Diffracted and pseudo-physical waves from spatially limited arrays using source-receiver interferometry (SRI)

Abstract

Source-receiver interferometry (SRI) refers to a technique to construct the Green's function between a source and a receiver using only energy that has travelled from and to surrounding boundaries of sources and receivers. If a background medium is perturbed, the corresponding interferometric equation can be expressed as the sum of eight terms, which result from the separation of the total wavefield into an unperturbed background field and the perturbed scattered field. Here, the contribution of each individual term is identified for singly diffracted waves using the methods of stationary phase analysis and waveform modelling. When the data acquisition boundary requirements for seismic interferometry are violated, non-physical energy is introduced into Green's function estimates. Our results show that four terms produce purely non-physical, non-stationary energy and that these can be suppressed, and that a combination of only two terms can be used to estimate diffracted wavefields robustly. One of the two terms is precisely that used in geophysical imaging schemes. A key result is that this term also produces non-physical energy, except when the integration boundaries are truncated to span only part of the medium's free surface: we thus show that in this sense, partial boundaries can be seen as a positive advantage for migration or imaging methods. The other term produces non-physical energy which nevertheless emulates physical energy; such energy is therefore called pseudo-physical. We present for the first time a complete mathematical derivation of this new category of energy complemented with illustrative examples. Overall, this work significantly enhances our understanding of how scattered wave SRI works. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.