Optimization of seismometer arrays for the cancellation of Newtonian noise from seismic body waves

Newtonian noise from seismic fields is predicted to become a sensitivity limiting noise contribution of the gravitational-wave detectors Advanced LIGO and Virgo in the next few years. It also plays a major role in the planning of next-generation detectors, which might be constructed underground, as planned for the Einstein Telescope, mostly to suppress Newtonian noise. Coherent noise cancellation using Wiener filters provides a way to mitigate Newtonian noise. So far, only the cancellation of Newtonian noise produced by seismic surface waves has been studied in detail due to its relevance for Advanced LIGO and Virgo. However, seismic body waves can still contribute significantly to Newtonian noise in surface detectors, and they might be the dominant source of gravity fluctuations in underground detectors. In this paper, we present the first detailed analysis of coherent cancellation of Newtonian noise from body waves. While the required number of seismometers to achieve a certain level of noise suppression is higher than for seismic surface waves, we show that optimal seismometer arrays can greatly reduce body-wave Newtonian noise. The optimal array configurations and achieved residuals depend strongly on the composition of the seismic field in terms of average compressional-wave and shear-wave content. We propose Newtonian-noise cancellation to achieve the ambitious low-frequency target of the Einstein Telescope.