116G Attenuation Analysis Sri Atmaja

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of the well-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe(1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure based on Wavelet Spectrogram

Sri Atmaja P. Rosyidi, Ph.D.Presented in KoNTekS 7, Universitas Sebelas Maret, 24 October

2013

Department of Civil EngineeringUniversitas Muhammadiyah Yogyakarta

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

Outline

• Introduction• Research Methods• Results and Discussion• Conclusion

2

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

GeoEarthquake Engineering

3

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

Geo-Disaster

4

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

5

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

6

Soil Dynamic Parameters

Diubahsuai daripada Ishihara (1996)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

In Situ Te

st !

Lab !

7

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

8

Soil damping measurementSoil damping measurement

Laboratory testing:- Resonant column test- Torsional shear test- Bender element test- Cyclic triaxial test- etc.

Field (in situ) testing:- Crosshole test- Surface wave test- etc.

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

9

Resonant Column/ Torsional Shear Testing System

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

10 10

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

11

Non-Invasive (Surface) Methods

Refraction (ASTM D5777)

Reflection

Surface Wave

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

12

Seismic Wave Propagation

(from Woods, 1968)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

13

Surface Wave MeasurementsParticleMotion

ParticleMotion

Layer 1

Layer 2

Layer 3

Depth Depth

lshort

llong

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet SpectrumThe SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

Research Methods

14

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

1515

Data Collection of SASW Measurement

d1 d2

Time, sec0.0 0.5 1.0

(Portable Device Configuration)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

ADC & Spectrum Analysis

Geophones

Accelerometer

Sources Sensors

16

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

17

Damping ratio profile calculation

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

18

In situ damping measurement test• Surface wave measurement for damping ratio (Rix, 2000)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

19

Modelling the soil as a layered linear viscoelastic system

• Displacements for a harmonic point source

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

20

Example of regression result

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

21

Continuous Wavelets Transform (CWT)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

22

Example of regression result

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

23

Attenuation Analysis using Wavelet Spectrum

tRkiRfn

reeRKIGRGR

ARA 0,

tRkiRRf

n

Rf

Rf

reeRKIGRGR

RsuWsuW

2112

2

1,,

21

1

2

2

1ln,

,ln RRf

n

Rf

Rf eRKIGRG

R

R

suW

suW

21

1

2

lnlnln,

,ln

2

1 RRf

n

Rf

Rf eRKIGRG

R

R

suW

suW

21

2

1ln,

,ln

1

2

RRfRKIGRGR

R

suW

suWn

Rf

Rf

RfksuW

suWRf

Rf

,

,ln

1

2

tkRine

R

ARA 0, (Bornitz) tRkiRf

nree

R

ARA 0,

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

24

Developed procedure on attenuation analysis by wavelet transform

),(

),(

*1

*1

su

Xf

su

Yf

W

W

dts

ut

stX

dts

ut

stY

fX

fYfH

),(),(

),(

,

,,

*

,,

suWsuW

esuW

suW

suWsuH

Xf

Xf

babaiXYf

XXf

XYf

XY

tRkiRfn

reeRKIGRGR

ARA 0,

21

2

1ln,

,ln

1

2

RRfRKIGRGR

R

suW

suWn

Rf

Rf

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

25

NsF

FsF

Fs

sf

h

hl

l

,0

,1

1,0

NuT

TuT

Tu

uf

h

hl

l

,0

,1

1,0

-0.00005

-0.00003

-0.00001

0.00001

0.00003

0.00005

0.00007

0.00009

0 1 2 3 4 5 6

Masa, saat

Am

pli

tud

, m

/s

Isyarat Asal

Isyarat Buatan Terbina Kembali (Reconstructed Synthetic Signal)

