title: Representation theorems and Green's function retrieval for scattering in acoustic media.
abstract: Reciprocity theorems for perturbed acoustic media are provided in the form of convolution- and correlation-type theorems. These reciprocity relations are particularly useful in the general treatment of both forward and inverse-scattering problems. Using Green's functions to describe perturbed and unperturbed waves in two distinct wave states, representation theorems for scattered waves are derived from the reciprocity relations. While the convolution-type theorems can be manipulated to obtain scattering integrals that are analogous to the Lippmann-Schwinger equation, the correlation-type theorems can be used to retrieve the scattering response of the medium by cross correlations. Unlike previous formulations of Green's function retrieval, the extraction of scattered-wave responses by cross correlations does not require energy equipartitioning. Allowing for uneven energy radiation brings experimental advantages to the retrieval of fields scattered by remote lossless and/or attenuative scatterers. These concepts are illustrated with a number of examples, including analytic solutions to a one-dimensional scattering problem, and a numerical example in the context of seismic waves recorded on the ocean bottom.
authors.affiliation: ION Geophysical, GXT Imaging Solutions, 1st Floor, Integra House, Vicarage Road, Egham, Surrey TW20 9JZ, United Kingdom.
authors.forename: Ivan
authors.initials: I
authors.lastname: Vasconcelos
authors.forename: Roel
authors.initials: R
authors.lastname: Snieder
authors.forename: Huub
authors.initials: H
authors.lastname: Douma
mesh_terms: D000162:Acoustics; D003198:Computer Simulation; D008962:Models, Theoretical; D012542:Scattering, Radiation