[CCoE Notice] MS Thesis Presentation

[Abercrombie, Irene F]

MS Thesis Defense

INVERSE ACOUSTIC SCATTERING SERIES USING THE VOLTERRA RENORMALIZATION OF THE
LIPPMANN-SCHWINGER EQUATION IN ONE DIMENSION

Jie Yao

Date: Monday, July 15th, 2013

Location: MECE Small Conference Room
Time: 10:30 am


Committee Chair:
Dr. Donald Kouri

Committee Members:
Dr. Bernhard Bodmann
Dr. Fazle Hussain


The inverse scattering problem has enormous importance both for practical and theoretical applications. Based on the early work of Jost and Kohn, Moses, Razavy and Prosser, Weglein and co-workers have pioneered inverse scattering series methods that do not require an assumed propagation velocity model. The only limitation of their approach appears to the finite radius of convergence of the Born-Neumann series of the acoustic Lippmann-Schwinger equation. Despite this limitation, Weglein and co-workers have made significant progress using this approach by introducing the idea of "subseries" which are associated with specific inversion tasks. Kouri showed that one could carry a renormalization transform of the Lippmann-Schwinger equation from a Fredholm into a Volterra Equation form. It can be further proved that the Born-Neumann series solution of the Volterra equation converges absolutely, irrespective of the strength of the interaction. Kouri and co-workers formulated the 1-D acoustic scattering series in terms of Volterra kernel with reflection and transmission data. Following this previous work of Kouri, higher orders of the Volterra Inverse Scattering Series (VISS) with reflection and transmission data ($R_k/T_k$) are analyzed. In addition, for the seismic exploration applications, we also extended the VISS approach to the case where only the reflection data is available. The cases of single square barriers or wells and Gauss barriers and wells  are studied to illustrate how well the Volterra Inverse Scattering Series performs the inversion.

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