• 2D tomography
• Beamforming
• Geophysics
• natural seismic sources
• Plane Wave Fitting
• Rayleigh wave dispersion curve
• rotation measures
• shear wave profile
• SPAC

This work aims at investigating the propagation of seismic waves in the vicinity of the VIRGO
gravitational-wave detector (Cascina, Pisa) and to infer a shallow shear-wave velocity structure
from the dispersion characteristics of Rayleigh waves.
For the study, I used earthquake and noise
recordings from a temporary, 50-station array deployed in the vicinity of VIRGO, whose data have
been made available by the EGO (European Gravitational Wave Observatory) consortium. In order to
obtain the general kinematic properties of the earthquakes wavefields, I first applied a
deterministic approach based on the common-waveform model of the signal, namely a frequency-domain
Beam-Forming. This method allow measuring the propagation direction and horizontal slowness of the
incoming signal; it was applied to short time windows sliding along the array seismograms, using
different subarrays whose apertures were selected in order to match different frequency bands.

As expected, the early portions of the earthquake signals are dominated by waves propagating from the
epicentral region; apparent velocities of the P- and S-wave arrivals are around 8km/s and 3km/s,
respectively. For the Rayleigh-wave arrivals, velocities range between 0.5 Km/s and 5 km/s, indicating
interferences of other wavetypes and / or propagation effects (reflections, refractions) associated
with the local geological and topographical complexities. For these same time intervals, the propagation
directions are scattered throughout a wide angular interval. These results suggest therefore that
deterministic methods are not appropriate for estimating Rayleigh waves phase velocity.

Thanks to array density and geophones sensitivity, and assuming that the gradient of the displacement
is constant throughout the array, I then attempted the estimation of the solid-block ground rotations w_t
around an axis parallel to the surface, which is related to Rayleigh-waves phase velocity.
By calculating w_t from properly bandpass filtered seismograms spanning the Rayleigh-wave arrivals from
different subarray configurations, Rayleigh wave phase velocity dispersion data can be obtained.
This analysis requires that the wavelength is about 5 times the array extent along the wave propagation
direction. In order to obtain phase velocity data over a range of frequencies, I therefore extended
the analyses over a set of subarrays of different aperture.


From the scaled average of the displacement – rotation ratios I then obtained phase velocity estimates
which finally allowed deriving a dispersion relationship.

If the wavefield is stochastic and stationary in both space and time, an indipendent Rayleigh wave phase
velocity dispersion curve can also be obtained through the stochastic method SPAC.
The average of the dispersion curves obtained by SPAC is inverted to obtain a shear wave velocity
profile using a perturbational approach.

For each frequency and for each station pair, the ratio between inter-station distance and the
Rayleigh-wave phase velocity provides an estimate of the corresponding traveltime. The final part
of the work consists of the tomographic inversion of these traveltimes in order to obtain 2D Rayleigh
wave phase velocity maps, that highlight ground inhomogeneity of the area at that particular frequency.

Further developments will involve a through assessment of uncertainties in the estimates of Rayleigh
wave phase velocities, in order to better constrain tomography results.