Correlated noise sources, particularly magnetic noise, form a risk to future gravitational-wave searches aimed at detecting the gravitational-wave background. To investigate potential noise contamination, we project noise levels based on accurate measurements of how strongly the noise couples to the detector. To make these estimates, we inject, for the first time, broadband, coherent magnetic noise between two gravitational-wave detectors, LIGO Hanford and LIGO Livingston, separated by several thousands of kilometers. We describe the noise injection and its impact on the analysis pipelines, then investigate the accuracy of noise projection techniques used over the past decade. Finally, we present a proof-of-concept demonstration of noise subtraction using Wiener filtering, while also highlighting potential risks associated with this method. This unique dataset with correlated noise caused by magnetic field fluctuations in two gravitational-wave detectors, as well as in an array of witness sensors, provides an excellent testing ground for additional future studies. Ultimately, this study demonstrates that Wiener filtering is effective and can be applied in the eventual detection of the gravitational-wave background by the LIGO-Virgo-KAGRA Collaboration.

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• Gravitational wave detection
• Gravitational waves