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