Title: A new inversion scheme for elastic diffraction tomography Show Chinese title

Title: 一种弹性衍射层析成像的新反演方案

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. Show Chinese abstract

Abstract: 我们考虑弹性衍射层析成像的问题，即从介质外部散射波的全场数据中重建弱散射介质的弹性性质（即质量密度和弹性Lamé参数）。弹性衍射层析成像指的是在使用一阶Born近似进行线性化后的弹性逆散射问题。在本文中，我们证明了傅里叶衍射定理，该定理将散射波的二维傅里叶变换与散射体在三维空间傅里叶域中的傅里叶变换相关联。进行了弹性波模式分离，将波分解为四种模式。开发了一种新的两步反演过程，首先提供模式的信息，其次提供弹性参数的信息。最后，我们分别讨论了不同断层扫描设置和不同平面波激励频率下的平面波激励实验的重建结果。