Seismic interferometry, surface waves and source distribution

Seismic interferometry can be used to estimate interreceiver surface wave signals by cross-correlation 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.