  Seismic noise, generated by oceanic microseisms and other sources,
illuminates the crust in a manner different from tectonic sources, and
therefore provides independent information. The primary measurable is the
two-point cross-correlation, evaluated using traces recorded at a pair of
seismometers over a finite-time interval. However, raw seismic traces contain
intermittent large-amplitude perturbations arising from tectonic activity and
instrumental errors, which may corrupt the estimated cross-correlations of
microseismic fluctuations. In order to diminish the impact of these
perturbations, the recorded traces are filtered using the nonlinear one-bit
digitizer, which replaces the measurement by its sign. Previous theory shows
that for stationary Gaussian-distributed seismic noise fluctuations one-bit and
raw correlation functions are related by a simple invertible transformation.
Here we extend this to show that the simple correspondence between these two
correlation techniques remains valid for {\it non-stationary} Gaussian and a
very broad range of {\it non-Gaussian} processes as well. For a limited range
of stationary and non-stationary Gaussian fluctuations, we find that one-bit
filtering performs at least as well as spectral whitening. We therefore
recommend using one-bit filtering when processing terrestrial seismic noise,
with the substantial benefit that the measurements are fully compatible with
current theoretical interpretation (e.g., adjoint theory). Given that seismic
records are non-stationary and comprise small-amplitude fluctuations and
intermittent, large-amplitude tectonic/other perturbations, we outline an
algorithm to accurately retrieve the correlation function of the
small-amplitude signals.

Earth and Planetary Astrophysics