A new inversion scheme for elastic diffraction tomography

TL;DR

This paper introduces a novel two-step inversion scheme for elastic diffraction tomography, utilizing Fourier diffraction theorem and elastic wave mode separation to reconstruct elastic properties from scattered wave data.

Contribution

It presents a new inversion method that combines Fourier diffraction theorem and wave mode separation for elastic property reconstruction.

Findings

Proved the Fourier diffraction theorem for elastic waves.

Developed a two-step inversion process for elastic tomography.

Demonstrated reconstructions with various plane wave frequencies.

Abstract

We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lam\'e 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.