  After the first direct detection of gravitational waves (GW), detection of
stochastic background of GWs is an important next step, and the first GW event
suggests that it is within the reach of the second-generation ground-based GW
detectors. Such a GW signal is typically tiny, and can be detected by
cross-correlating the data from two spatially separated detectors if the
detector noise is uncorrelated. It has been advocated, however, that the global
magnetic fields in the Earth-ionosphere cavity produce the environmental
disturbances at low-frequency bands, known as Schumann resonances, which
potentially couple with GW detectors. In this paper, we present a simple
analytical model to estimate its impact on the detection of stochastic GWs. The
model crucially depends on the geometry of the detector pair through the
directional coupling, and we investigate the basic properties of the correlated
magnetic noise based on the analytic expressions. The model reproduces the
major trend of the recently measured global correlation between the GW
detectors via magnetometer. The estimated values of the impact of correlated
noise also match those obtained from the measurement. Finally, we give an
implication to the detection of stochastic GWs including upcoming detectors,
KAGRA and LIGO India. The model suggests that LIGO Hanford-Virgo and
Virgo-KAGRA pairs are possibly less sensitive to the correlated noise, and can
achieve a better sensitivity to the stochastic GW signal in the most
pessimistic case.
