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Three-dimensional inverse scattering: layer-stripping formulas and ill-posedness results

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Author

Summary, in English

The authors consider the three-dimensional direct and inverse scattering problems for the Schrodinger equation and for the reduced wave equation with variable velocity. The scatterer is probed with either point sources or plane waves of fixed frequency. They ask the question, 'How does the wave field change when the scatterer is truncated?' Simple formulae for the derivative of the wave field with respect to the truncation parameter are obtained. Similar formulae are obtained for the scattering amplitudes. These formulae are used to derive ill-posedness results for various inverse scattering problems. The ill-posedness results apply when data are collected over a range of frequencies.

Publishing year

1988

Language

English

Pages

625-642

Publication/Series

Inverse Problems

Volume

4

Issue

3

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Status

Published

ISBN/ISSN/Other

  • ISSN: 0266-5611