论文标题
弹性衍射断层扫描的新反转方案
A new inversion scheme for elastic diffraction tomography
论文作者
论文摘要
我们考虑了弹性衍射断层扫描的问题，该问题包括重建弹性的弹药介质（即从介质外散射波的全场数据中）重建弹性特性（即质量密度和弹性拉梅参数）。弹性衍射断层扫描是指使用第一阶生成近似线性化后弹性反向散射问题。在本文中，我们证明了傅立叶衍射定理，该定理将散射波的2d傅立叶变换与3D空间傅立叶域中的散射器的傅立叶变换相关联。进行弹性波模式分离，将波分解为四个模式。开发了一个新的两步倒置过程，首先提供有关模式的信息，其次是弹性参数。最后，我们通过平面波激发实验讨论了不同的层析成像设置和不同的平面波激发频率的重建。
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.
