High‐frequency asymptotics in inverse scattering by ellipsoids

Yani Arnaoudov, George Dassios, Vladimir Simeonov Gueorguiev

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High‐frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high‐frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non‐zero‐measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalMathematical Methods in the Applied Sciences
Volume16
Issue number1
DOIs
Publication statusPublished - 1993
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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