Source-receiver wave field interferometry

Correlation or convolution of recordings of diffuse fields at a pair of locations have been shown to result in estimates of the Green's function between the two locations. Variously referred to as wave field or seismic interferometry in different fields of research, Green's functions can thus be constructed between either pairs of receivers or pairs of energy sources. Proofs of these results rely on representation theorems. We show how to derive three acoustic and elastic representation theorems that unify existing correlational and convolutional approaches. We thus derive three forms of interferometry that provide Green's functions on source-to-receiver paths, using only energy that has propagated from surrounding sources or to surrounding receivers. The three forms correspond to three possible canonical geometries. We thus allow interferometric theory and methods to be applied to commonly used source-receiver configurations.