Terrestrial gravity noise, also known as Newtonian noise, produced by ambient seismic and infrasound fields will pose one of the main sensitivity limitations in low-frequency, ground-based, gravitational-wave (GW) detectors. It was estimated that this noise foreground needs to be suppressed by about 3 -- 5 orders of magnitude in the frequency band 10,mHz to 1,Hz, which will be extremely challenging. In this article, we present a new approach that greatly facilitates cancellation of gravity noise in full-tensor GW detectors. The method uses optimal combinations of tensor channels and environmental sensors such as seismometers and microphones to reduce gravity noise. It makes explicit use of the direction of propagation of a GW, and can therefore either be implemented in directional searches for GWs or in observations of known sources. We show that suppression of the Newtonian-noise foreground is greatly facilitated using the extra strain channels in full-tensor GW detectors. Only a modest number of auxiliary, high-sensitivity environmental sensors are required to achieve noise suppression by a few orders of magnitude.
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