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

Fingerprint

Inverse Scattering
Ellipsoid
Linear systems
Acoustics
Boundary conditions
Scattering
Sojourn Time
Angle
Elliptic integral
Scattering Amplitude
Acoustic Waves
Numerics
Plane Wave
Inversion
Excitation
Linear Systems
Unknown

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

High‐frequency asymptotics in inverse scattering by ellipsoids. / Arnaoudov, Yani; Dassios, George; Gueorguiev, Vladimir Simeonov.

In: Mathematical Methods in the Applied Sciences, Vol. 16, No. 1, 1993, p. 1-12.

Research output: Contribution to journalArticle

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