IKCC D1MEGT1ML-B1PRHHNONOBBBB
B(B(CC P>P>F1M1LEG1D1L0 HHNNB(B(PP
B(IKCC LGPRD1QLGQGS1D1HHNONBB(B P
B(IKCC DM1D1QGEGSB1D1HHNONBBBB
B(B(CC P>P>F1M1LEG-D1E2 HHNONOB(B(PP
B(IKCC LGP>DDF1M1ELHHNONOBB(B P
B(IKCC DM1TQGTFS1F1HHNONOBBBB
B(B(C C P>(T(S%4P>T(36SPRS157HHNI&) B1BL B
B(B(CC QGLGD1TSEGF1S1HHNNBBBB
B(B(CC LGP>F1MS1L-LPRHHNNBBBB
* : $fO G."',# : #'G\Q G$*$1%(T3ed4E*K" P, 6* : E$(4\Q EK1.( %"gND(*$fO
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16.0
km
km
km
km
Frequency (
)
scenario
=5 at 30
=7 at 30
=5 at 80
=7 at 80
10.0
soil A
soil C
4.0
0.0
10.0
20.0
Time ( )
Q * q,S !%2#MVQ #>} '%1dhN .$1\(a."'#O"VQ ( "1.%,$" k "$#1.#E" "%"C kV3#E1PbGsG*
kAOdPsgs' C%"'*#"`QV(R9"\Q%R"(#U$*$1%)&#$6]R%!1.%2#4QV "}>'%*1#d kV"(#U\[RN#,1%(
#;%1." s\ 0*$(M>L E* %"CQ " .K%1%d
d $B/[ )E, VQ (G 9H1PbB" Rk~}H'(y* q\s'
Z
R
6
PGA; σ=0.2962
0.999
0.997
0.99
0.98
0.95
0.90
Probability
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−4
−3
−2
−1
0
1
2
3
log(PGAobs / PGAlaw−att) (x σ)
AI; σ=0.5473
0.999
0.997
0.99
0.98
0.95
0.90
Probability
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−4
−3
−2
−1
0
1
log(AIobs / AIlaw−att) (x σ)
2
3
N*#$"-1I$f Oa(5E d4 t="-/1.'f[&'#$ : ND%1.%2PJO(<\Q
Q *CB S )( [<~# }>',>$#R
P^k1.(" "%"!s@,%1+)>'f[&3D%@\QU=kV(6tk t=$"!s QV@vN;%bbO( ('<1%1.%#$.$(4L
&)E")>%" i d\L;E *4" (P Oj[/$8'*$(0gE*QV#}>'%1dg3,P]C$=EW(g1.%2#
QV " }>'.#1 ddI ) *%"g [/4# N (3,3*$#$Oi d N#$"G1.F [^N 9" $3'=$B\ Q E 9 %" $',#$"
]COE aE *-*(g [/#" $3*'*( k" .0#$ s'
6
* n ) ) ) ] ) U ) K ) T U ) T ) U ]. ) ) ) + T 4i) d
! ) ) ) ] ) ; K ) T!
SMD; σ=0.2866
0.999
0.997
0.99
0.98
0.95
0.90
Probability
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−5
−4
−3
−2
−1
0
log(SMDobs / SMDlaw−att) (x σ)
1
2
Fbc; σ=0.1321
0.999
0.997
0.99
0.98
0.95
0.90
Probability
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−4
−3
−2
R
F6
−1
0
1
log(Fbcobs / Fbclaw−att) (x σ)
Q * BS ='O
2
3
4
6.0
6.0
6.0
4.0
4.0
4.0
2.0
2.0
2.0
0.0
0.0
0.0
-2.0
-2.0
-2.0
-4.0
-4.0
-4.0
-6.0
-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0
-6.0
-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0
-6.0
-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0
QVF [ E T
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s .<uU..>" P1%."jk o6zPLCFz? rJz8b[jsQ( "(#] RN#$ . K O(' * o6z R@ 1+
6] 1.( %"gND(*" W"[&'#EA$"ND%QV(g[6%=]COE7B"J[/[/\O(O'*\TL eI1+h
1.(#$'f6[ 1.( %"N;(*"-C"\[6C$"FP*1% ) ." "[&'#EA$", : 3D%%^;N .VQ (/
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K (O ' *o\-o "; 6C] ") #; %1.)\TQ $1.%"fO O $Oi<d \SQ E* -" ($#d (O ('*l6[ $(F
W m Q : .>"2L #$H1I%NAXFz b[y(L N %1.(. ( : ) * G6[ * $" (%"T1%( %";N N *; %.2)" ($#;idGDN %"L ) 1% I" $ OhVQ ">} '.1#?
d 1%>%2)$";N .1."*N $3# C] Ed 1% I" $fO
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d \Q "(#$"#RL "B#IPd "'fOFO %" %`3ed K (O ' * q B"<>% %" $fO 78, /E -Y$"N##$/J; %1.%[3e7
d E* a"(#Rid ;N J@L " #IPd>6[ %2$(.[$ T '"" ?\6#=Vk w\z\zer es\
U (. : %#L % "K#$O#QuU .%*1%$d'(?\6[ (fNO uU .%2 1I"%"bk "C$1%.a3ead E ?
