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