Unified double- and single-sided homogeneous Green's function representations

Unified double- and single-sided homogeneous Green's function representations

Wapenaar, C.P.A. (TU Delft Applied Geophysics and Petrophysics)
van der Neut, J.R. (TU Delft Applied Geophysics and Petrophysics)
Slob, E.C. (TU Delft Applied Geophysics and Petrophysics)

2016

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.

http://resolver.tudelft.nl/uuid:9289514b-58c6-4e80-948b-fed8dcafa4e1

https://doi.org/10.1098/rspa.2016.0162

2017-07-31

1364-5021

Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, 472 (2190)

Institutional Repository

journal article

© 2016 C.P.A. Wapenaar, J.R. van der Neut, E.C. Slob