" /1.(O$ 1.='/
1.$.>"b6[ %2(% $ ) 3#$^* *es' ) B Oi2 N #-$ K (O ' R*o\<o "* C] "
1%( ."gDN (f6
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FF
* n ) ) ) ] ) U ) K ) T U ) T ) U ]. ) ) ) + T 4i) d
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13.0
/ 2)
Acceleration (
13.0
PGA = 11.5
/
2
0.0
11.0
22.0
-13.0
0.0
/
2
11.0
M73D050S1
22.0
/
2
11.0
-4.0
0.0
Time ( )
22.0
/
2
0.0
M60D030S1
22.0
11.0
PGA = 0.503
0.0
M60D010S1
-13.0
0.0
4.0
PGA = 0.938
0.0
2
/
0.0
4.0
PGA = 3.15
/ 2)
PGA = 1.84
M73D030S1
4.0
-4.0
0.0
2
/
0.0
M73D010S1
-13.0
0.0
Acceleration (
13.0
PGA = 3.44
11.0
Time ( )
M60D050S1
22.0
-4.0
0.0
11.0
22.0
Time ( )
R Q *uo6z S ;%1\Q\ Q<*%1% I" $fO [<\O'^k1.(#$'f[6HsCWg$1.%"fO<" 1%jk ]
s
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[/H%#0
892 5 626= ;/ ?.A92 6@ 2 A9; 5 5 : :<@<:0A
Q!\Q E* K : 2PJO(%"T\Q,E"+"FH1+," $1`[/H%#H$"S" 3*$#$OidQ "N*H'1%RE!#$%(d
d \;Q E (O (' [6(F 6( %]1.F[^NC"[&'#$. 6(3". : % O('*^[6:
: E3$#i
$ : E3*$#$OidFHL %Oi2 1%1%.#$.F(O \6
[ "VVQ (C rk /[ \/[ .>/[ \(O *'*9 : %2Q#=1%.8AT\z6b[
(g "(# Z , : 43D%.g1%\[^N '=%x ?E .""4
[ '#E$(*""=L N \6[ .% : #$'*%")".#$.1..
]CE* $eE df(O d\)Q (d" , : EA$h('* hN .$1\% /[ .E : #$': %" "Hd 2E \$1."& /1.F[R,N . 8(3*"% : . X .- %1%"L /" I 1+>VQ (-.1%( "5 X .
,P3,"Q#$#C
] fO_Xzxw $ /[ F6[ %2 <[ \O 'Qo4z b[ $<$"FP1. dO$ML
,.-G, -0/
F6
1.5
4.0
PGA = 1.02 / 2
KNET M60D030S5
0.8
soil
soil
soil
soil
soil
0.0
soil E
-0.8
-1.5
/ 2)
PGA = 1.03 / 2
KNET M60D030S4
A
B
C
D
E
3.0
soil D
PGA = 1.09 / 2
KNET M60D030S3
0.8
2.0
0.0
/ 2)
Acceleration (
SA (
1.5
soil C
-0.8
-1.5
PGA = 0.956 / 2
KNET M60D030S2
soil B
1.0
1.5
2
PGA = 0.938 /
KNET M60D030S1
0.8
0.0
soil A
-0.8
-1.5
0.0
5.0
10.0
Time ( )
15.0
10 -2
10-1
100
0.0
Period ( )
o\oS| U.1.KJQSB$*1%%"fO4 O(id&\Q "(#;B"[&'#EA% [/)1.1%%#%(9" (%"
kW LR Fz8b[ s'7@1+7[/ " (d_"4"[&'#$. QV(
B " ($#@1.(O$",L L TL
* =&
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Amplitude (m/s)
3
101
2
100
10-1
10-2
= 5.0
= 6.0
= 6.5
= 7.0
10-1
100
101
102
frequency (Hz)
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F H
KNET M54D030S3
/ 2)
PGA = 0.765
2
/
PGA = 0.421
2
/
TKY010
0007240652
KNET
PGA = 0.840
TKY010
0006291530
KNET
PGA = 0.429
MYG013
0307260013
KNET
PGA = 0.573
MYG008
0307260013
KNET
PGA = 0.451
MYG007
0307260013
KNET
PGA = 0.738
KGS008
9704030433
KNET
PGA = 0.587
KGS006
9704030433
KNET
PGA = 0.533
HRS001
0010081317
KNET
PGA = 0.544
/
2
/
2
/
2
/
2
/
2
/
2
/
2
/
2
Acceleration (
1.0
0.5
0.0
-0.5
PGA = 1.12
2
/
-1.0
PGA = 0.613
PGA = 0.427
PGA = 1.17
0.0
5.0
10.0
Time ( )
15.0
2
/
PGA = 0.625
PGA = 1.13
2
/
2
/
/
/
2
