Inverse elastic scattering for a random source
Inverse elastic scattering for a random source
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随机源的逆弹性散射
DOI：
10.1137/18m1235119
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发表时间：
2019
影响因子：
2
通讯作者：
李培军
中科院分区：
文献类型：
--
作者：
李建樑;李培军
考虑线性载荷作用下二维时谐弹性波方程的随机源散射反问题。源被建模为一个microlocalized各向同性。广义高斯随机函数，其协方差算子是一个经典的伪微分。目标是从远离源的域中测量的位移恢复协方差算子的主符号。对于这样一个分布源，我们通过引入一个等价的Lippmann-Schwinger积分方程，证明了正问题的唯一解。对于逆问题，我们证明，概率为1，主符号的协方差算子可以唯一地确定的振幅的位移平均的频带，由一个单一实现的随机源。分析采用玻恩近似、绿色张量的渐近展开和傅里叶积分算子的微局部分析。
Consider the inverse random source scattering problem for the two-dimensional timeharmonic.elastic wave equation with a linear load. The source is modeled as a microlocally isotropic.generalized Gaussian random function whose covariance operator is a classical pseudodifferential.operator. The goal is to recover the principal symbol of the covariance operator from the displacement.measured in a domain away from the source. For such a distributional source, we show that the direct.problem has a unique solution by introducing an equivalent Lippmann--Schwinger integral equation..For the inverse problem, we demonstrate that, with probability one, the principal symbol of the.covariance operator can be uniquely determined by the amplitude of the displacement averaged over.the frequency band, generated by a single realization of the random source. The analysis employs.the Born approximation, asymptotic expansions of the Green tensor, and microlocal analysis of the.Fourier integral operators.