Early attempts to verify this theory in practice quickly failed and we came to realize that the essential physical feature is real-world three dimensionality while both our data and our mathematical theory were merely one dimensional. We didn't have a three-dimensional theory, but we did have a conjecture:
By cross-correlating noise traces recorded at two locations on the surface, we can construct the wavefield that would be recorded at one of the locations if there was a source at the other.
Cole (1988, 1995) initially tried to verify this conjecture on a passive 3-D survey recorded with an array of 4056 geophones covering more than a half kilometer square on the Stanford campus. Unfortunately, however, only twenty minutes of passive seismic data was recorded, and beam steering showed ambient noise was predominately incident from only one direction. His cross-correlation results were not conclusive. The proximity of the San Andreas fault makes the Stanford area difficult to analyze, and we were also troubled by poor coupling between the geophones and the dry summer soil.
Nobody expected the geophones to record plunging waves from great distances but that is exactly what happened. We saw seismic waves apparently coming from the American Midwest. Earthquake seismologists were surprised to learn that we could receive seismic waves from so far at such high frequency (10 Hz) because with their small numbers of seismometers they cannot. Unfortunately, we were not able to observe what we sought, the much smaller scale reflected waves that we would crosscorrelate within our array. Such waves would illuminate the area within drilling distance so proof of concept would interest our sponsors.
Modeling studies Rickett and Claerbout (1996) showed that longer time-series, and a white spatial distribution of random noise events would be necessary for the conjecture to work in practice.