Strong Motion Observation - Data Analysis
Transcript of Strong Motion Observation - Data Analysis
Strong Motion Observation- Data Analysis -
Toshihide KashimaIISEE, BRI
Contents
Intensity indexIntegrationFourier spectrumResponse spectrumApplication
Intensity indexes
Peak ground acceleration (PGA) and peak ground velocity (PGV)JMA seismic intensity (IJMA) scale (0 to 7)Housner’s spectrum intensity, SI
2.5
0.1( ) ( , )SI h pSv T h dT= ∫
Intensity indexesPeak values
Peak ground acceleration (PGA) and peak ground velocity (PGV)
2 2X Y
max( ) ( )PGA a t a t= +
2 2 2X Y Z
max( ) ( ) ( )PGA a t a t a t= + +
X max( )PGA a t=
Intensity indexesJMA seismic intensity scale
JMA seismic intensity (IJMA) scale (0 to 7)
Filtering 3-component accelerationCompute vectorial amplitude
Find a0 satisfies;
Compute IJMA
2 2 2( ) ( ) ( ) ( )v t x t y t z t′ ′ ′= + +
0( , ) 0.3
Tdw t a dt ≥∫ 0( , ) 0, ( )w t a v t a= <
0( , ) 1, ( )w t a v t a= ≥
JMA 02 log 0.94I a= +
Intensity indexesJMA seismic intensity scale
Filters1/ 2
T ( ) (1/ )w f f=2 4 6
H8 10 12 1/ 2
( ) (1 0.694 0.241 0.0557
0.009664 0.00134 0.000155 )
w f y y y
y y y −
= + + + +
+ +3 1/ 2
L ( ) (1 exp( ( / 0.5) ))w f f= − −
Intensity indexesJMA seismic intensity scale
Scale Explanation
7In most buildings, wall tiles and windowpanes are damaged and fall. In some cases, reinforced concrete-block walls collapse.
6+In many buildings, wall tiles and windowpanes are damaged and fall. Most unreinforced concrete-block walls collapse.
6- In some buildings, wall tiles and windowpanes are damaged and fall.
5+In many cases, unreinforced concrete-block walls collapse and tombstones overturn. Many automobiles stop due to difficulty to drive.
Intensity indexesJMA seismic intensity scale
Scale Explanation5- Most people try to escape from a danger. Some
people find it difficult to move4 Many people are frightened. Some people try to
escape from a danger. Most sleeping people awake.
3 Felt by most people in the building. Some people are frightened.
2 Felt by many people in the building. Some sleeping people awake.
1 Felt by only some people in the building.0 Imperceptible to people.
Intensity indexesHousner’s spectrum intensity
Housner’s spectrum intensity, SI2.5
0.1( ) ( , )SI h pSv T h dT= ∫
Intensity indexesRelation among indexes
391 records from K-NET during the 2007 Off Chuetsu Earthquake
(a) IJMA vs. PGA (b) IJMA vs. PGV
0.1
1
10
102
103
104
105
PGA*
PGV
(cm
2 /s3
)
0 1 2 3 4 5 6 7IJMA
Intensity indexesRelation among indexes
391 records from K-NET during the 2007 Off Chuetsu Earthquake
(c) IJMA vs. SI (d) IJMA vs. PGA*PGV
0.1
1
10
102
103
104
105
PGA*
PGV
(cm
2 /s3
)
1 10 100 1000PGA (cm/s2)
Intensity indexesRelation among indexes
Relation to PGA
(e) PGA vs. PGV (f) PGA vs. SI (g) PGA vs. PGA*PGV
Intensity indexesRelation among indexes
Relation to PGA
(h) PGV vs. SI (i) PGV vs. PGA*PGV (j) SI vs. PGA*PGV
Integration
Conversion from acceleration to velocity and displacement
Integration in time domain with baseline correction in velocity and/or displacementIntegration in frequency domain with high pass filterSimulation of seismograph using a SDOF model (pendulum)
IntegrationTime domain
Trapezoidal method (require baseline correction and/or low-cut filter)
1 1( ) 2j j j jv v a a t+ += + + Δ
IntegrationFrequency domain
FFT and invert FFT (with low-cut filter)Fourier transform
Integration in frequency domain
Low-cut filtering
Invert Fourier transform
( ) ( )a t A ω→
( ) ( ) /V A iω ω ω=
L( ) ( ) ( )V F Vω ω ω′ =
( ) ( )V v tω′ →
IntegrationSimulation of seismograph
Simulate simple seismograph
2 2g 0 0
12i
xx hω ω ω ω
= −− +&&
2 2g 0 0
i2i
xx h
ωω ω ω ω
= −− +&
2
2 2g 0 02ixx h
ωω ω ω ω
=− +
0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
ampl
itude
0.05 0.1 0.2 0.5 1 2 5 10 20ω/ω0
0
90
180
phas
e (d
eg)
0.05 0.1 0.2 0.5 1 2 5 10 20ω/ω0
h=0.1h=0.3h=0.7h=1.0h=2.0h=5.0
x/xg..
