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

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Abstract

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.

Detaljer

Författare
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Elektroteknik och elektronik
Originalspråkengelska
Sidor (från-till)625-642
TidskriftInverse Problems
Volym4
Utgåva nummer3
StatusPublished - 1988
PublikationskategoriForskning
Peer review utfördJa