Inverse Elastic Scattering for a Random Potential
Inverse Elastic Scattering for a Random Potential
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DOI：
10.1137/21m1430200
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发表时间：
2020-07
期刊：
影响因子：
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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
研究了具有粗糙势的时谐弹性波方程的逆散射问题。解释为一个分布，潜在的被假定为一个微局部各向同性的广义高斯随机场的协方差算子被描述为一个经典的伪微分算子。我们的目标是确定主符号的协方差算子从散射波测量在一个有界的域，它有一个积极的距离域的潜力。对于这样一个粗糙势，通过研究等价的Lippmann-Schwinger积分方程，建立了直接散射问题在分布意义下的适定性。对于逆散射问题，它示出的协方差算子的主符号可以唯一地确定由散射波的振幅平均在频带上从一个单一的实现的随机潜在的概率1。分析采用玻恩近似在高频下，渐近的绿色张量的弹性波方程，和微局部分析的傅里叶积分算子。
This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a rough potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudo-differential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent Lippmann-Schwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. The analysis employs the Born approximation in high frequency, asymptotics of the Green tensor for the elastic wave equation, and microlocal analysis for the Fourier integral operators.