  In this paper, we develop a new approach to gravity-gradient noise
subtraction for underground gravitational-wave detectors in homogeneous rock.
The method is based on spatial harmonic expansions of seismic fields. It is
shown that gravity-gradient noise produced by seismic fields from distant
sources, stationary or non-stationary, can be calculated from seismic data
measured locally at the test mass. Furthermore, the formula is applied to
seismic fields from stationary local sources. It is found that gravity
gradients from these fields can be subtracted using local seismic measurements.
The results are confirmed numerically with a finite-element simulation. A new
seismic-array design is proposed that provides the additional information about
the seismic field required to ensure applicability of the approach to realistic
scenarios even with inhomogeneous rock and non-stationary local sources.
