It can be shown that for a 1-D Earth model illuminated by random plane waves
from below, the cross-correlation of noise traces recorded at two points on the
surface is the same as what would be recorded if one location contained a
shot and the other a receiver. If this is true for real data, it could
provide a way of building `pseudo-reflection seismograms' from background
noise, which could then be processed and used for imaging.
This conjecture is tested on synthetic data from simple
1-D and point diffractor models,
and in all cases, the kinematics of observed events
appear to be correct.
The signal to noise ratio was found to increase as
, where
is
the length of the time series. The number of incident
plane waves does not directly affect the signal to noise ratio; however,
each plane wave contributes only its own slowness to the common
shot domain, so that if complete hyperbolas are to be imaged
then upcoming waves must be incident from all angles.
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