An inversion integral for crack-scattering data

J. D. Achenbach*, K. Viswanathan, A. Norris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.

Original languageEnglish (US)
Pages (from-to)299-316
Number of pages18
JournalWave Motion
Issue number4
StatePublished - Oct 1979

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics


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