2
20.0
0.0
5.0
10.0
15.0
20.0
Time ( )
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Simulations
KNET
+ 1 sigma
0 sigma
- 1 sigma
variability
/ 2)
2.0
Records
= 4.5
= 30km
SA (
1.0
0.0
SA (
/ 2)
5.0
/ 2)
10-1
100
Simulations
10 -2
10-1
100
Records
= 6.0
= 40km
4.0
3.0
2.0
1.0
0.0
SA (
10 -2
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
10 -2
10-1
100
Simulations
10 -2
10 -2
10-1
100
Records
10-1
100
10 -2
Period ( )
= 7.3
= 70km
10-1
100
Period ( )
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103
102
101
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soil A
soil C
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soil E
M_w 4.5
107
106
105
104
103
102
101
100
10 -1
4.5 <M_w 5.5
107
106
105
104
103
102
101
100
10 -1
107
106
105
104
103
102
101
100
10 -1
soil B
5.5 <M_w 6.5
6.5 M_w
10 0
101
102
(
100
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101
102
(
100
101
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(
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102
(
100
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2
1
0
coefficients
−1
−2
−3
−4
−5
−6
−7
a
(weak dataset)
bx1000 (weak dataset)
a
(strong dataset)
bx1000 (strong dataset)
−8
−9
−1
0
10
10
period (s)
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·G¾«Vù§·`´µ«G¸±oIÆ«VÖ®N½«G{®}±«`³ðÁ´º±{¶o®ÅÂ~®N·G±¾#¾NÂ Ç ÊÊÊ)®N¸³ð«`¯µ®}±{«G³ð±¾"®}¸«`¯µ®N°T±´µ·£®}±T±{«`¸>²M®k±{´µ¾N¸',-¾}:
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ïµ¾N±T±{«`³PÃ@«G¸)±´Ä®}¸½¯µ«G°e·`¾N«G°Ã¾¸³<±{¾q±{¶«#¬}®N¯º²«`°¾»±g®N´º¸«`³ÅÂ/¾e±¶« 3
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Residual
σ(PGA)=0.3263
σ(0.2)=0.367
2
2
1
1
0
0
−1
−1
−2
1
10
−2
2
1
10
Residual
σ(1)=0.3334
2
1
1
0
0
−1
−1
1
10
−2
2
1
10
2
10
Distance (km)
Í «`°T´µ³²M®}¯?¬}®N¯º²«`°'»@«V±Á-«G«`¸q±{¶«
10
σ(4)=0.358
2
−2
2
10
10
Distance (km)
N¾ ÂM±{¶«-¾»°T«` ¬«`³£°TÃ@«G·G±{®N¯®}·`·`«G¯µ«G{®}±´µ¾¸®}± 3Æ
ÊÉ?Æ Ç ®}¸³æÍ°®N¸³æ±{¶«-ÃT«`³´º·G±{«G³q¾¸«}ÆN²°T´µ¸½*±{¶«1äVá~Ü{Ý Û à Ýká~âXÝ Ü{Ø ß â á~âXÝ Ø`ÞÙNá~âXÝ Ã«G°«`¸±«`³
´µ¸Õ±¶´µ°*°T±²³¹ /Â/¾*¶¾T´µèG¾¸±g®N¯¿§¾N±{´º¾¸ÆÑ%wÓ³M®}¿Àôº¸½>fÆM³«`ë`¸³´µ¸½C¾N¸"±{¶«·`¯º¾°«G°T±³´µ°T±{®N¸·G«±{¾
±{¶«Â~®N²¯i±M7*«®¬>¹)¶¾´ºè`¾¸±{®N¯¯µ´º¸«`°®}«#¯µ¾?·®}±«`³)®}±±{¶
« é¬}®N¯µ²«}¶«G°«3ïµ¾N±°®N«#³«`®N¯µ´º¸½qÁ´º±{¶
«`°T²¯º±°¾»±g®}´µ¸«G³<Á´i±{¶Å±{¶«¯µ®N½N«¿®}½¸´º±²³«$¬}®N¯º²«`°°T²»°«V±
xzy%{ }Z~
à
E
E
E
E
Residual
σ(PGA)=0.3263
σ(0.2)=0.367
2
2
1
1
0
0
−1
−1
−2
3
4
5
6
7
−2
8
3
4
Residual
σ(1)=0.3334
2
1
1
0
0
−1
−1
3
4
5
6
6
7
8
7
8
σ(4)=0.358
2
−2
5
7
−2
8
3
Mw
4
Ñ «`°´º³²M®N¯>¬}®N¯µ²«`°»«G±Á«`«G¸q±{¶«
5
6
Mw
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σ(PGA)=0.3452
