An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 165-188, February 2024.
Abstract. 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 first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the two-dimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second 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.