In 1968, J. F. Claerbout derived a remarkable relation between the transmission and reflection responses of a horizontally layered medium bounded by a free surface (Claerbout, 1968). He showed that the autocorrelation of the transmission response is equal to the reflection response plus its time-reversed version (plus an impulse at time zero). This implies that when one measures the response of a plane-wave source in the subsurface by a geophone at the free surface, the reflection response is obtained by taking the causal part of the autocorrelation of the observed response. Primary as well as multiple reflections are recovered correctly by that procedure. The source wavelet in the recovered reflection response is equal to the autocorrelation of the source signal in the subsurface.
Hence, if one would measure the response of a band-limited white-noise source in the subsurface, the autocorrelation would give the impulsive reflection response, convolved with a band-limited delta function. This shows that noise observed at the surface can be turned into a signal with information about the subsurface. The principle of using passive-noise measurements to derive the reflection response and subsequently form an image of the earth’s interior was called acoustic daylight imaging.
Later, Claerbout conjectured that his relation could be generalized for offset measurements in 3D inhomogeneous media, i.e., that by crosscorrelating noise traces recorded at two locations on the surface, one could construct the wavefield that would be recorded at one of the locations as if there were a source at the other.