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1
Quantification et extraction d’ondes de
surface par méthode temps-fréquence
K. Meza-Fajardo(1,2), A. Papageorgiou(3)
J-F Semblat(1), F. Bonilla(1)
(1) IFSTTAR, GERS/SV
(2) Universidad Nacional Autónoma
de Honduras (3) University of Patras
JTAV 2014, Bordeaux
2
Importance of surface waves
• In vibration engineering:
JTAV 2014, Bordeaux
surface waves
In earthquake eng.:
Surface waves polarization
• Polarization of Rayleigh waves:
pro-grade or retro-grade
• Influence of time shift for vertical component
• 3 cases: linear, circular, elliptical polarization
3 JTAV 2014, Bordeaux
Time-freq. polarization analysis
• 3 steps procedure – Time-freq. Analysis > Stockwell transform:
4 JTAV 2014, Bordeaux
[ ]∫∞+
∞−−
−−= τπ
τ
πτ !"#$
#%$&#%&'%#($&) !"#$
!"#$
!
!!
!"#$%
!"#$&!"#$
τ
ττϕ =
!!
!!
!
"
!
"
!"#$%&'(
!"#$%&')
+−=
++=
τ
τ
( )!"!"!"
!"!"!"
!"!"!"
##$$%%&'()*
##$$%%&'()+
##$$%%&'()*
++−=
−+−+−=
+++++=
!
!!!!!!
!!!!!!
τ
τ
τ
semi-minor axis
semi-major axis
!"!"#$% >τϕ
Rayleigh
+ filtering:
ellipticity
threshold
– Instantaneous reciprocal ellipticity!
– Inverse Stockwell transform: time domain
5
Synthetics: t-f analysis
• Synthetics (combination of sinusoids)
JTAV 2014, Bordeaux
• Time-frequency analysis
Synthetics: filtering
6 JTAV 2014, Bordeaux
Instantaneous reciprocal
ellipticity and related filter
Filter based on ϕ
Alternative: normalized inner
product and related filter
Filter based on NIP
Synthetics: filtered signals
7 JTAV 2014, Bordeaux
Compute azimuth +
new frame (R,T,V)
Rc(t) Tc(t) Vc(t)
8
Actual motions: Chi-chi qke
JTAV 2014, Bordeaux
Actual motions: t-f analysis
9 JTAV 2014, Bordeaux
10
Actual motions: filtered signals
JTAV 2014, Bordeaux
11
Actual motions: filtered signals
JTAV 2014, Bordeaux
12
Actual motions: synthesis
• Identification at various stations
JTAV 2014, Bordeaux
-10
0
10
Azimuth: 293.757 degrees
Dis
p. (c
m)
-10
0
10
Azimuth: 265.8207 degrees
Dis
p. (c
m)
-10
0
10
Azimuth: 294.2067 degrees
Dis
p. (c
m)
-10
0
10
Azimuth: 254.5216 degrees
Dis
p. (c
m)
-10
0
10
Azimuth: 279.9617 degrees
Dis
p. (c
m)
TCU129
TCU122
CHY025
TCU141
TCU113
13
Conclusions
JTAV 2014, Bordeaux
• Instantaneous Reciprocal Ellipticity and
Normalized Inner Product are efficient for:
– Surface wave identification
– Surface wave extraction
• Time-frequency transform needed (S)
• Verification on synthetic signals
• Validation on actual recordings
• Application to vibrations