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.