  Direct detection of gravitational waves (GWs) from compact binary systems
suggests that the merger rate of such events is large, and the sum of their GWs
can be viewed as stochastic signals. Because of its random nature,
cross-correlating the signals from multiple detectors is essential to
disentangle the GWs from instrumental noise. However, the global magnetic
fields in the Earth-ionosphere cavity produce the environmental disturbances at
low-frequency bands, known as Schumann resonances, and coupled with GW
detectors, they potentially contaminate the stochastic GW signal as a
correlated noise. Previously, we have presented a simple analytical model to
estimate its impact on the detection of stochastic GWs. Here, extending the
analysis to further take account of the effects of anisotropic lightning source
distributions, we present a comprehensive study of the impact of correlated
magnetic noise at low-frequency bands, including non-tensor-type GWs, as well
as circularly polarized tensor-type GWs. We find that as opposed to a naive
expectation, the impact of correlated magnetic noise does not always increase
with anisotropies in the lighting source distribution. Even in the presence of
large anisotropies, there is a robust detector pair for which the amplitude of
correlated magnetic noise becomes comparable to or well below detectable
amplitude of stochastic GWs. The results indicate that the properties of the
correlated magnetic noise depend crucially on both the geometrical and
geographical setup of the detector's pair, and Virgo and KAGRA would be
potentially the most insensitive detector pair against the correlated magnetic
for both tensor- and non-tensor-type stochastic GWs.
