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Trasformate Wavelet complesse per la misura dello Splitting delle onde di taglio e le relative variazioni temporali del campo di stress al Vesuvio. F. Bianco , G. Gargiulo, e L. Zaccarelli Istituto Nazionale di Geofisica e Vulcanologia, sez. Napoli – Osservatorio Vesuviano. - PowerPoint PPT Presentation
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Trasformate Wavelet complesse per la misura dello Splitting delle onde di
taglio e le relative variazioni temporali del campo di stress al Vesuvio.
F. Bianco, G. Gargiulo, e L. Zaccarelli
Istituto Nazionale di Geofisica e Vulcanologia, sez. Napoli – Osservatorio Vesuviano
The Splitting phenomenon & the stress field
T=time delay between the split S waves
crack system characteristics (density & geometry)Stress field Stress field IntensityIntensity
= qS1 polarization
stress field main direction
How e T are measured: Visual Inspection
Cross- Correlation windowed signal rotated step by step
Diagonalization of the covariance matrix
Singolar Value Decomposition
………………………………………………
Wavelet Transform (WT)and now introducingThe goal: to improve the splitting estimates in semi-automatic algorithms by using the WT properties (e.g. CWT application does not change the amplitude and phase feature of the waveform)
•Complex Wavelet Morlet - type
1. We rotate each signal clockwise in 2° steps
2. We applied the CWT
3. We calculated the complex coefficient of CWT according to the following relationship:
4. We define the complex function
5. For each wavelet we define the Phase Alignment Index PAI as
6. And then
The splitting parameters are obtained searching for the maximum value of MP
Some details…..
The PAI rapresentation and the splitting parameter measurements
tempo (s)
ango
lo d
i rot
azio
ne (°
)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
50
100
150
200
250
300
350
qS1 qS2
5 5.1 5.2 5.3 5.4 5.5 5.6 5.7-1.5
-1
-0.5
0
0.5
1
x 104
T
Wavelets and doublets at MT. VesuviusWavelets and doublets at MT. Vesuvius
Recognized
Anisotropic volume (e.g. Bianco et
al. 1999)
BKE
The data
EO
In order to avoid any spatial
dependence on the time
behaviour of the retrieved splitting
parameters we search for
doublets/multipletdoublets/multipletss at each selected
station
1999 – 2000 dataset (including the M=3.6 event)
Selection Rules: 1) S/R>6 ; 2) i<sww (35°); 3) clear S onsets
Data recorded at SGV, BAF, BKN and BKE 3C digital stations
Doublets or multipletsevents recorded at the same station
similar waveforms cross-correlation max. > 0.9 almost same locations hypocentral distance < 100 m
same source & ray pathdoublet changes reflect time variation of the medium elastic properties
Poupinet et al., 1984Geller and Mueller, 1980
EO
NS
The retrieved doublets/multiplets inside
swwBAF BKE BKN SGV06/06 02:40 13/08 13:59 22/09 04:34 25/09 10:06
06/06 02:40 22/09 04:34
06/06 02:40 13/08 13:59
22/09 04:34 25/09 10:06
25/09 06:27 09/11 08:28
25/09 06:27 09/11 08:28
25/09 06:27 09/11 08:28
25/09 06:27 09/11 08:28
27/11 00:35 21/12 00:18
27/11 00:35 21/12 00:18
The doublets location
EO
NS
Doublets/multiplets inside the sww
Vesuvio - The Wavelet choice
In details:
We used 4 Ψ (a,t) with different c
Mother Wavelet
c=2 c=5 c=50 c=250
Localized in the space
We constructed a Matlab algorithm
For each earthquake at each station
=48°
T=0.024s
50 150 250 350te m p o (g io rn i da l1 \1 \1 9 99 )
0
5
10
15
20
25
tem
po d
i rita
rtdo
norm
alizz
ato
(ms\k
m)
50 150 250 350te m po (g io rn i d a l 1 \1 \19 9 9 )
0
5
10
15
20
25
tem
po d
i rita
rdo
norm
alizz
ato
(ms\k
m)
50 150 250 350te m p o (g io rn i d a l 1 \1 \1 9 9 9 )
0
5
10
15
20
25
tem
po d
i rita
rdo
norm
aliz
zato
(ms\
km)
50 150 250 350te m p o (g io rn i d a l 1 \1 \19 9 9 )
0
10
20
30
40
50
tem
po d
i rita
rdo
(ms)
Results -Time variation of T
BKE M=3.6
M=3.6SGV
BKN
BAF
M=3.6
M=3.6Clear increase sometime followed by a sudden decrease
50 150 250 350te m p o (g io rn i d a l 1 \1 \19 9 9 )
0
40
80
120
160
dire
zion
e di
pol
ariz
zazi
one
(°)
50 150 250 350tem p o (g io rn i da l 1 \1 \19 9 9 )
0
40
80
120
160
dire
zion
e di
pol
ariz
zazi
one
(°)
50 150 250 350te m p o (g io rn i d a l 1 \1 \19 9 9)
0
40
80
120
160
dire
zion
e di
pol
ariz
zazi
one
(°)
50 150 250 350te m p o (g io rn i d a l 1 \1 \199 9 )
0
40
80
120
160
dire
zion
e di
pol
ariz
zazi
one
(°)
BKE
90°-flip
90°-flip
BKN
90°-flip
90°-flip
SGV
BAF
The results
Clear 90°-flipClear 90°-flipClear 90°-flipClear 90°-flip
M=3.6 M=3.6
M=3.6 M=3.6
the compressional stress acting on the system increases i.e. crack aspect ratio increases … T increase (long term)
the system reaches the overpressurized regime … 90º-flip of
stress relaxation & eruption /earthquake … T decrease (sudden)
THEORY (Zatsepin & Crampin 1997)
….and this is roughly what we have observed
Conclusions
•We observe a time variation for and before the occurrence of a major earthquake at Mt. Vesuvius•The variation is compatible with the one retrieved using other methods and dataset including also non-doublets events (e.g. Del Pezzo et al., 2004)Interestingly:Coda Wave Interferometry on the same dataset showed a velocity variation in the same period (Pandolfi et al, 2007)• CWI and SWS analysis are sensitive to even small stress field
variations indicator of crustal stress state in time
• v and T show the same temporal trends volcano monitoring and eruption forecasting
Using Wavelets:•Preserved the signal signature•Faster algorithm•Easy implementation