  We report Earth-scale distance magnetic correlations from lightning strokes
in the frequency range 1-1000 Hz at several distances ranging from 1100 to 9000
km. Noise sources which are correlated on Earth-scale distances can affect
future searches for gravitational-wave signals with ground-based
gravitational-wave interferometric detectors. We consider the impact of
correlations from magnetic field fluctuations on gravitational-wave searches
due to Schumann resonances ($<$50 Hz) as well as higher frequencies ($>$100
Hz). We demonstrate that individual lightning strokes are a likely source for
the observed correlations in the magnetic field fluctuations at
gravitational-wave observatories and discuss some of their characteristics.
Furthermore, we predict their impact on searches for an isotropic
gravitational-wave background, as well as for searches looking for
short-duration transient gravitational waves, both unmodeled signals (bursts)
as well as modeled signals (compact binary coalescence). Whereas the recent
third observing run by LIGO and Virgo was free of an impact from correlated
magnetic field fluctuations, future runs could be affected. For example, at
current magnetic coupling levels, neutron star inspirals in third generation
detectors are likely to be contaminated by multiple correlated lightning
glitches. We suggest that future detector design should consider reducing
lightning coupling by, for example, reducing the lightning-induced beam tube
currents that pass through sensitive magnetic coupling regions in current
detectors. We also suggest that the diurnal and seasonal variation in lightning
activity may be useful in discriminating between detector correlations that are
produced by gravitational waves and those produced by lightning.