σ(0.2)=0.3587
2
2
1
1
0
0
−1
−1
−2
1
10
2
−2
1
10
Residual
σ(1)=0.3474
2
1
1
0
0
−1
−1
1
10
10
σ(4)=0.3328
2
−2
2
10
2
−2
1
10
2
Distance (km)
10
10
Distance (km)
ê ®N¿§«£®N°4´µ½²«qÍÆ»²±²°´µ¸½<±¶«<×-ØÙkÚ à Ýká~âXÝ Ü{Ø ß â áâXÝ Ø`ÞÙNá~âXÝ ¾N»±g®N´º¸«`³
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σ(PGA)=0.3452
σ(0.2)=0.3587
2
2
1
1
0
0
−1
−1
−2
3
4
5
6
7
8
−2
3
4
Residual
σ(1)=0.3474
2
1
1
0
0
−1
−1
3
4
5
6
6
7
8
7
8
σ(4)=0.3328
2
−2
5
7
8
−2
3
Mw
4
5
6
Mw
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SA(PGA); σ=0.3263
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
2
log(SAobs / SAGMPE) x σ
SA(0.2 s); σ=0.367
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
log(SA
obs
0
/ SA
1
)xσ
2
3
GMPE
W 1¾N¿À®N¯Ô>²M®}¸>±´µ¯º«Cïµ¾}±q´µ¸³´µ·®k±{´µ¸½"¾¸±{¶«C¹>:®kÖ´µ°æ±¶«Å·`²¿3²¯Ä®}±´º¬N«CÃ@«G·G«`¸±g®N½N«)¾}Â
³M®}±g®)/·`¾N°°g-±¶M®}±*«`®N·g¶«`°1®q¸>²¿æ»«`¾N ï/¾¸<±{¶«Ö>:9®kÖ´º°ge®}± ÆMÊWÉÆ Ç ®N¸³)Í£°`M¶«¯µ´º¸«
®N°°T²¿À«G°*®£¯º¾½¸¾N¿À®N¯@³´µ°T±´º»²±{´º¾¸¶«`°T«Ã¯º¾N±{°®}«³«`®N¯µ´º¸½æÁ´º±¶)T«`°T²¯º±°*¾N»±g®N´º¸«`³ÅÁ´i±{¶Å±{¶«
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à Wá
SA(1 s); σ=0.3334
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
log(SAobs / SAGMPE) x σ
2
3
SA(4 s); σ=0.358
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
2
log(SAobs / SAGMPE) x σ
3
4
W ,-¾¸±{´º¸?²«`³
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SA(PGA); σ=0.3452
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
log(SAobs / SAGMPE) x σ
2
3
SA(0.2 s); σ=0.3587
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
log(SAobs / SAGMPE) x σ
2
È ®N¿§«£®N°4´µ½²«q^Æ»²±²°´µ¸½<±¶«<×-ØÙkÚ à Ýká~âXÝ E Ü{Ø ß â áâXÝ
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SA(1 s); σ=0.3474
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
log(SAobs / SAGMPE) x σ
2
3
SA(4 s); σ=0.3328
0.999
0.997
0.99
0.98
0.95
Probability
0.90
0.75
0.50
0.25
0.10
0.05
0.02
0.01
0.003
0.001
−3
−2
−1
0
1
2
log(SAobs / SAGMPE) x σ
3
4
È ,-¾¸±{´º¸?²«`³
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/ 2)
0.46
1.4
M : 4.0
X : 10 km
depth: 100 m
0.7
M : 6.5
X : 10 km
depth: 100 m
20.9
SA (
0.23
41.9
M : 5.0
X : 10 km
depth: 100 m
0.00
/ 2)
0.12
10 -2
10-1
100
0.0
10 -2
0.36
M : 4.0
X : 30 km
depth: 100 m
100
0.0
11.2
M : 5.0
X : 30 km
depth: 100 m
0.18
10 -2
10-1
100
M : 6.5
X : 30 km
depth: 100 m
5.6
SA (
0.06
10-1
0.00
/ 2)
0.014
10 -2
10-1
100
0.00
10 -2
0.046
M : 4.0
X : 99 km
depth: 100 m
100
0.0
1.7
M : 5.0
X : 99 km
depth: 100 m
0.023
10 -2
10-1
100
M : 6.5
X : 99 km
depth: 100 m
0.9
SA (
0.007
10-1
0.000
10 -2
10-1
100
0.000
10 -2
