### 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

Original language | English |
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Pages (from-to) | 1043-1059 |

Number of pages | 17 |

Journal | Geophysical Journal International |

Volume | 196 |

Issue number | 2 |

Early online date | 23 Nov 2013 |

DOIs | |

Publication status | Published - 1 Feb 2014 |

### Keywords

- Acoustic properties.
- Interferometry
- Theoretical seismology
- Wave scattering and diffraction

### ASJC Scopus subject areas

- Geophysics
- Geochemistry and Petrology

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## Cite this

L̈oer, K., Meles, G. A., Curtis, A., & Vasconcelos, I. (2014). Diffracted and pseudo-physical waves from spatially limited arrays using source-receiver interferometry (SRI).

*Geophysical Journal International*,*196*(2), 1043-1059. https://doi.org/10.1093/gji/ggt435