(ed.). Gravitational waves (IOP, 2001)(422s).

The overlap reduction function 195Figure 12.2. The overlap reduction function for the correlation of VIRGO with a coalignedinterferometer whose central (corner) station is located at: (A) (43.2 ◦ N, 10.9 ◦ E),d = 58.0 km (Italy); (B) (43.6 ◦ N, 4.5 ◦ E), d = 482.7 km (France); (C) the GEO-600(see table 12.2).function intervening in expression (12.45) of ρ k , there are always frequencies forwhich γ(f ) vanishes. Second, in all the considered cases |γ(f )| is well below oneon the whole frequency range, and practically zero for f > 100 Hz. In the caseof correlation with the two LIGOs and TAMA-300, |γ(f )| becomes its maximumvalue (≃0.2) before the first zero or immediately after it, that is in the frequencyregion of 10–20 Hz, just where the sensitivity of the interferometric detectors islower because of the thermal noise. The case is different where the correlationis between VIRGO and GEO-600. In this case, in fact, as a consequence of therelatively small distance between the two detectors, |γ(f )|, eveniflow(≃ 0.1),remains constant up to ∼ 100 Hz. This implies that from the point of view ofthe frequency-averaged value of |γ(f )|, this correlation is more efficient than theothers. Let us note that in terms of gw the minimum detectable signal by a pairof detectors is proportional to |γ(f )| −1 (see equations (12.26) and (12.34)) and,therefore, the low values shown in figure 12.1 lead to a substantial (even one orderof magnitude) reduction of the sensitivity of the correlation.As an example, figure 12.2 shows the overlap reduction function for thecorrelation of VIRGO with three coaligned interferometers located at about 50 km(probably the minimum distance sufficient to decorrelate local seismic and emnoises) (curve A), 480 km (curve B) and 960 km (curve C), respectively, fromthe VIRGO site. The frequency location of the first zero of γ(f ) turns out to be