Periods ( )
10-1
100
0.0
Periods ( )
10 -2
10-1
100
Periods ( )
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ëG³´µ·V±{«`³õÂ/¾q±{¶T«`«Õ³´ºí@«`T«`¸±¿À®N½¸´º±{²³«Å«®N ±{¶Ô>²M®}¼N«`° Æ ð®N¸³ ±¶«)°¾²T·`«
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01$! #231&01%*)45#67$89$:91+;1&,*<$1$%>=? @
= 4.1
102
= 5.7
102
PGA at GL-100m
Mw 5.0 (weak)
Mw>5.0 (strong)
. 2)
101
100
100
(
101
10-1
10-1
10-2
10-2
10-3
10-3
10-4
101
10 2
= 4.6
= 6.5
101
101
. 2)
102
100
100
(
102
10-4
102
101
10-1
10-1
10-2
10-2
10-3
10-3
10-4
101
10 2
= 5.2
= 7.3
101
101
. 2)
102
100
100
(
102
10-4
102
101
10-1
10-1
10-2
10-2
10-3
10-3
10-4
101
10 2
(
)
10-4
102
101
(
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à
100
Nice Event
= 4.6
Estaing Event
= 4.4
100
10-2
10-2
/ 2)
PGA (
/ 2)
10-1
10-3
10-4
10-3
Ambraseys et al. (1996)
Sabetta-Pugliese (1996)
Rock
Soil
101
102
Epicentral distance(
100
Nice Event
10 1
10-4
102
Epicentral distance(
)
= 4.6
Estaing Event
)
= 4.4
100
10-1
10-2
10-2
/ 2)
10-1
PGA (
/ 2)
PGA (
PGA (
10-1
10-3
10-4
10-3
Berge-Thierry et al. (2003)
Pousse et al. (2005)
Rock
Soil
101
102
Hypocentral distance(
10 1
)
ÇIê ,-¾¿§ÃM®N´º°¾¸Å»«G±Á«`«G¸"T«`·`¾N³«G³
10-4
102
Hypocentral distance(
)
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354
Modulus Reduction Curves for Sand
Damping Curves for Sand
32.5
Damping Ratio, %
Shear Modulus Ratio, G/Gmax
1.0
0.8
0.5
0.3
0.0
10 -4
10-3
10-2
Shear Strain,%
10-1
100
GL-000m
GL-007m
GL-016m
GL-037m
GL-076m
GL-151m
24.5
up
up
up
up
up
up
to
to
to
to
to
to
GL-006m
GL-015m
GL-036m
GL-075m
GL-150m
GL-300m
16.6
8.6
0.6
10 -4
10 -3
10-2
10-1
100
Shear Strain,%
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Magnitude
8.0
7.0
6.0
5.0
0.0
50.0
100.0
Distance (km)
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PGA = 1.35
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Acceleration (
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PGA = 2.72
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/
PGA = 0.761
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8.0
16.0
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0.0
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PGA = 0.540
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Time ( )
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Mw = 6.0
X = 25km
station ABSH06
10-3
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station TKCH07
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10-2
Period ( )
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10-3
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Distance (km)
