Future searches for a gravitational-wave background using Earth-based gravitational-wave detectors might be impacted by correlated noise sources. A well-known example are the Schumann resonances, which are extensively studied in the context of searches for a gravitational-wave background. Earlier work has shown that a technique termed "gravitational-wave geodesy"can be used to generically differentiate observations of a gravitational-wave background from signals due to correlated terrestrial effects, requiring true observations to be consistent with the known geometry of our detector network. The key result of this test is a Bayes factor between the hypotheses that a candidate signal is astrophysical or terrestrial in origin. Here, we further formalize the geodesy test, mapping distributions of false-alarm and false-acceptance probabilities to quantify the degree with which a given Bayes factor will boost or diminish our confidence in an apparent detection of the gravitational-wave background. To define the false alarm probability of a given Bayes factor, we must have knowledge of our null hypothesis: the space of all possible correlated terrestrial signals. Since we do not have this knowledge, we instead construct a generic space of smooth functions in the frequency domain using Gaussian processes, which we tailor to be conservative. This enables us to use draws from our Gaussian processes as a proxy for all possible nonastrophysical signals. During the O2 observing run, the LIGO and Virgo collaborations observed an SNR=1.25 excess in their search for an isotropic gravitational-wave background. To demonstrate the utility of gravitational-wave geodesy, we apply the method to the observed cross-correlated data.
Bibliographical noteFunding Information:
The authors acknowledge access to computational resources provided by the LIGO Laboratory supported by National Science Foundation Grants No. PHY-0757058 and No. PHY-0823459. This paper has been given LIGO DCC number P2100383 and Virgo TDS number VIR-1126A-21. This material is based upon work supported by Fonds Wetenschappelijk Onderzoek Vlaanderen (FWO). K. J. is supported by FWO-Vlaanderen via Grant No. 11C5720N. M. W. C. acknowledges support from the National Science Foundation with Grants No. PHY-2010970 and No. OAC-2117997. I. M. was supported by the University of Florida through a Graduate Teaching Assistantship.
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