Dating from about the same time, an exercise in Claerbout's first book 1976 asks the reader to prove that the temporal autocorrelation of a transmission seismogram with a source deep underground is equivalent to a reflection seismogram. This may have inspired his conjecture that by crosscorrelating two passive traces, we can create the seismogram that would be computed at one of the locations if there was a source at the other. Cole (1995) attempted to verify this conjecture with data collected using a 4000 channel 2-D field array on Stanford campus. Unfortunately, again, possibly due to the short (20 minute) records or bad coupling between the geophones and the dry California soil, his results were inconclusive.

Following Cole's work, Rickett and Claerbout (1996) generated
synthetic data with a phase-shift method. Their earth reflectivity
models consisted of (both flat and dipping) planar layers and point
diffractors embedded in a *v*(*z*) velocity function, and illuminated by
random plane waves from below.
They generated both *pseudo shot gathers* (by
crosscorrelating one passive trace with many others nearby),
and *pseudo zero-offset sections* (by autocorrelating many
traces).
In these crosscorrelated domains, the kinematics for both point
diffractors and planar reflectors, were identical to those predicted
for real shot gathers and zero-offset sections.
Rickett (1996) then experimented with moving the
passive source location close to the receivers and reflectors, and
included modeling with a *v*(*x*,*z*) velocity model. He observed that
these changes did indeed affect the kinematics of the correlograms;
however, changes were small, and would probably not cause the method
to fail in most situations.

The idea that a pseudo-reflection seismogram could be created by
crosscorrelating two passive seismic records was rediscovered
independently by the helioseismologists Duvall et al. (1993), who
created *time-distance* curves by cross-correlating passive solar
dopplergrams recorded by the Michelson Doppler Imager Scherrer et al. (1995).
Point-to-point traveltimes derived from these time-distance curves
could then be used in a range of helioseismic applications
[e.g. Giles et al. (1997) and Kosovichev (1999)].
If helioseismic time-distance curves are averaged spatially, the
result is equivalent to a multi-dimensional autocorrelation.
Rickett and Claerbout
demonstrated that
multi-dimensional spectral
factorization provides spatially averaged time-distance curves with
more resolution than those calculated by autocorrelation.

9/5/2000