marginalizing over all three spectral indices, using the priors described in the Supplementary Material. These limits are shown in Table \[tab:nongrUL\], again for both choices of amplitude prior.

*Estimate of correlated magnetic noise*— Coherent noise between gravitational-wave interferometers may be introduced by terrestrial sources such as Schumann resonances, which are global electromagnetic modes of the cavity formed by the Earth’s surface and ionosphere [@Schumann_theory]. These fields have very long coherence lengths [@Schumann_4] and can magnetically couple to the gravitational-wave channel and lead to broadband noise that is coherent between different gravitational-wave detectors. As the detectors become more sensitive, eventually this source of correlated noise may become visible to the cross-correlation search, and, if not treated carefully, will bias the analysis by appearing as an apparent . Unlike the lines and combs discussed in [@CWStochDetchar], we cannot simply remove affected frequency bins from the analysis because Schumann noise is broadband.

Here, we estimate the level of correlated electromagnetic noise (from Schumann resonances or other sources) in O2 following [@Schumann_1; @Schumann_2; @stoch_O1]. We first measure the cross-power spectral density $M_{12}(f)$ between two Bartington Model MAG-03MC magnetometers [@bartington] installed at Hanford and Livingston. We then estimate the transfer function $T_{i}(f)$ ($i=\{1,2\}$) between the 