.Continuous Wavelet Transform Filtration (CWT-F) Technique

CW T

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

26

data_signal1_2m.xls

Continuous Wavelet Time-Frequency Spectrum

Integrated Power, Time=0,3.99805

2.5564,1.4524e-09

52.784,2.0271e-11

123.51,6.7838e-13 186.04,2.76e-13

0.1 1 10 100 1000Frekuensi

0

0.5

1

1.5

2

2.5

3

3.5

4

Mas

a

-5e-10

0

5e-10

1e-09

1.5e-09

Mag

nitu

d

data_signal2_2m.xls

Continuous Wavelet Time-Frequency Spectrum

Integrated Power, Time=0,3.99805

3.9708,1.6402e-10

6.0219,1.8062e-10

23.969,1.8439e-11 54.736,1.0822e-11

0.1 1 10 100 1000Frekuensi

0

0.5

1

1.5

2

2.5

3

3.5

4

Mas

a

-5e-11

0

5e-11

1e-10

1.5e-10

2e-10

Mag

nitu

d

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

Frekuensi, Hz

Nila

i Koh

eren

(M

agn

itu

d)

fsuW

suWRf

Rf 0118.068.3

,

,ln

1

2

kfkRfsuW

suWRf

Rf

02

,

,ln

1

2

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

27

Attenuation Curve

10 20 30 40 50 60 70 800

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Frequency, Hz

Att

enua

tion,

1/m

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

28

Attenuation Inversion

1s

Vk

N

1j s

s1p

Vkp

pN

1j

1R j

pj

j

j

sj

j QV

cc

VQ

Vc

c

VQ

j

pj

jj

sj

jf s

Vf

N

1j s2

sp

Vf

N

1j p2

pR D

Vc

c

VD

Vc

c

Vf2

Anderson et al. (1965)

Mitchell (1975)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

29

Attenuation Inversion

Linear Problem

MR

2R

1R

sN

2s

1s

D

D

D

dm

dGm

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

30

Least SquaresDefine two objective functions as follows:

M

1i

2i

2N

1jjiji

2 mGdX

si = uncertainty in di

NxN

21

N

1j

21jj1

11

11

11

0

mR

mmR

22

M21

WGmWdX

1,1,1diagW

Minimize ‘roughness” Minimize data misfit

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

31

Constrained Least SquaresUse a Lagrange multiplier to combine the two objective functions:

2*

212 XWGmWdmmU

Setting the derivative of U(m) equal to zero to find the minimum yields:

WdWGWGWGm̂

0WdWGmmmU

T1TT

TT

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

32

Least Squares

d Gmtheoretical

0

3

6

9

12

15

0.0% 0.5% 1.0% 1.5% 2.0%

Shear Damping Ratio (%)

Dep

th (

m)

0

5

10

15

20

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Attenuation Coefficient (1/m)

Wav

elen

gth

(m)

Experimental

Theoretical

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

33

Residual soil (UKM)

10 20 30 40 50 60 70 800

0.020.040.060.08

0.10.120.14

Frequency, Hz

Att

enua

tion,

1/m

0.01 0.02 0.03 0.04 0.05 0.060

2

4

6

8

10

12

14

16

Damping Ratio (D)

Dept

h, m

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

34

Note for damping measurement by surface wave method

• the predicted damping ratio based on attenuation – amplitude decay (radiation/geometric damping)

• some assumptions:– the geometric spreading function to be inversely

proportional to the square root of the distance from the source

– The implicit dependence of the complex-valued phase angle on the source-to-receiver distance is eliminated by assuming: Ψ(r,ω) ≈ K(ω)r.

• appropriate for non-complex soil profiles• the best data of damping – RC laboratory test

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

35

Damping Ratio Comparison

0

3

6

9

12

15

0% 2% 4% 6% 8% 10%Shear Damping Ratio (%)

Dep

th (

m)

