F. Bianco , G. Gargiulo, e L. Zaccarelli

1. 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

2. The Splitting phenomenon & the stress field  = qS1 polarization  stress field main direction DT=time delay between the split S waves  crack system characteristics (density & geometry) Stress field Intensity DT

3. How F e DT are measured: • Visual Inspection • Cross- Correlation windowed signal rotated step by step • Diagonalization of the covariance matrix • Singolar Value Decomposition • ……………………………………………… and now introducing Wavelet Transform (WT) The 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

4. Some details….. • We rotate each signal clockwise in 2° steps • We applied the CWT • We calculated the complex coefficient of CWT according to the following relationship: • We define the complex function • For each wavelet we define the Phase Alignment Index PAI as • And then • The splitting parameters are obtained searching for the maximum value of MP

5. The PAI rapresentation and the splitting parameter measurements DT F

6. BKE Recognized Anisotropic volume(e.g. Bianco et al. 1999) Wavelets and doublets at MT. Vesuvius

7. The data • 1999 – 2000 dataset (including the M=3.6 event) • Selection Rules: 1) S/R>6; 2) i<sww (35°); 3) clear S onsets EO Datarecorded at SGV, BAF, BKN and BKE 3C digital stations In order to avoid any spatial dependence on the time behaviour of the retrieved splitting parameters we search for doublets/multiplets at each selected station

8. Doublets or multiplets • events recorded at the same station • similar waveformscross-correlation max. > 0.9 • almost same locationshypocentral distance < 100 m  same source & ray path doublet changes reflect time variation of the medium elastic properties Poupinet et al., 1984 Geller and Mueller, 1980

9. The retrieved doublets/multiplets inside sww EO NS

10. The doublets location EO Doublets/multiplets inside the sww NS

11. Vesuvio - The Wavelet choice In details: Mother Wavelet We used 4 Ψ(a,t) with different wc Localized in the space wc=2 wc=5 wc=50 wc=250 We constructed a Matlab algorithm

12. DT=0.024s F=48° For each earthquake at each station

13. Results -Time variation of DT Clear increase sometime followed by a sudden decrease M=3.6 BKE M=3.6 BKN M=3.6 SGV M=3.6 BAF

14. Clear 90°-flip The F results M=3.6 M=3.6 90°-flip 90°-flip BKE SGV Clear 90°-flip Clear 90°-flip Clear 90°-flip M=3.6 M=3.6 90°-flip 90°-flip BKN BAF

15. ….and this is roughly what we have observed THEORY (Zatsepin & Crampin 1997) • the compressional stress acting on the system increases • i.e. crack aspect ratio increases … DT increase (long term) • the system reaches the overpressurized regime … 90º-flip ofF • stress relaxation & eruption /earthquake … DT decrease (sudden)

16. Conclusions • Using Wavelets: • Preserved the signal signature • Faster algorithm • Easy implementation • We observe a time variation for f and DT 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 DT show the same temporal trends  volcano monitoring and eruption forecasting