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In order to fully characterize the local ground motion induced by earthquakes, one needs to determine three components of translation, six components of strain and three components of rotation (Aki and Richards, 2002). The first two quantities are commonly studied by seismologists with the use of classical seismological instrumentation, like accelerometers/seismometers and strainmeters.
Rotational motions in seismology have always been considered negligible, mainly because of the lack of instrumentation of adequate sensitivity. Indeed, the rotation rates which have been observed thus far, range from 10^-1 rad/s close to seismic sources (Nigbor, 1994), to 10^-11 rad/s for large telesismic earthquakes (Igel et al.2005, 2007). It is expected that collocated measurements of translations and rotations may (1) allow the estimate of velocities and propagation directions of the incoming wavefield (2) help to further constrain rupture processes and (3) provide additional hazard-relevant information to earthquake engineers (Igel et al.2007). But as reported just a decade ago by Aki and Richards (2002): “...seismology still awaits a suitable instrument for making such measurements.”
Over the last few years ring laser gyroscopes, based on the Sagnac effect, demonstrated a high potential in investigating the rotational ground motion, and they appear to be the most promising instruments to address Aki and Richard's requirements.
Theory suggests a general link between rotational and translational motions induced by earthquakes. In the case of horizontally and vertically polarized surface waves (Love and Rayleigh-waves) the relations are particularly simple. Vertical acceleration and rotation rate about a horizontal axis should be in phase and scaled by a factor that corresponds to local Rayleigh-waves phase velocity. By the same token, transverse acceleration and rotation rate about vertical axis should be in phase and scaled by two times Love-waves phase velocity.
According to the above relationships, under the plane-wave approximation, collocated measurements of translation and rotation can provide the estimate of phase velocities and propagation directions, otherwise only accessible through seismic array measurements, polarization analysis, or additional strain measurements.

This thesis focuses on the data collected by the G-Pisa ring laser gyroscope, developed by the University of Pisa (Department of Physics) and INFN. This instrument has been operating for almost 2 years at the European Gravitational Observatory in Cascina (Pisa), in the framework of the VIRGO project.
In particular, I report the very first seismic analysis of the rotational data from a gyrolaser lying in the vertical plane, which is sensitive to rotation about a horizontal axis (tilt). The main part of the thesis is dedicated to the analysis of the Mw=9.0, March 11th, 2011, Japan earthquake; in addition, I also account for recordings from some events occurred at regional distances.

The first objective of this work is to characterize the performance of G-Pisa in relation to a collocated accelerometer and to verify the ground-coupling of the instrument.
By calculating power spectral density (PSD) of rotation rate and acceleration I first identify the signal to noise ratio as a function of frequency and, by computing time-frequency transforms (spectrograms), I individuate the most energetic frequency bands as a function of time for both the instruments during several selected earthquakes. Then, rotation rates and accelerations are correlated within subsequent frequency bands, in order to quantify similarity between the signals.
The second objective of the thesis is to compare the recorded rotation rates with those obtained through an array-based analysis. Applying the seismo-geodetic method by Spudich et al. (2008), I derive the rotation rate from a tripartite array of three-components accelerometers. This method provides an independent estimation of ground rotations that should be in agreement with that directly recorded by the gyrolaser. Results from this analysis show that the two measurements are in general agreement; I attribute the discrepancies to both the geometrical setting of the array and the band limitations of its sensors.
The third objective concerns phase velocities estimation and derivation of surface waves dispersion curves from collocated measurements of rotation and translation. Following Igel et al. (2005, 2007) and Kurrle et al. (2010), I address this issue by calculating the zero-lag correlation coefficient between translational and rotational traces. When the correlation coefficient is above an arbitrary threshold, phase velocity is obtained through a linear regression within overlapping sliding time windows. Iterating the procedure after a narrow band-pass filtering of both traces, it is possible to derive a dispersion curve for the selected wave packet.
A theoretically equivalent dispersion curve could be derived in frequency domain as showed by Suryanto et al (2006), both for Love- and Rayleigh-waves, simply by calculating the spectral ratios between translation and rotation. I implemented this second procedure using a multitaper method (MTM, Thomson, 1982), in order to reduce variance and bias by averaging periodograms obtained using a properly-designed taper.
The dispersion curves calculated in this manner are compared to those obtained with a multi-frequency Plane Wave Fit (PWF) analysis. This method that consists in estimating wavefield slowness for an array of sensors provides independent information about velocities and direction of propagation (azimuth) for plane waves crossing the array.
Rayleigh-waves dispersion curves derived from the Japan earthquake, are then compared against the theoretical phase velocities derived from a standard (AK135) Earth Model.
Since Rayleigh-waves are fully recorded by the gyrolaser only when their direction of propagation is perpendicular to G-Pisa area vector, I implemented a rotation rate signal correction method that takes into account the different directions of propagation of Rayleigh-waves (as estimated from PWF inversion) with respect to G-Pisa axis of sensitivity. This correction leads to a more reliable result in estimating phase velocities, that otherwise would be overestimated.
Collocated measurements of rotation about vertical axis and transverse acceleration for horizontally-polarized seismic waves (SH- and Love-waves) allow estimating direction of propagation and azimuth of the incoming wavefield. Following Igel et al. (2007), and Hadziioannou et al. (2012), I conducted these estimates for Love waves recorded when G-Pisa was configured with area vector oriented vertically.

This thesis is organised into five chapters. In the first chapter, I briefly report the general theory behind rotational motions, and present the relationships between rotation and translation in the context of classical elasticity. Here I show that surface-waves phase velocities and thus dispersion curves can be obtained from collocated measurements or rotation and translation.
In the second chapter I present the instrumentation and data, with particular reference to G-Pisa and its ability to investigate both Rayleigh-and Love-waves with a sensitivity in the order of a few nrad/s/over the 0.02-1 Hz frequency band.
In the third chapter I describe the data analysis methods, and their practical implementation in terms of Matlab scripts.
In the fourth chapter I present and critically comment the results from the analysis. This chapter is divided into two sections, dedicated respectively to the Love- and Rayleigh-waves results.
The last chapter is dedicated to the general discussion and conclusions.