Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential

Jie Yao, Anne Cécile Lesage, Bernhard G. Bodmann, Fazle Hussain, Donald J. Kouri

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green's function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.

Original languageEnglish (US)
Article number123512
JournalJournal of Mathematical Physics
Issue number12
StatePublished - Dec 29 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential'. Together they form a unique fingerprint.

Cite this