  A first detection of terrestrial gravity noise in gravitational-wave
detectors is a formidable challenge. With the help of environmental sensors, it
can in principle be achieved before the noise becomes dominant by estimating
correlations between environmental sensors and the detector. The main
complication is to disentangle different coupling mechanisms between the
environment and the detector. In this paper, we analyze the relations between
physical couplings and correlations that involve ground motion and LIGO strain
data h(t) recorded during its second science run in 2016 and 2017. We find that
all noise correlated with ground motion was more than an order of magnitude
lower than dominant low-frequency instrument noise, and the dominant coupling
over part of the spectrum between ground and h(t) was residual coupling through
the seismic-isolation system. We also present the most accurate gravitational
coupling model so far based on a detailed analysis of data from a seismic
array. Despite our best efforts, we were not able to unambiguously identify
gravitational coupling in the data, but our improved models confirm previous
predictions that gravitational coupling might already dominate linear
ground-to-h(t) coupling over parts of the low-frequency, gravitational-wave
observation band.
