S U M M A R YSeismic interferometry can be used to estimate interreceiver surface wave signals by crosscorrelation of signals recorded at each receiver. The quality of the estimated surface waves is controlled by the distribution of sources exciting the cross-correlated wavefields, and it is commonly thought that only sources at or near the surface are required to generate accurate estimates. We study the role of source distribution in surface wave interferometry for both surface and subsurface sources using surface wave Green's functions for laterally homogeneous media. We solve the interferometric integral using a Rayleigh wave orthogonality relationship combined with a stationary phase approach. Contrary to popular opinion we find that sources at depth do indeed play a role in the recovery of surface waves by interferometry. We find that interferometry performs well when surface sources are distributed homogeneously at the surface of the Earth. However, when this homogeneous distribution is not available amplitude errors are introduced, and when multiple modes are present strong spurious events appear and higher mode surface waves may not be correctly estimated. In order to recover higher mode surface waves we propose an additional step in the processing of surface wave data for seismic interferometry: by separating modes and applying interferometry to each mode individually it is possible to recover the interreceiver surface wave modes, without the artefacts introduced by limited source coverage.

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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.

It is known that there is a link between the theory of seismic interferometry and theories of seismic imaging and inversion. However, although this has been discussed in several studies, there are few where any explicit links have been derived. We use reciprocity theorems for scattering media to derive a new form of seismic interferometry that describes the scattered wavefield between a source and a receiver in an acoustic medium, using both sources and receivers on two enclosing boundaries. This form of seismic interferometry is equivalent to a generalized imaging condition ͑IC͒ that combines the full wavefield inside any finite-sized subregion of the medium of interest. By using the Born ͑single-scattering͒ approximation, this generalized IC reduces to the method of imaging by double-focusing originally derived by Michael Oristaglio in 1989. Thus an explicit link is made between seismic interferometry, new generalized full-wavefield ICs, and existing single-scattering imaging methods.