Inverse Random Potential Scattering for Elastic Waves
Inverse Random Potential Scattering for Elastic Waves
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DOI：
10.1137/22m1497183
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发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
Jianliang Li;Peijun Li;Xu Wang
中科院分区：
文献类型：
--
作者：
Jianliang Li;Peijun Li;Xu Wang
本文研究三维随机势场的弹性散射反问题。解释为一个分布，潜在的被假定为一个微局部各向同性高斯随机场的协方差算子是一个经典的伪微分算子。通过研究等价的Lippmann-Schwinger积分方程，证明了在给定势的情况下，直接散射问题在分布意义下是适定的。对于逆散射问题，我们证明了随机势的微局部强度可以唯一地确定概率1由一个单一的实现的平均压缩或剪切背散射的散射波的远场图案的高频限制。分析采用积分算子理论，玻恩近似在高频区，傅立叶积分算子的微局部分析，和遍历的波场。
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance operator is a classical pseudo-differential operator. Given the potential, the direct scattering problem is shown to be well-posed in the distribution sense by studying the equivalent Lippmann--Schwinger integral equation. For the inverse scattering problem, we demonstrate that the microlocal strength of the random potential can be uniquely determined with probability one by a single realization of the high frequency limit of the averaged compressional or shear backscattered far-field pattern of the scattered wave. The analysis employs the integral operator theory, the Born approximation in the high frequency regime, the microlocal analysis for the Fourier integral operators, and the ergodicity of the wave field.