IntegrationSimulation of seismograph
Acceleration
gx x&&
IntegrationSimulation of seismograph
Velocity
gx x&
0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
ampl
itude
0.05 0.1 0.2 0.5 1 2 5 10 20ω/ω0
180
270
360
phas
e (d
eg)
0.05 0.1 0.2 0.5 1 2 5 10 20ω/ω0
h=0.1h=0.3h=0.7h=1.0h=2.0h=5.0
x/xg
IntegrationSimulation of seismograph
Displacement
gx x
IntegrationComparison among methods
GL at Kushiro Gov. Office Bldg., 2003 Acceleration
Integrated velocity
0
20
Dis
p. (c
m) 257-GL (peak: 11.049 cm)
-20
-50
0
50
Dis
p. (c
m) 257-GL (peak:- 24.548 cm)
-20
0
20
Dis
p. (c
m)
0 10 20 30 40 50 60 70 80Time (sec)
257-GL (peak:- 14.154 cm)
Trapezoidal
FFT
Seismograph
IntegrationComparison among methods
GL at Kushiro Gov. Office Bldg., 2003 Acceleration
Integrated displacement
Fourier analysis
Conversion from the time domain to the frequency domain
Conversion from the frequency domain to the time domain (inverse Fourier transform)
(2 )( ) ( ) i ftX f x t e dtπ∞ −
−∞= ∫
1(2 / )
0
Ni km N
k mm
TX x eN
π−
−
=
= ∑
(2 )( ) ( ) i ftx t X f e dfπ∞
−∞= ∫
1(2 / )
0
Ni km N
m kk
x X e π−
=
=∑
Fourier analysisFourier and power spectra
Fourier (amplitude) spectrum
Power spectrum
Smoothing by spectrum window
Parzen window
*1( ) ( ) ( )XXP f E X f X fT
⎡ ⎤= ⎣ ⎦
( ) ( ) ( )P f P f W f g dg∞
−∞= −∫
4
sin3 2( )4
2
uf
W f u uf
π
π
⎛ ⎞⎜ ⎟
= ⎜ ⎟⎜ ⎟⎝ ⎠
( ) ( )F f X f=
Fourier analysisSmoothing effect
Fourier analysisTransfer function
Fourier spectral ratio
Cross power spectrum
Transfer function
2( ) ( ) ( )YY YXH f P f P f=
0 ( ) ( ) / ( )H f Y f X f=
1( ) ( ) ( )XY XXH f P f P f=
*1( ) ( ) ( )XYP f E X f Y fT
⎡ ⎤= ⎣ ⎦
0 ( ) ( ) ( )H f Y f X f=
Fourier analysisExample
Site effect at Kushiro (GL/GL-34m)
Response spectrum
Relation between natural period and maximum response of Single-degree-of-freedom (SDOF) system
Displacement response spectrum (Sd)Velocity response spectrum (Sv)Acceleration response spectrum (Sa)Pseudo velocity response spectrum (pSv=ωSd or pSv=Sa/ω)
Response spectrumDefinition
Relative displacement
Relative velocity
Absolute acceleration
( )0 20
( ) ( ) cos ( ) sin ( )1
t h td d
hx t x e t t dh
ω ττ ω τ ω τ τ− − ⎡ ⎤= − − −⎢ ⎥
−⎣ ⎦∫& &&
( )00
1( ) ( ) sin ( )t h t
dd
x t x e t dω ττ ω τ τω
− −= −∫ &&
2( )
0 0 2 20
2( ) ( ) ( ) 1 sin ( ) cos ( )1 1
t h td d d
h hx t x t x e t t dh h
ω τω τ ω τ ω τ τ− − ⎡ ⎤⎛ ⎞+ = − − + −⎢ ⎥⎜ ⎟− −⎝ ⎠⎣ ⎦
∫&& && &&
2
2
1
2 1d h
h T
ω ω
π
= −
= −
Response spectrumDefinition
Response spectrum
Relation between T and Sd, Sv or Safor a certain hPseudo velocity response spectrum
vd
SSω
≈
d max( , ) ( )S T h x t= v max
( , ) ( )S T h x t= &
a 0 max( , ) ( ) ( )S T h x t x t= +&& &&
a vS Sω≈
p v dS Sω=
ap v
SSω
=
Response spectrumExample
Sa
Sd Sv
Response spectrumTripartite plot
In full-log coordinates
Response spectrumRelation among Sa, Sv and Sd
Sv ~ pSv=Sa/ω ~ pSv=Sdω
Response spectrumDifference by damping
h=0%, 5%, 10% and 20%Fourier spectrum
Application
Attenuation formulas of seismic intensity indexes
Relation between (PGA, PGV, IJMA, etc) and (M, X, site condition, etc)
Discussion on effect of surface geologyInvestigation into shallow/deep geological structureEstimation of stronger ground motions
Application
Warranty for seismic codeImprovement of seismic codeVerification of structural designVerification of new technologyExamination of failure mechanism of structure
Application
Early warning systemEstimation seismic intensity before S-wave arrival
Structural health monitoring systemReal-time identification of structural damage