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(#&5)(V;*3,5?7:#=,x-&G)%*D)7:y7<!zJ?2&5? ¶ -&(p-&*D?,!1#&'(pC45)9e'NM&x-&G"!H)9;245)' |{ *D#&9;)M4*DN!A}4~; 4}
Å 91*q(I!0& 7+}1;1;!4}X} ° 2KJ?* s!05,!LS!1& 7+}0;\ ÂF 7 n H(#&5)(V;*3,5?7:#=,I'915)5)()CP9;#&-&(#= ¶ -&I%(/1%L
#47:#=,_-4 7!0V;#&*D)2&-&:'9;7:C&5?*3):#=)5)! Â&}bcL:A}b(_R%(,(#&-&(#F6?2&5_2 "!15?V;:V=!17:7<6-&
-4*3?,!1#&'(}p!1D"!1#=:-&~;}w ¶ ;14}wF7 7 n <#&5?V;*D?,5?7:#=,<'9;D3('(,%(<'(9;5)5??Ct9;#4-&#= ¶ -&
%L/;%(#&7:#=,:!B=!0#F6(23*3(2-&(C&2&*D[3-4%X&246-4]^9;#&'L,*391#&#&7:#=\-&[5?%)!12AucJ?24)EF2R ¶ 3!.Z#
-427<91*3S-Rb9e'()9;X&5?-&<aRb!1#&#&%(1;{ Â 7 9;24_'(_)%(*3)7:`)9;#=\2AuF
Q7 ¼ 7:?*D)2&%WJ?2&)EF2R ¶ 2&#&
C45)91]^9;#4-&2&5v]^9A'!13x7!zu4*D7!03r-&@/ UF7 7 #4Z#};3!U'!15,!1'L,%(5)*3)!0,*D9;#\V1%91)'NM&#&*DEF2&W-&)*D)q?9;2&
'NM&!1'2-&(o?,!0,*D9;#&y)*D)7:*3EF2&(p5?#&?*3V1#&U?2&5oDyC&5?91Z3y-&G/e*D,()?U-&(o9;#4-& 7ee2&5p3!SX&!1)
-4<'(S*3#4]^9;5?7!K,*391#&}t2&#'("!1?)7:#=S-&(\?,!0,*D9;#&S!8%(,%:5)%!13*D)%[-Rb!1C&5 ½ S3(SC45)9;CP9;)*+,*D9;#&H-&
|R 2&5?9A'(9A-4 2&5)9e'9e-& ?*3V;#.91]v?,5?2&'()2&5)(G]^915WB!15,M&EF2Z!10`5??*3?,!1#&'(1}t1;=1 7
!0#&H3 ÀoM&!1C&*D)5)6e}TaR%()2&-&_N!0)*3,*3EF2&\-&HXZ!0)I-&\-&9;#&#&%(S! 5)%L/;%(3%[EF2&[3\5)%?B!12
{
#&(H(?S#&L),(7<(#=I7<9;*D#&U]^912&5)#&*v#CP(,*+,%L/;%(#&7:#=, Â4}w A}b=UEF2&63\5)%?B!12
{ *D=
#&( 7-Ào())`-4* » %5)(#&'`EF2&\#&912&#&S)917<7:GCZ!1G#7<()2&5?\-RLuAC&D*3EF2&5GCP9;2&5N!1#=U"!
?9;2&5?'S-&@%'!15?)@-&IC&5)%(-&*3'L,*391#.?Ct('()5,!1DS91X&)(5?/;%(U(#=,5)S'(U-42Au85?%?B!12Au!0v2 ÀoMZ!0C&*D)5) Â 7
ÀoF ÀoMZ!1C&*+,5?$ Â:#&9;24!6Ct(5)7:*3W-R%(,!1X&D*35W-&(U5?"!K,*391#&WC&5)%(-&*3'L,*+/;G-Rb!1''(%D%5,!K,*391#.?Ct('L
)5,!1DU'!13*DX&5)%(x)2&5p3(oXZ!1?s-4-&9;#4#&%(kJ)!1CP9;#Z!1*D)$ 7 ´ 9;2&o!B/;9;#&oLuAC&391*D,%G"!I5)("!0)*39;#:C&5?%-&*D'L
)*D/1H-Rw!0''%(3%(5,!0)*39;#?Ct('(,5)!13H'!13*DX&5)%(?2&5 {
#&(sCt9;245W7<9e-&*D&5oDsC45)9;CP9;)*+,*D9;#&s-&H?Ct('()5)
]^915?]!1*+N!1*D5)\-&|R 2&5?9A'(9A-4 #/e2&-4|Rb%("!1XP9;5,!K,*391#-&.)9;#!1#&#&mu4.#Z!0)*39;#&!13 ]^5)!1# !0*3) 7
Å 2A
Q-4 ¶ -&6|Rw!1?Ct('(I5?%V;D7:#=N!1*D5)0}T'4 ÀoMZ!0C&*D)5) Â.!]!0*DH5?)?9;5?)*35IEF2&63(H)CP'()5)(\C&5?%-&*+,
?2&5_-&(_)913_7:2&X43`9;#=_2&#'(9;#=,(#e2 ¶ CP%5?*39e-&D9;#&V;24C&D2&\*D7<CP9;5?,!1#=SEe24'2euC&5?%-&*+,
T K
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xÀd¿ ´ À n AO¿ ´ ¹ · ´ µÅn )2&5U-&U)9;DGC432&G5)*DV;*3-&( 7ÀRH2&#c#49;24/;!12 5?%)24DN!KEF2&*k#&SCt(24CZ!0 ¼ ,5)`9;X4)#F2$!B/;('\-&(
XZ!1)(U-4`-&91#&#&%(U(2&5)91Ct%(#&#&(}PCt912&5@3?EF2&D3@D@*3#4]^915)7<!0,*D9;#&oV1%91)'NM&#&*DEF2&U)9;#=U7<9;*D#&
