  It is a well-established principle that cross-correlating seismic
observations at different receiver locations can yield estimates of
band-limited inter-receiver Green's functions. This principle, known as seismic
interferometry, is a powerful technique that can transform noise into signals
which allow us to remotely image and interrogate subsurface Earth structures.
In practice it is often necessary and even desirable to rely on noise already
present in the environment. Theory that underpins many applications of ambient
noise interferometry makes an assumption that the noise sources are
uncorrelated in space and time. However, many real-world noise sources such as
trains, highway traffic and ocean waves are inherently correlated both in space
and time, in direct contradiction to the current theoretical foundations.
Applying standard interferometric techniques to recordings from correlated
energy sources makes the Green's function liable to estimation errors that so
far have not been fully accounted for theoretically nor in practice. We show
that these errors are significant for common noise sources, always perturbing
and sometimes obscuring the phase one wishes to retrieve. Our analysis explains
why stacking may reduce the phase errors, but also shows that in
commonly-encountered circumstances stacking will not remediate the problem.
This analytical insight allowed us to develop a novel workflow that
significantly mitigates effects arising from the use of correlated noise
sources. Our methodology can be used in conjunction with already existing
approaches, and improves results from both correlated and uncorrelated ambient
noise. Hence, we expect it to be widely applicable in real life ambient noise
studies.
