2022/10/04 by Éric Bonnetier, Bonnetier, Eric, Angèle Niclas +4
Computer Science · Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geophysical Methods and Applications #Mathematical Physics (math-ph) #Optical measurement and interference techniques #Seismic Imaging and Inversion Techniques #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2210.01899
openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The aim of this work is to present theoretical tools to study wave\npropagation in elastic waveguides and perform multi-frequency scattering\ninversion to reconstruct small shape defects in a 2D and 3D elastic plate.\nGiven surface multi-frequency wavefield measurements, we use a Born\napproximation to reconstruct localized defect in the geometry of the plate. To\njustify this approximation, we introduce a rigorous framework to study the\npropagation of elastic wavefield generated by arbitrary sources. By studying\nthe decreasing rate of the series of inhomogeneous Lamb mode, we prove the\nwell-posedness of the PDE that model elastic wave propagation in 2D and 3D\nplanar waveguides. We also characterize the critical frequencies for which the\nLamb decomposition is not valid. Using these results, we generalize the shape\nreconstruction method already developed for acoustic waveguide to 2D elastic\nwaveguides and provide a stable reconstruction method based on a mode-by-mode\nspacial Fourier inversion given by the scattered field.\n