2022/12/06 by Bochra Méjri, Otmar Scherzer, Mejri, Bochra +1
Earth and Planetary Sciences · Engineering · Mathematics · #35R30 #74J25 #78A45 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2212.02798
openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lamé parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a firstorder Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the 2D Fourier transform of scattered waves with the Fourier transform of the scatterer in the 3D spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into four modes. A new two-step inversion process is developed, providing information on the modes first and secondly on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.