  Terrestrial gravity perturbations caused by seismic fields produce the
so-called Newtonian noise in gravitational-wave detectors, which is predicted
to limit their sensitivity in the upcoming observing runs. In the past, this
noise was seen as an infrastructural limitation, i.e., something that cannot be
overcome without major investments to improve a detector's infrastructure.
However, it is possible to have at least an indirect estimate of this noise by
using the data from a large number of seismometers deployed around a detector's
suspended test masses. The noise estimate can be subtracted from the
gravitational-wave data; a process called Newtonian-noise cancellation (NNC).
In this article, we present the design and implementation of the first NNC
system at the Virgo detector as part of its AdV+ upgrade. It uses data from 110
vertical geophones deployed inside the Virgo buildings in optimized array
configurations. We use a separate tiltmeter channel to test the pipeline in a
proof-of-principle. The system has been running with good performance over
months.
