title: Unified double- and single-sided homogeneous Green's function representations.
abstract: In wave theory, the homogeneous Green's function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green's function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green's function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green's function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green's function retrieval.
authors.affiliation: Department of Geoscience and Engineering , Delft University of Technology , 2600 GA Delft, The Netherlands.
authors.forename: Kees
authors.identifier: 0000-0002-1620-8282
authors.initials: K
authors.lastname: Wapenaar
authors.affiliation: Department of Geoscience and Engineering , Delft University of Technology , 2600 GA Delft, The Netherlands.
authors.forename: Joost
authors.initials: J
authors.lastname: van der Neut
authors.affiliation: Department of Geoscience and Engineering , Delft University of Technology , 2600 GA Delft, The Netherlands.
authors.forename: Evert
authors.initials: E
authors.lastname: Slob
keywords: Green’s function; focusing; holographic imaging; representation; time-reversal acoustics; wave propagation and scattering