Newtonian Noise studies in 2nd and 3rd generation gravitational-wave interferometric detectors

This thesis work fits in the Newtonian noise (NN) cancellation framework for gravitational-wave (GW) detectors of 2nd and 3rd generation. At frequencies below 20 Hz the NN affects GW detectors by generating gravity gradients that mask the GW signals that we want to measure. My work can be divided in three main tasks: the optimization of a seismic array for the NN cancellation in underground detectors, the optimization of a seismic array for Advanced Virgo + (which, respect to the former one, relied on seismic measurements and not on a seismic model) and the evaluation of the NN and the seismic field at the KAGRA site. I will briefly summarize in the following the main results of these three works. In the first work I performed a global optimization for finding the optimal locations of an array of sensors for the NN cancellation for underground detectors. Since we need to search for the optimal positions of N sensors in a 3D space, the computational efforts required are very demanding. At the present time, seismic correlations in the relevant frequency band for ET from 3Hz to 20Hz are not available. So we modelled the seismic field as isotropic and homogeneous. With this work I was able to assess the feasibility of applying active NN reduction in underground detectors and reaching a factor 10 of noise reduction with 15 sensors at 10 Hz. In 2019 this work was published. The second work I made during my PhD was conceptually similar to the previous one but very different in the approach used to solve it. Exploiting a theoretical model in Virgo was not an option given its complicated structure. I then used Virgo's seismic data to run the optimization of sensor locations. The main challenge here was that I had to perform a gaussian process regression over a 4D space, and not enough data were available for this purpose. I found a way to bypass the regression over the 4D space by exploiting the convolution theorem. This allowed me to perform the regression over a space with reduced dimension, i.e., in 2D. The global optimization algorithm was then run hundreds of times in order to statistically prove the global minimum, exactly as done in the work for the underground optimization. The results proved that with 15 seismometers we can reach a noise reduction factor of 3-7, which is enough for the aimed sensitivity of the next observing runs. The results of this work were then used to set the array that will be used to cancel the NN in Advanced Virgo +. This work has been published in 2020. This approach could also be useful in future, where it will be needed to optimize underground seismic arrays with real seismic data. Finally, in the third work I used seismic data collected in the Kamioka mine (where the gravitational-wave detector KAGRA is hosted) to investigate the seismic noise caused by the infrastructure and to calculate a NN budget. These are important aspects that need to be investigated in view of the 3rd generation GW detector Einstein Telescope. The data indicated that the infrastructure noise starts to be important well above 10 Hz, where the NN loses its impact on the detector and where the seismic isolation system is capable of killing the noise. Moreover, I used the data from three seismometers to perform a beamforming analysis and find the seismic velocities and the seismic wave main directions. The extracted values were then used as a reference for the estimation of the NN budget. For completeness, I also estimated the NN budget coming from surface Rayleigh waves. This was made by exploiting the data of the F-net network, in Japan. I then showed that the NN from surface and body waves can be neglected for KAGRA.