Surface Wave

Crosshole

Resonant Column

Torsional Shear

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

36

Developed procedure on attenuation analysis by wavelet transform

),(

),(

*1

*1

su

Xf

su

Yf

W

W

dts

ut

stX

dts

ut

stY

fX

fYfH

),(),(

),(

,

,,

*

,,

suWsuW

esuW

suW

suWsuH

Xf

Xf

babaiXYf

XXf

XYf

XY

tRkiRfn

reeRKIGRGR

ARA 0,

21

2

1ln,

,ln

1

2

RRfRKIGRGR

R

suW

suWn

Rf

Rf

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

37

data_signal1_2m.xls

Continuous Wavelet Time-Frequency Spectrum

Integrated Power, Time=0,3.99805

2.5564,1.4524e-09

52.784,2.0271e-11

123.51,6.7838e-13 186.04,2.76e-13

0.1 1 10 100 1000Frekuensi

0

0.5

1

1.5

2

2.5

3

3.5

4

Mas

a

-5e-10

0

5e-10

1e-09

1.5e-09

Mag

nitu

d

data_signal2_2m.xls

Continuous Wavelet Time-Frequency Spectrum

Integrated Power, Time=0,3.99805

3.9708,1.6402e-10

6.0219,1.8062e-10

23.969,1.8439e-11 54.736,1.0822e-11

0.1 1 10 100 1000Frekuensi

0

0.5

1

1.5

2

2.5

3

3.5

4

Mas

a

-5e-11

0

5e-11

1e-10

1.5e-10

2e-10M

agni

tud

fsuW

suWRf

Rf 0118.068.3

,

,ln

1

2

kfkRfsuW

suWRf

Rf

02

,

,ln

1

2

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

38

Attenuation analysis

y = -0.0118x + 3.6795

R2 = 0.67

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10 12 14 16 18 20

Frekuensi, Hz

Nis

bah

(A2/

A1)

dal

am L

N

alpha-0.005dataalpha-0.03

alpha-0.05regresi eksperimen

0 = 0.050 = 0.03

0 = 0.005

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

39

RMS error during matching process

0

1

2

3

4

5

6

00.020.040.060.080.10.12

Pekali pengurangan, 0 (s/m)

RM

S (

nis

bah

am

pli

tud

)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

40

Attenuation curve

0

5

10

15

20

25

30

0 0.1 0.2 0.3

Pekali pengurangan bersandar frekuensi ( ), 1/m

Pan

jan

g ge

lom

ban

g, m

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8

Pekali pengurangan bersandar frekuensi ( ), 1/m

Fre

kuen

si, H

z

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

41

Inversion and damping ratio profile

0

5

10

15

20

25

30

0 0.1 0.2 0.3

Pekali pengurangan bersandar frekuensi ( ), 1/m

Pan

jan

g ge

lom

ban

g, m

datamodel teori

model mula

lelaran 1

lelaran 3

lelaran 4

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0.00% 2.00% 4.00% 6.00% 8.00%

Nisbah redaman (%)

Ked

alam

an, m

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

42

PerbandingandenganKajianSebelumnya

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Halaju Gelombang Ricih, m/s

o (sa

at/m

)

Athanasopoulos et al. (2000)

Yang (1995)

Kelas 4

Kelas 2

Kelas 3

A

B

Woods & Jedele (1985);Woods (1997)Lempung lembut Kelang

(Kelang soft clay)

- Kajian ini

Kelompok Batuan (Rocks) daripada Shale, Limestones & Sandstone

Kelas 1

Hasil kajian

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

43

Shear Damping Profile

Kaedahnisbahspektrum (Champanella et al. 1994)

Kaedahfungsiperpindahan (Rix et al. 2002)

Kaedah CWSASW

0

5

10

15

20

25

30

0 0.1 0.2 0.3

Pekali pengurangan bersandar frekuensi ( ), 1/m

Pan

jang

gel

omba

ng, m

Kaedahfungsiperpindahan

Kaedah CWSASW

GeophonesShaker

SignalAnalyzer

r

Accelerometer

1

,

,

1

rrKi

l

i erG

rG

F

F

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

44

2 D Shear Wave Velocity

Contour Graph 1

Jarak Keratan (m)

0 5 10 15 20 25

Ked

ala

man

(m

)

0

2

4

6

8

10

12

14

16

40 60 80 100 120 140 160 180

ν12GE

ρVM

ρVG

maxmax

2pmax

2smax

ν12GE

ρVM

ρVG

maxmax

2pmax

2smax

Elastic Theory

S

zs V

u = 1.48 10-5

%.

