论文标题
衰减的一维Helmholtz方程的逆随机源问题
An inverse random source problem for the one-dimensional Helmholtz equation with attenuation
论文作者
论文摘要
本文与衰减有关的一维随机Helmholtz方程的逆随机源问题有关。源被认为是微核的各向同性高斯随机场，其协方差操作员是经典的伪差异操作员。所考虑的随机来源等效于广义的分数高斯随机场，这些源包括粗糙场，甚至比白噪声更粗糙，因此应将其解释为分布。直接源散射问题的适合性是在分布意义上确定的。事实证明，随机源的微相关强度似乎是协方差算子的主要符号的强度，在开放测量集中是由波场唯一确定的。为白噪声模型提供了数值实验，以证明所提出方法的有效性和有效性。
This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation with attenuation. The source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-differential operator. The random sources under consideration are equivalent to the generalized fractional Gaussian random fields which include rough fields and can be even rougher than the white noise, and hence should be interpreted as distributions. The well-posedness of the direct source scattering problem is established in the distribution sense. The micro-correlation strength of the random source, which appears to be the strength in the principal symbol of the covariance operator, is proved to be uniquely determined by the wave field in an open measurement set. Numerical experiments are presented for the white noise model to demonstrate the validity and effectiveness of the proposed method.
