  Newtonian gravitational noise from seismic fields will become a limiting
noise source at low frequency for second-generation, gravitational-wave
detectors. It is planned to use seismic sensors surrounding the detectors' test
masses to coherently subtract Newtonian noise using Wiener filters derived from
the correlations between the sensors and detector data. In this work, we use
data from a seismometer array deployed at the corner station of the LIGO
Hanford detector combined with a tiltmeter for a detailed characterization of
the seismic field and to predict achievable Newtonian-noise subtraction levels.
As was shown previously, cancellation of the tiltmeter signal using seismometer
data serves as the best available proxy of Newtonian-noise cancellation.
According to our results, a relatively small number of seismometers is likely
sufficient to perform the noise cancellation due to an almost ideal two-point
spatial correlation of seismic surface displacement at the corner station, or
alternatively, a tiltmeter deployed under each of the two test masses of the
corner station at Hanford will be able to efficiently cancel Newtonian noise.
Furthermore, we show that the ground tilt to differential arm-length coupling
observed during LIGO's second science run is consistent with gravitational
coupling.
