Qualitative indicator functions for imaging crack networks using acoustic waves

Lorenzo Audibert (1, 2) , Lucas Chesnel (2, 3) , Houssem Haddar (2, 3) , Kevish Napal (4)

1 EDF R&D PRISME - Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation
2 IDEFIX - Inversion of Differential Equations For Imaging and physiX
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 Department of Civil and Environmental Engineering [Fort Collins]

We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose two novel approaches that can be seen as extensions of linear sampling-type methods and that provide indicator functions which are sensitive to local cracks densities. The first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles. The second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency. The indicator function is built using a similar concept as for differential sampling methods: compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks. The performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method.

Mots clés: Generalized linear sampling method; cracks; interior transmission problem; artificial background

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Audibert, Lucas Chesnel, Houssem Haddar, Kevish Napal. Qualitative indicator functions for imaging crack networks using acoustic waves. SIAM Journal on Scientific Computing, 2021, ⟨10.1137/20M134650X⟩. ⟨hal-02873118v2⟩