LuAMZ!12&,*+/;UEF2Rw!02 !1CP9;# ¢Å 7_X&5,!0)(eG(!1& 7+}11;= 7&\Rw!024,5?SC&!15?}Z#&9;2&U!B/;9;#&G-&%(7<9;#=)5)%I3
'9;#=,(#F2 MZ!124)G]^5?%EF2&(#&'U-&p)*3V1#Z!12AuJ)!0Ct9;#&!1*3(}=Ee24*P?G)5,!1-42&*DxCZ!15y2&#<'9;#=)#F2 )CP'L,5)!1C&32&
*37:Ct9;5N!1#= ¶ CP%5?*39e-&_'912&5?) p zEF2&:'6EF2&6-Rb!124,5?S5)("!0)*39;#&C&5)%(-&*3'L,*D/1I-&67:9;2A
/;7:#=_]^915?`)2&V;V ½ 5)(#= ¢Å 7_X&5,!0)(e_L[!1 7D}y~1 4}v4!1XP(?N! r2&V;D*3()1}x~; 4} Å X&5)!1MZ!17:)9;#
A*3+/1!A}~;=A
} p9A9;5?`LH!1 7D}~B;=A} o(5)V;m
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aRb!1#Z!1+A?p-42_7<9e- ½ 3x-&oC&5?%-&*D'()*39;#`-&2_7:9;24/;(7<(#=r)*D)7:*3EF2&x9;X4,(#F2[!B/;'WDv#&5?V;*D?,5?7:#=,
-&`C45)91]^9;#4-&2&5@-& { *3;
Q#4( Z#&9;2&U!B/;9;#4!1*D#&)*C42c7:())5)I#.'B!02&)`3@?9;3J)!1CP9;#Z!1*DW-Z!1#&G'
C&M&%#49;7 ½ #&I-Rb!17<C43*D&'B!0)*39;# M&!124,H]^5?%EF2'S-&@)*DV;#Z!12eu.!1''(%D%5)917<%L,5)*DEF2&$ 7
!1#&G3$ ÀoMZ!1C4*D,5? 4}Z"![XZ!1?`-4S-49;#&#&%( {
#&(U!6)5/e*v!02-&%L/;(39;C&CP7:#=U-R2&#&S#&9;2A
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7<9;2A/;7:#=)G]^9;5,G9;#=G%(,%S'B!03'243%(UCP9;2&5@-&(U*D#&-&*D'B!0)2&5?G?*3?7<*DEe24 =
4 0
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9;#&-&(U-&H/19;32&7: ( s}!1*D#&)*EF2&S"!_'(9A-Z! 7 # !B/0!1#=N!0V;I-&27:9e- ½ DH5)%?*3-&I(#)!<'B!0CZ!1'*+,%
?*37_2435o"!_/0!15)*3!1X&*3D*D)%U#Z!K,2&5?3D-&2.7<9124/;(7<(#F}ZEF2&`#49;2&G!B/;9;#&G*3#=)5)9e-&2&*D)#!124)9;5)*D,!1#=
2&#&@LuAC&D9;5,!0)*39;# 9;#=, Às!05)39S-&(x-4*3?)5)*DX&24,*D9;#&rC&5?%-&*+,(x-4G'NM&!1EF2&U*D#&-&*D'B!0)2&5r?*3)7:*3EF2& 7iÀo(
!1)CP'L_#&9/0!0,(2&5I]!1*DS-&2d7<9e- ½ D62&#XP9;#'!1#&-&*D-Z!0`Ct912&5I-&`%(,24-&_#49;#A
QD*3#&%!1*35?H-&<'9;7[
Ct9;5,(7<(#Fp-&UXZY0,*D7<(#=,x9;2-&U)9;Dp(# 5)%(Ct91#&) 2&#&U)9;D3*D'*D,!0,*D9;#_?*3)7:*3EF2& |{ 5)!17<(5}Z~1 4}
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7<%L,M&9e-&6C&5)%()(#F) aRb!B/0!1#=N!1V;6-&<Ct9124/;9;*D5 ¼ ,5?:)5,!1#4)CP9;,!1X43<!12Au#4-&5)9;*+,I9 d-&`XZ!1)(\-&
-&9;#&#&%(muA*3?)#=B}T)2 ,!07<(#F-&9A'(2&7:#=,%(CP9;2&5UCt9;2A/;9;*D5%(,!1X&D*35@-&5)3!0,*D9;#&GC&5)%(-&*3'L,*+/;
-&I7<9;2A/;7:#=@]^9;5 7
n ÀoM&!1C&*D)5)_<#&9;2&!!1*3#&?*vCP5?7<*DU-4_'B!1D*3X&5?5G"!:7<%L,M&9e-&_?2&52&#&\XZ!1)\-&_-&9;#4#&%(
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Ct9;245W)*37\2&3(5s3H7:9;24/17:#=U!125?9A'NM45 7
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9;2&.!B/;9;#4.)#=,%-Rb!1C&CP9;5?)58-Z!1#&8D¯
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3!:,!1*3D3I-&2 ?%*3?7<\!12&V;7:#=) !1"!1V1#&*3#&* LH!1 7D} ~;14} Å #&-&(5))91#}11;4}-¿_RÃÀo9;#4#&D Å 01}
0;=A} Å 7_X&5)!1)LeH(S!1 7D}T1; 1 7 n R%()2&-&[-&%(7<9;#=)5)[EF2Rb!/1':2&#$7:9A- ½ 3_-4_7<9124/;(7<(#FH]^915?
