title: The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem.
abstract: By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields.
authors.affiliation: ION Geophysical∕GXT Imaging Solutions, 225 East 16th Avenue, Suite 1200, Denver, Colorado 80203, USA. huub.douma@iongeo.com
authors.forename: Huub
authors.initials: H
authors.lastname: Douma
authors.forename: Ivan
authors.initials: I
authors.lastname: Vasconcelos
authors.forename: Roel
authors.initials: R
authors.lastname: Snieder