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Updated: Jun 18, 2026

Scattering And Absorption of Light in Planetary Regoliths
Published on: July 1, 2019
Representation theorems and Green's function retrieval for scattering in acoustic media
Ivan Vasconcelos1, Roel Snieder, Huub Douma
1ION Geophysical, GXT Imaging Solutions, 1st Floor, Integra House, Vicarage Road, Egham, Surrey TW20 9JZ, United Kingdom.
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.
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