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

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-compactmore » support velocity potential.« less
Authors:
 [1] ; ;  [2] ;  [3] ;  [4]
  1. Department of Mechanical Engineering, University of Houston, Houston, Texas 77204 (United States)
  2. Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)
  3. Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)
  4. Department of Physics, University of Houston, Houston, Texas 77204 (United States)
Publication Date:
OSTI Identifier:
22403072
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTORTED WAVE THEORY; FOURIER TRANSFORMATION; INVERSE SCATTERING PROBLEM; LIPPMANN-SCHWINGER EQUATION; NEUMANN SERIES; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; SCATTERING