Qualitative indicator functions for imaging crack networks using acoustic waves

TL;DR

This paper introduces two novel multi-static acoustic wave imaging methods for crack networks, utilizing indicator functions sensitive to crack density, and compares their effectiveness with classical techniques through synthetic examples.

Contribution

The paper develops two new indicator function approaches extending linear sampling methods for imaging crack networks using acoustic waves, incorporating multi-frequency and single-frequency data.

Findings

Methods successfully detect crack densities in synthetic tests.

Performance compares favorably with classical factorization method.

Single-frequency approach offers practical advantages.

Abstract

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.