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.
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