*D)?2-R2&#&!1#Z!1+A?-&:)%(*3?7<(\7:9A-&%(5)%(} aRLue,5)!1CP9;"!0)*39;#$-4\C45)%-4*3'()*39;#4 2&#?'%#&!15)*D9c-&
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#4Z#T};-Z!1#&v3
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-4%(/;(39;C4Ct%(:-&!1#&H3: ÀoMZ!1C&*+,5) LI'B!1D*3X&5?%_?2&5H"! X&!1)[-&[-49;#&#&%(I-&[C&5?91]^9;#&-&(2&5 { *3;
Q#4(
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&#&*3( !05? º Dq(S!1 7D}1;\ Â4} ¿ Å Ct9;245H-&%(/1391C&Ct(5H-&H]^9;#4'(,*D9;#&H-Rb!17:C&3*+Z'B!K,*391#-&2
7:9;24/17:#=`!125)9e'NM&5H(#dC45)91]^9;#4-&2&5 *qL`!1& 7+}11;=!1C4C&3*D'B!1X&D 3! ?,!0,*D9;#$-&25)%?B!12
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(#24,*D3*D,!1#=S-&\5)3!0,*D9;#&SC&5)%(-&*3'L,*+/;`-& 7:9;24/17:#=\]^9;5_'!13*DX&5)%(S)2&5_D`XZ!1)(_-& -49;#A
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n !c7:%()M&9A-4<-&%L/;(39;C&CP%-Z!1#&`3ÀoMZ!1C&*+,5)#&%('())*+, -4[!17:%D*39;5)!0,*D9;#&24D,%(5)*D2&5?
CP9;2&5kCP5)7:(?,5?x-4o)*D7_2&D5-&(v/0!13(2&5) -&p"K! 4 C&D2& %D(/;%($7 912&vCP#4)9;#&
EF2&'1R?_"!.]^915)7:<'NM&91*3)*D<CP9;2&5`aR#=/;(39;C4Ct:,7:CP9;5)(336-&(_)*DV;#Z!12euEF2&*x[#'B!12&?(k)*
(3DU)!0,*D?]!1*D,!1#=)HCt9;245W3@?%*3?7<(W7<9e-&%(5)%(}ZD3-&91*D ¼ ,5)S!17:%D*39;5?%CP9;2&5WCP5?7<L))5)H-&
5?#&-45).'9;7:C4,8-&8|Rb » L<-4.?9;2&5?'.%(,(#&-&2&-&6V;5?9;6)%(*3)7:$ 7BÀo2AuF
Q V;%# ½ 5)(#F# » (
C432&?*3245)s,5)!1*3#4s-R9;#&-&I)24''()?*D]^}C&5?9/;9eEe2&!1#=U24#.%LN!1D7:#=W-&2.)*DV;#Z!1T!128'9;245)W-&2,(7<C4 7
Ào@C&5?9KJ?(r-4W5)'NM45)'NM4Umu4M4*3XPW-&y-&%L]!124,r-4W"!U]^9;5?7_2&3!0,*D9;#`'NM49;*3?*3WCP9;2&5qDq5?"!K,*391#&
C45)%-4*3'()*D/1H-&[7:9;24/17:#=H]^9;5? 7 n ($ ÀoMZ!1C&*+,5)(S( 7:9;#=,5?#=H3(-&%L]!124,H-427:9e- ½ D\-&
CP9;*D#Fk?9;2&5)'(o5?)CP'L,*+/;7:#=Ct9;245kDk*3#&-4*3'B!K,245) -&x7<9;2A/;7:#=v)*D)7:*3EF2&y(vCt912&5 3y)CP'L,5)
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xÀd¿ À n AO¿ µÅn aR*37:Ct(5?]^('(,*D9;#H-&2`7<9e- ½ Dy-&2\CP9;*3#=k)912&5)'(oCP9;2&5k'5N!1*D#&k*3#&-&*D'B!0)2&5? r 4
0 kL N \
ro ) 7 #[5,! #&(7<(#=q-&2[7:9A- ½ 3x-&2[CP9;*3#=v)9;245)'W-49;*Dv-&9;#&'
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