Seismic array measurements at Virgo's West End Building for the configuration of a Newtonian-noise cancellation system

Terrestrial gravity fluctuations produce so-called Newtonian noise (NN) which is expected to limit the low frequency sensitivity of existing gravitational-waves (GW) detectors LIGO and Virgo, when they will reach their full potential, and of next-generation detectors like the Einstein Telescope. In this paper, we present a detailed characterization of the seismic field at Virgo's West End Building as part of the development of a Newtonian noise cancellation system. The cancellation system will use optimally filtered data from a seismometer array to produce an estimate of the Newtonian-noise generated by the seismic field, and to subtract this estimate from the gravitational-wave channel of the detector. By using an array of 38 seismic sensors, we show that, despite the influence of the complexity of Virgo's infrastructure on the correlation across the array, Wiener filtering can still be very efficient in reconstructing the seismic field around the test-mass location. Taking into account the division of the building's foundations into separate concrete slabs, and the different properties of the seismic field across them, we conclude that the arrays to be used for the Newtonian-noise cancellation at Virgo will require a relatively large number of seismometers per test mass, i.e. significantly more than 10. Moreover, observed variations of the absolute noise residuals over time, related to the daily evolution of anthropogenic noise, suggest that the Wiener filter will need to be updated regularly, probably more often than every hour, to achieve stationarity of the background level after subtraction.