Data processing of earthquake-induced rotational ground motion observed by Ring Laser Gyroscopes

In recent years the development of the ring laser gyroscope (RLG) technology permitted to achieve a sensitivity suitable for extending the observation of ground motion to the rotational part of the seismic induced wavefield. As predicted by the classical theory of elasticity, to fully characterize the rigid body type of ground motion we need to measure not only the usual translational degrees of freedom (hereinafter d.o.f) but also three additional rotational d.o.f . In this work I use of the data provided by the three largest ring laser gyroscopes installed in Europe (i.e. ROMY,G-Wettzell and GINGERINO) to study, in a single station approach, important properties of the local structures under the above mentioned instruments as well as the direction of propagation of the seismic waves generated by earthquakes from local to teleseismic distances. Thanks to the availability of these unique data sets I will show the advantages of extending classical seismology to rotational observations. In chapter 1 I show the physical principles on which the rotational sensors are based i.e. the Sagnac effect and outline how this principle ensures a complete decoupling from translations, making then the RLG a perfect rotational sensor. In an active interferometer (RLG) the difference in travel time of the counter-propagating light, which is the basis of the Sagnac effect, is translated in a frequency difference detection problem. It’s possible to calculate the angular rotation by measuring the Sagnac frequency. A RLG is sensitive to rotations along the axis perpendicular to the surface enclosed in the path of the laser beams . It means that, in an X-Y-Z system, a RLG placed horizontally (in the X-Y plane) is sensitive to vertical rotations (along Z) induced by horizontally polarized S and Love waves (i.e SH waves). The G-Wettzell and GINGERINO stations record the rotations induced by SH waves with sensitivity not far from 10^-14 rad/sec (/sqrt(Hz)) and 10^-10 rad/sec (/sqrt(Hz)) respectively. Today theROMY station is a triaxial RLG that also perceives horizontal rotations, induced by vertically polarized shear waves (i.e SV) and by Rayleigh waves, with a sensitivity of. In a second step in this chapter I derive from the theory of linear elasticity the key equations that we will use for data processing. It is shown that, during the transit of Love waves, the transverse acceleration and rotation rate are in phase and scaled by a factor -1/2cL, with cL being the horizontal phase velocity for Love waves. Similarly the two observables (i.e. transverse rotation rate and vertical acceleration) are scaled by the phase velocity of the Rayleigh waves cR. These theoretical relations, obtained in the context of a single phase wave, can be easily extended in the case of seismic signals with variable frequency content. Thus the direct ratio between transversal acceleration and rotation rate allows us to estimate the local phase velocity of surface seismic waves which, at telesismic distance, are recorded with considerable amplitude both by the seismometer and by the RLG. In chapter 2 I describes in detail the experimental apparata used to collect the rotational data analyzed in this work. In chapter 3, I report the detection and the analysis of the underground rotational signals from some M7+ telesismic events observed from these stations. Following the references of previous works, I describe some methods to measure the direction of the wave field, also called the backazimuth direction (BAZ hereinafter). I have treated the BAZ as unknown and I searched for directions of propagation that maximize the zero-lag correlation coefficient (ZLCC hereinafter) between the rotation rate and ground acceleration, rotating the NS and EW components of the seismometer associated with the laser ring through a rotation matrix. The correlation was measured by sliding windows of appropriate length along the whole seismogram. For each event I prove that the data are compatible with the theoretical estimates of the direction of the wave field with a 5 degrees uncertainty in angle. In a second step I look for an estimate of the local phase velocity of the seismic waves recorded by the instruments. The phase velocity estimation is calculated in the time domain, using a narrow band FIR filtering, applied simultaneously to the transverse acceleration and angular rotation signals. The phase velocity is calculated in a discrete range of frequencies, through the ratio between the envelopes of the bandpass signals. Then wavefield direction and phase velocity measurements are extended to the time/frequency domain using the Wavelet decomposition method (CWT hereinafter). For the events at teleseismic distance, resulting phase velocities are compatible with theoretical predictions for PREM Earth’s model. In chapter 4 the local events recorded by GINGERINO are studied. I present the analysis of translational and rotational motions in the case of 18 local seismic events. The data belong to two seismic sequences that affected Italy in August-November 2016, with the seismic sequence of ”Amatrice-Visso-Norcia”, and in April-August 2018 with the ”seismic sequence of Molise”. I use co-located measurements of the vertical ground rotation rate and the three components of ground acceleration from a broad-band seismometer. I collected events spanning the 3.5-5.9 Magnitude range. This data set constitutes an observation of the vertical rotational motions associated with an intense seismic sequence at local distance. The first step of our analyses consisted in investigating the general relationships between ground rotation and translation. I therefore compared peak values of the rotation rate (PRR) with an intensity measure commonly used in earthquake engineering, namely Peak ground acceleration (PGA). Using the time derivative of the ground-velocity seismograms recorded by the seismometer, we estimated PGA as the geometric mean of the peak values measured separately at the two horizontal components of motion, NS and EW. PGA and PRR are linked by a linear relation that allows to calculate the apparent phase velocity; it is not necessarily a true phase velocity, but rather a scaling factor characterizing the seismicwavefield beneath the recording station. Results of the fitting data yield an apparent velocity value compatible with that estimated in the literature for the seismic sequence of Amatrice Visso-Norcia. After this first step, the CWT- coherence is used for identifying those regions in time-frequency domain where the rotation rate and transverse acceleration signals exhibit significant correlation. For these high correlation sections, I extract phase velocity dispersion curves. This analysis is performed on the rotational signals present in the P-coda, S-coda and Lg phase. The results are compared with those obtained in literature regarding the dispersion of surface waves in the Central Apennines. I process the data set in order to get an experimental estimation of the events backazimuth. I compare this results to the theoretical ones obtained by the station/epicenter location. The misfit of 10°±20° is recurrent in the estimation of the direction of the wavefield. This misfit has been evaluated by previous works on the determination of the BAZ at local distances with the GINGERINO station