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

Abstract

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 one-dimensional 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
Title of host publicationSociety of Exploration Geophysicists International Exposition and 84th Annual Meeting SEG 2014
PublisherSociety of Exploration Geophysicists
Pages569-573
Number of pages5
ISBN (Print)9781634394857
DOIs
StatePublished - 2014
EventSociety of Exploration Geophysicists International Exposition and 84th Annual Meeting SEG 2014 - Denver, United States
Duration: Oct 26 2014Oct 31 2014

Publication series

NameSociety of Exploration Geophysicists International Exposition and 84th Annual Meeting SEG 2014

Conference

ConferenceSociety of Exploration Geophysicists International Exposition and 84th Annual Meeting SEG 2014
CountryUnited States
CityDenver
Period10/26/1410/31/14

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