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A seismic array has been deployed at the Sanford Underground ResearchFacility in the former Homestake mine, South Dakota, to study the undergroundseismic environment. This includes exploring the advantages of constructing athird-generation gravitational-wave detector underground. A major noise sourcefor these detectors would be Newtonian noise, which is induced by fluctuationsin the local gravitational field. The hope is that a combination of a low-noiseseismic environment and coherent noise subtraction using seismometers in thevicinity of the detector could suppress the Newtonian noise to below theprojected noise floor for future gravitational-wave detectors. In this paper,we use Wiener filtering techniques to subtract coherent noise in a seismicarray in the frequency band 0.05 -- 1\,Hz. This achieves more than an order ofmagnitude noise cancellation over a majority of this band. We show how thissubtraction would benefit proposed future low-frequency gravitational wavedetectors. The variation in the Wiener filter coefficients over the course ofthe day, including how local activities impact the filter, is analyzed. We alsostudy the variation in coefficients over the course of a month, showing thestability of the filter with time. How varying the filter order affects thesubtraction performance is also explored. It is shown that optimizing filterorder can significantly improve subtraction of seismic noise, which gives hopefor future gravitational-wave detectors to address Newtonian noise.

Wiener filtering with a seismic underground array at the Sanford Underground Research Facility