Inverse Random Source Scattering for the Helmholtz Equation with Attenuation
Inverse Random Source Scattering for the Helmholtz Equation with Attenuation
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DOI：
10.1137/19m1309456
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Peijun Li;Xu Wang
中科院分区：
文献类型：
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作者：
Peijun Li;Xu Wang
本文提出了带衰减的亥姆霍兹方程随机源逆散射问题的一个新模型。假设源由分数阶高斯场驱动，其协方差由经典伪微分算子表示。这项工作包含三个贡献。首先，建立了分数阶高斯场与具有主符号特征的粗糙源之间的联系。其次，证明了直接源散射问题在分布意义上是适定性的。第三，我们证明了随机源的微相关强度可以唯一地由波场的无源测量来确定，而波场的无源测量与强度函数的支持是不相交的。分析依赖于对格林函数和亥姆霍兹方程的傅里叶积分的仔细研究。
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a classical pseudo-differential operator. The work contains three contributions. First, the connection is established between fractional Gaussian fields and rough sources characterized by their principal symbols. Second, the direct source scattering problem is shown to be well-posed in the distribution sense. Third, we demonstrate that the micro-correlation strength of the random source can be uniquely determined by the passive measurements of the wave field in a set which is disjoint with the support of the strength function. The analysis relies on careful studies on the Green function and Fourier integrals for the Helmholtz equation.