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

45

2 D Shear Modulus and Damping

Contour Graph 2

Jarak Keratan (m)

0 5 10 15 20 25

Ked

ala

man

(m

)

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16 18

Contour Graph 3

Jarak Keratan (m)

0 5 10 15 20 25K

ed

ala

man

(m

)

0

2

4

6

8

10

12

14

16

0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054

G (MPa) D [%]

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

46

Comparing with MASW (SurfSeis), KGS

(a) Profile from MASW (b) Profile from CWSASW

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

47

Lengkung Pekali Pengurangan dan Prosedur Songsangan

Lengkung serakan teori pekali

pengurangan vs frekuensi/panjang

gelombang

Profil kekukuhan anggaran

Proses songsangan

Lengkung serakan pekali pengurangan

tak bergantung f

Lengkung serakan eksperimen pekali

pengurangan vs frekuensi/panjang

gelombang

Proses perpadanan

ralat RMS

Profil nisbah redakam, halaju

gelombang R, ricih, dan mampatan

Profil 1-D redaman tanah

Analisis gandingan

Tidak diterima

Diterima

i

N

i iS

RiS

iP

RiP

R

DV

VVK

V

VV

V

ff ,,2

2

D, VR, VP, VS

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

Songsangan Pekali Pengurangan

j

pj

jj

sj

jf s

Vf

N

1j s2

sp

Vf

N

1j p2

pR D

Vc

c

VD

Vc

c

Vf2

Mitchell (1975)

Masalah Lelurus dalam Songsangan :

MR

2R

1R

sN

2s

1s

D

D

D

dm

dGm

i

N

i iS

RiS

iP

RiP

R

DV

VVK

V

VV

V

ff ,,2

2Rix et al. (2000)

48

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

49

Profil Nisbah Redaman

0

5

10

15

20

25

30

0 0.1 0.2 0.3

Pekali pengurangan bersandar frekuensi ( ), 1/m

Pan

jan

g ge

lom

ban

g, m

datamodel teori

model mula

lelaran 1

lelaran 3

lelaran 40

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0.00% 2.00% 4.00% 6.00% 8.00%

Nisbah redaman (%)

Ked

alam

an, m

0

0.4

0.8

1.2

1.6

2

0 1 2 3 4

Lelaran

Ral

at R

MS

(p

ekal

i p

engu

ran

gan

, 1/

m)

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

50

Pengesahan Profil Nisbah Redaman

Kaedah nisbah spektrum (Champanella et al. 1994)

Kaedah fungsi perpindahan (Rix et al. 2002)

Kaedah CWSASW

0

5

10

15

20

25

30

0 0.1 0.2 0.3

Pekali pengurangan bersandar frekuensi ( ), 1/m

Pan

jang

gel

omba

ng, m

Kaedah fungsi perpindahan

Kaedah CWSASW

GeophonesShaker

SignalAnalyzer

r

Accelerometer

1

,

,

1

rrKi

l

i erG

rG

F

F

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

51

Tomografi 2-D Parameter VS

Contour Graph 1

Jarak Keratan (m)

0 5 10 15 20 25

Ked

ala

man

(m

)

0

2

4

6

8

10

12

14

16

40 60 80 100 120 140 160 180

ν12GE

ρVM

ρVG

maxmax

2pmax

2smax

ν12GE

ρVM

ρVG

maxmax

2pmax

2smax

Teori Elastik

S

zs V

u = 1.48 10-5

%.

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of thewell-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe (1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by

Attenuation Analysis on Soil Structure Based on Wavelet Spectrum

52

Tomografi 2-D Parameter G dan D

Contour Graph 2

Jarak Keratan (m)

0 5 10 15 20 25

Ked

ala

man

(m

)

0

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16 18

Contour Graph 3

Jarak Keratan (m)

0 5 10 15 20 25K

ed

ala

man

(m

)

0

2

4

6

8

10

12

14

16

0.036 0.038 0.040 0.042 0.044 0.046 0.048 0.050 0.052 0.054

Profil Modulus Ricih (MPa) Profil Nisbah Redaman

The SASW method has been utilized in different applications over the past decade after the advancement and improvement of the well-known steady-state (Jones 1958) technique. Much of the basis of the theoretical and analytical work of this method for pavement investigation has been developed by Heisey et al. (1982), Nazarian & Stokoe(1984), Röesset et al. (1990, 1991). For practical purposes, an empirical correlation between the seismic parameter (i.e. shear wave velocity) produced by