Fast imaging of local perturbations in a unknown bi-periodic layered medium

• Published in: Journal of computational physics 2024-03, Vol.501, p.112773, Article 112773
• Main Authors: Cakoni, Fioralba, Haddar, Houssem, Nguyen, Thi-Phong
• Format: Article
• Language: English
• Subjects: Differential imaging; Fast reconstruction methods; Infinite bi-periodic layered medium; Inverse scattering problem; Local perturbations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2024.112773

We discuss a novel approach for imaging local faults inside an infinite bi-periodic layered medium in R3 using acoustic measurements of scattered fields at the bottom or the top of the layer. The faulted area is represented by compactly supported perturbations with erroneous material properties. Our method reconstructs the support of perturbations without knowing or reconstructing the constitutive material parameters of healthy or faulty bi-period layer; only the size of the period is needed. This approach falls under the class of non-iterative imaging methods, known as the generalized linear sampling method with differential measurements, first introduced in [2] and adapted to periodic layers in [25]. The advantage of applying differential measurements to our inverse problem is that instead of comparing the measured data against measurements due to healthy structures, one makes use of periodicity of the layer where the data operator restricted to single Floquet-Bloch modes plays the role of the one corresponding to healthy material. This leads to a computationally efficient and mathematically rigorous reconstruction algorithm. We present numerical experiments that confirm the viability of the approach for various configurations of defects. •A novel approach for imaging local faults inside an infinite bi-periodic layered medium in R3 using electromagnetic waves.•The faulted area is represented by compactly supported perturbations with erroneous material properties.•Little prior knowledge of the medium's structure is needed, and only minimal measurements are required to perform accurately.•Fast and non-iterative method with computationally efficient and mathematically rigorous reconstruction algorithm.