Multi-dimensional Inverse acoustic scattering series using the Volterra renormalization of the Lippmann-Schwinger equation

Anne Cecile Lesage, Jie Yao, Nelka Wijesinghe, Fazle Hussain, Donald J. Kouri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations


We report the extension of the Volterra inverse acoustic scattering series (VISS) approach presented in (Lesage et al., 2013) using reflection data (Rk) to multi-dimensions. The approach consists in combining two ideas: the renormalization of the Lippmann-Schwinger equation to obtain a Volterra equation framework (Kouri and Vijay, 2003) and the formal series expansion using reflection coefficients (Moses, 1956). The benefit of formulating acoustic scattering in terms of a Volterra kernel is substantial. Indeed the corresponding Born-Neumann series solution is absolutely convergent independent of the strength of the coupling characterizing the interaction. While treating the depth variation in the same manner as in the onedimensional case, additional lateral and longitudinal variations are addressed through Fourier expansions of the pressure wave, the reflection data and the velocity perturbation. We derive new multi-dimensional inverse acoustic scattering series for reflection data which we evaluate numerically for 2-dimensional velocity models presenting depth and lateral variations. Our results compare well to results obtained by (Liu et al., 2005).

Original languageEnglish (US)
Title of host publicationSEG Technical Program Expanded Abstracts 2014
PublisherSociety of Exploration Geophysicists
Number of pages5
StatePublished - 2014
EventSociety of Exploration Geophysicists: 2014 Annual Meeting - Denver, United States
Duration: Oct 26 2014Oct 31 2014


ConferenceSociety of Exploration Geophysicists
Abbreviated titleSEG
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Geophysics


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